REAL is non empty non trivial non finite V117() V118() V119() V123() set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal V117() V118() V119() V120() V121() V122() V123() Element of bool REAL
bool REAL is non empty non trivial non finite set
K649() is strict doubleLoopStr
the carrier of K649() is set
COMPLEX is non empty non trivial non finite V117() V123() set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal V117() V118() V119() V120() V121() V122() V123() set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
RAT is non empty non trivial non finite V117() V118() V119() V120() V123() set
INT is non empty non trivial non finite V117() V118() V119() V120() V121() V123() set
[:REAL,REAL:] is non empty non trivial V35() V36() V37() non finite set
bool [:REAL,REAL:] is non empty non trivial non finite set
K357() is non empty strict multMagma
the carrier of K357() is non empty set
INT.Ring is non empty non degenerated non trivial non finite left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed V181() doubleLoopStr
addint is Relation-like [:INT,INT:] -defined INT -valued Function-like quasi_total V35() V36() V37() Element of bool [:[:INT,INT:],INT:]
[:INT,INT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() non finite set
[:[:INT,INT:],INT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() non finite set
bool [:[:INT,INT:],INT:] is non empty non trivial non finite set
multint is Relation-like [:INT,INT:] -defined INT -valued Function-like quasi_total V35() V36() V37() Element of bool [:[:INT,INT:],INT:]
1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
K633(1,INT) is V11() V12() integer ext-real V113() Element of INT
0 is empty V4() V5() V6() V8() V9() V10() V11() V12() integer ext-real non positive non negative finite V49() cardinal {} -element V113() V117() V118() V119() V120() V121() V122() V123() Element of NAT
{} is empty V4() V5() V6() V8() V9() V10() V11() V12() integer ext-real non positive non negative finite V49() cardinal {} -element V117() V118() V119() V120() V121() V122() V123() set
K633(0,INT) is V11() V12() integer ext-real V113() Element of INT
doubleLoopStr(# INT,addint,multint,K633(1,INT),K633(0,INT) #) is non empty non trivial strict doubleLoopStr
the carrier of INT.Ring is non empty non trivial non finite V117() V118() V119() V120() V121() set
[: the carrier of INT.Ring,NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
bool [: the carrier of INT.Ring,NAT:] is non empty non trivial non finite set
{{},1} is non empty finite V49() V117() V118() V119() V120() V121() V122() set
K455() is set
bool K455() is non empty set
K456() is Element of bool K455()
2 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
[:NAT,REAL:] is non empty non trivial V35() V36() V37() non finite set
bool [:NAT,REAL:] is non empty non trivial non finite set
1 -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like FinSequence-like Element of NAT * : len b1 = 1 } is set
[:COMPLEX,COMPLEX:] is non empty non trivial V35() non finite set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial V35() non finite set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite set
[:[:REAL,REAL:],REAL:] is non empty non trivial V35() V36() V37() non finite set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial non finite set
[:RAT,RAT:] is non empty non trivial RAT -valued V35() V36() V37() non finite set
bool [:RAT,RAT:] is non empty non trivial non finite set
[:[:RAT,RAT:],RAT:] is non empty non trivial RAT -valued V35() V36() V37() non finite set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial non finite set
bool [:INT,INT:] is non empty non trivial non finite set
[:NAT,NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[:NAT,NAT:],NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
bool the carrier of K649() is non empty set
[:NAT, the carrier of K649():] is set
bool [:NAT, the carrier of K649():] is non empty set
bool (bool REAL) is non empty non trivial non finite set
K155(0,1,2) is non empty finite V117() V118() V119() V120() V121() V122() set
[:K155(0,1,2),K155(0,1,2):] is non empty RAT -valued INT -valued V35() V36() V37() V38() finite set
[:[:K155(0,1,2),K155(0,1,2):],K155(0,1,2):] is non empty RAT -valued INT -valued V35() V36() V37() V38() finite set
bool [:[:K155(0,1,2),K155(0,1,2):],K155(0,1,2):] is non empty finite V49() set
bool [:K155(0,1,2),K155(0,1,2):] is non empty finite V49() set
Z_3 is strict doubleLoopStr
add3 is Relation-like [:K155(0,1,2),K155(0,1,2):] -defined K155(0,1,2) -valued Function-like quasi_total V35() V36() V37() V38() finite Element of bool [:[:K155(0,1,2),K155(0,1,2):],K155(0,1,2):]
mult3 is Relation-like [:K155(0,1,2),K155(0,1,2):] -defined K155(0,1,2) -valued Function-like quasi_total V35() V36() V37() V38() finite Element of bool [:[:K155(0,1,2),K155(0,1,2):],K155(0,1,2):]
unit3 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of K155(0,1,2)
zero3 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of K155(0,1,2)
doubleLoopStr(# K155(0,1,2),add3,mult3,unit3,zero3 #) is non empty strict doubleLoopStr
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of p is non empty non trivial set
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p || the carrier of p is set
the addF of p | [: the carrier of p, the carrier of p:] is Relation-like set
the multF of p || the carrier of p is set
the multF of p | [: the carrier of p, the carrier of p:] is Relation-like set
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
the carrier of p is non empty non trivial set
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the addF of p || the carrier of p is set
the addF of p | [: the carrier of p, the carrier of p:] is Relation-like set
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
the multF of p || the carrier of p is set
the multF of p | [: the carrier of p, the carrier of p:] is Relation-like set
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of p is non empty non trivial set
bool the carrier of p is non empty set
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a is non empty doubleLoopStr
the carrier of a is non empty set
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total 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 p || the carrier of a is set
the addF of p | [: the carrier of a, the carrier of a:] is Relation-like set
the multF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
the multF of p || the carrier of a is set
the multF of p | [: the carrier of a, the carrier of a:] is Relation-like set
1. a is Element of the carrier of a
the OneF of a is Element of the carrier of a
0. a is V61(a) Element of the carrier of a
the ZeroF of a is Element of the carrier of a
F1 is Element of the carrier of a
F2 is Element of the carrier of a
F1 * F2 is Element of the carrier of a
the multF of a . (F1,F2) is Element of the carrier of a
[F1,F2] is V26() set
{F1,F2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,F2},{F1}} is non empty finite V49() set
the multF of a . [F1,F2] is set
[F1,F2] is V26() Element of [: the carrier of a, the carrier of a:]
the multF of p . [F1,F2] is set
the multF of p . (F1,F2) is set
the multF of p . [F1,F2] is set
F1 is Element of the carrier of a
F2 is Element of the carrier of a
F1 + F2 is Element of the carrier of a
the addF of a . (F1,F2) is Element of the carrier of a
[F1,F2] is V26() set
{F1,F2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,F2},{F1}} is non empty finite V49() set
the addF of a . [F1,F2] is set
[F1,F2] is V26() Element of [: the carrier of a, the carrier of a:]
the addF of p . [F1,F2] is set
the addF of p . (F1,F2) is set
the addF of p . [F1,F2] is set
X is Element of the carrier of a
Y is Element of the carrier of a
X + Y is Element of the carrier of a
the addF of a . (X,Y) is Element of the carrier of a
[X,Y] is V26() set
{X,Y} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,Y},{X}} is non empty finite V49() set
the addF of a . [X,Y] is set
n1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
n1 + n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (n1,n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[n1,n] is V26() set
{n1,n} is non empty finite set
{n1} is non empty trivial finite 1 -element set
{{n1,n},{n1}} is non empty finite V49() set
the addF of p . [n1,n] is set
Y + X is Element of the carrier of a
the addF of a . (Y,X) is Element of the carrier of a
[Y,X] is V26() set
{Y,X} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,X},{Y}} is non empty finite V49() set
the addF of a . [Y,X] is set
n + n1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (n,n1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[n,n1] is V26() set
{n,n1} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,n1},{n}} is non empty finite V49() set
the addF of p . [n,n1] is set
X is Element of the carrier of a
Y is Element of the carrier of a
n1 is Element of the carrier of a
Y + n1 is Element of the carrier of a
the addF of a . (Y,n1) is Element of the carrier of a
[Y,n1] is V26() set
{Y,n1} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,n1},{Y}} is non empty finite V49() set
the addF of a . [Y,n1] is set
X + (Y + n1) is Element of the carrier of a
the addF of a . (X,(Y + n1)) is Element of the carrier of a
[X,(Y + n1)] is V26() set
{X,(Y + n1)} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,(Y + n1)},{X}} is non empty finite V49() set
the addF of a . [X,(Y + n1)] is set
n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (n,(Y + n1)) is set
[n,(Y + n1)] is V26() set
{n,(Y + n1)} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,(Y + n1)},{n}} is non empty finite V49() set
the addF of p . [n,(Y + n1)] is set
y1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
y1 + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (y1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[y1,a1] is V26() set
{y1,a1} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,a1},{y1}} is non empty finite V49() set
the addF of p . [y1,a1] is set
n + (y1 + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (n,(y1 + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[n,(y1 + a1)] is V26() set
{n,(y1 + a1)} is non empty finite set
{{n,(y1 + a1)},{n}} is non empty finite V49() set
the addF of p . [n,(y1 + a1)] is set
X + Y is Element of the carrier of a
the addF of a . (X,Y) is Element of the carrier of a
[X,Y] is V26() set
{X,Y} is non empty finite set
{{X,Y},{X}} is non empty finite V49() set
the addF of a . [X,Y] is set
(X + Y) + n1 is Element of the carrier of a
the addF of a . ((X + Y),n1) is Element of the carrier of a
[(X + Y),n1] is V26() set
{(X + Y),n1} is non empty finite set
{(X + Y)} is non empty trivial finite 1 -element set
{{(X + Y),n1},{(X + Y)}} is non empty finite V49() set
the addF of a . [(X + Y),n1] is set
the addF of p . ((X + Y),a1) is set
[(X + Y),a1] is V26() set
{(X + Y),a1} is non empty finite set
{{(X + Y),a1},{(X + Y)}} is non empty finite V49() set
the addF of p . [(X + Y),a1] is set
n + y1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (n,y1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[n,y1] is V26() set
{n,y1} is non empty finite set
{{n,y1},{n}} is non empty finite V49() set
the addF of p . [n,y1] is set
(n + y1) + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((n + y1),a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(n + y1),a1] is V26() set
{(n + y1),a1} is non empty finite set
{(n + y1)} is non empty trivial finite 1 -element set
{{(n + y1),a1},{(n + y1)}} is non empty finite V49() set
the addF of p . [(n + y1),a1] is set
X is Element of the carrier of a
X + (0. a) is Element of the carrier of a
the addF of a . (X,(0. a)) is Element of the carrier of a
[X,(0. a)] is V26() set
{X,(0. a)} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,(0. a)},{X}} is non empty finite V49() set
the addF of a . [X,(0. a)] is set
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
Y + (0. p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (Y,(0. p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[Y,(0. p)] is V26() set
{Y,(0. p)} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,(0. p)},{Y}} is non empty finite V49() set
the addF of p . [Y,(0. p)] is set
n1 is Element of the carrier of a
X is Element of the carrier of a
Y is Element of the carrier of a
Y * n1 is Element of the carrier of a
the multF of a . (Y,n1) is Element of the carrier of a
[Y,n1] is V26() set
{Y,n1} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,n1},{Y}} is non empty finite V49() set
the multF of a . [Y,n1] is set
X * (Y * n1) is Element of the carrier of a
the multF of a . (X,(Y * n1)) is Element of the carrier of a
[X,(Y * n1)] is V26() set
{X,(Y * n1)} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,(Y * n1)},{X}} is non empty finite V49() set
the multF of a . [X,(Y * n1)] is set
the multF of p . (X,(Y * n1)) is set
the multF of p . [X,(Y * n1)] is set
y1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a1 * n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (a1,n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a1,n] is V26() set
{a1,n} is non empty finite set
{a1} is non empty trivial finite 1 -element set
{{a1,n},{a1}} is non empty finite V49() set
the multF of p . [a1,n] is set
y1 * (a1 * n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (y1,(a1 * n)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[y1,(a1 * n)] is V26() set
{y1,(a1 * n)} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,(a1 * n)},{y1}} is non empty finite V49() set
the multF of p . [y1,(a1 * n)] is set
X * Y is Element of the carrier of a
the multF of a . (X,Y) is Element of the carrier of a
[X,Y] is V26() set
{X,Y} is non empty finite set
{{X,Y},{X}} is non empty finite V49() set
the multF of a . [X,Y] is set
y1 * a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (y1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[y1,a1] is V26() set
{y1,a1} is non empty finite set
{{y1,a1},{y1}} is non empty finite V49() set
the multF of p . [y1,a1] is set
(X * Y) * n1 is Element of the carrier of a
the multF of a . ((X * Y),n1) is Element of the carrier of a
[(X * Y),n1] is V26() set
{(X * Y),n1} is non empty finite set
{(X * Y)} is non empty trivial finite 1 -element set
{{(X * Y),n1},{(X * Y)}} is non empty finite V49() set
the multF of a . [(X * Y),n1] is set
(y1 * a1) * n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((y1 * a1),n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(y1 * a1),n] is V26() set
{(y1 * a1),n} is non empty finite set
{(y1 * a1)} is non empty trivial finite 1 -element set
{{(y1 * a1),n},{(y1 * a1)}} is non empty finite V49() set
the multF of p . [(y1 * a1),n] is set
X is Element of the carrier of a
X * (1. a) is Element of the carrier of a
the multF of a . (X,(1. a)) is Element of the carrier of a
[X,(1. a)] is V26() set
{X,(1. a)} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,(1. a)},{X}} is non empty finite V49() set
the multF of a . [X,(1. a)] is set
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
Y * (1. p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (Y,(1. p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[Y,(1. p)] is V26() set
{Y,(1. p)} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,(1. p)},{Y}} is non empty finite V49() set
the multF of p . [Y,(1. p)] is set
(1. a) * X is Element of the carrier of a
the multF of a . ((1. a),X) is Element of the carrier of a
[(1. a),X] is V26() set
{(1. a),X} is non empty finite set
{(1. a)} is non empty trivial finite 1 -element set
{{(1. a),X},{(1. a)}} is non empty finite V49() set
the multF of a . [(1. a),X] is set
(1. p) * Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((1. p),Y) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(1. p),Y] is V26() set
{(1. p),Y} is non empty finite set
{(1. p)} is non empty trivial finite 1 -element set
{{(1. p),Y},{(1. p)}} is non empty finite V49() set
the multF of p . [(1. p),Y] is set
Y is Element of the carrier of a
n1 is Element of the carrier of a
X is Element of the carrier of a
Y + n1 is Element of the carrier of a
the addF of a . (Y,n1) is Element of the carrier of a
[Y,n1] is V26() set
{Y,n1} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,n1},{Y}} is non empty finite V49() set
the addF of a . [Y,n1] is set
(Y + n1) * X is Element of the carrier of a
the multF of a . ((Y + n1),X) is Element of the carrier of a
[(Y + n1),X] is V26() set
{(Y + n1),X} is non empty finite set
{(Y + n1)} is non empty trivial finite 1 -element set
{{(Y + n1),X},{(Y + n1)}} is non empty finite V49() set
the multF of a . [(Y + n1),X] is set
the multF of p . ((Y + n1),X) is set
the multF of p . [(Y + n1),X] is set
n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
y1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
n + y1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (n,y1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[n,y1] is V26() set
{n,y1} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,y1},{n}} is non empty finite V49() set
the addF of p . [n,y1] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(n + y1) * a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((n + y1),a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(n + y1),a1] is V26() set
{(n + y1),a1} is non empty finite set
{(n + y1)} is non empty trivial finite 1 -element set
{{(n + y1),a1},{(n + y1)}} is non empty finite V49() set
the multF of p . [(n + y1),a1] is set
n * a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (n,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[n,a1] is V26() set
{n,a1} is non empty finite set
{{n,a1},{n}} is non empty finite V49() set
the multF of p . [n,a1] is set
y1 * a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (y1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[y1,a1] is V26() set
{y1,a1} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,a1},{y1}} is non empty finite V49() set
the multF of p . [y1,a1] is set
(n * a1) + (y1 * a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((n * a1),(y1 * a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(n * a1),(y1 * a1)] is V26() set
{(n * a1),(y1 * a1)} is non empty finite set
{(n * a1)} is non empty trivial finite 1 -element set
{{(n * a1),(y1 * a1)},{(n * a1)}} is non empty finite V49() set
the addF of p . [(n * a1),(y1 * a1)] is set
n1 * X is Element of the carrier of a
the multF of a . (n1,X) is Element of the carrier of a
[n1,X] is V26() set
{n1,X} is non empty finite set
{n1} is non empty trivial finite 1 -element set
{{n1,X},{n1}} is non empty finite V49() set
the multF of a . [n1,X] is set
the addF of p . (( the multF of p . (n,a1)),(n1 * X)) is set
[( the multF of p . (n,a1)),(n1 * X)] is V26() set
{( the multF of p . (n,a1)),(n1 * X)} is non empty finite set
{( the multF of p . (n,a1))} is non empty trivial finite 1 -element set
{{( the multF of p . (n,a1)),(n1 * X)},{( the multF of p . (n,a1))}} is non empty finite V49() set
the addF of p . [( the multF of p . (n,a1)),(n1 * X)] is set
Y * X is Element of the carrier of a
the multF of a . (Y,X) is Element of the carrier of a
[Y,X] is V26() set
{Y,X} is non empty finite set
{{Y,X},{Y}} is non empty finite V49() set
the multF of a . [Y,X] is set
the addF of p . ((Y * X),(n1 * X)) is set
[(Y * X),(n1 * X)] is V26() set
{(Y * X),(n1 * X)} is non empty finite set
{(Y * X)} is non empty trivial finite 1 -element set
{{(Y * X),(n1 * X)},{(Y * X)}} is non empty finite V49() set
the addF of p . [(Y * X),(n1 * X)] is set
X * (Y + n1) is Element of the carrier of a
the multF of a . (X,(Y + n1)) is Element of the carrier of a
[X,(Y + n1)] is V26() set
{X,(Y + n1)} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,(Y + n1)},{X}} is non empty finite V49() set
the multF of a . [X,(Y + n1)] is set
the multF of p . (X,(Y + n1)) is set
the multF of p . [X,(Y + n1)] is set
a1 * (n + y1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (a1,(n + y1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a1,(n + y1)] is V26() set
{a1,(n + y1)} is non empty finite set
{a1} is non empty trivial finite 1 -element set
{{a1,(n + y1)},{a1}} is non empty finite V49() set
the multF of p . [a1,(n + y1)] is set
a1 * n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (a1,n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a1,n] is V26() set
{a1,n} is non empty finite set
{{a1,n},{a1}} is non empty finite V49() set
the multF of p . [a1,n] is set
a1 * y1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (a1,y1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a1,y1] is V26() set
{a1,y1} is non empty finite set
{{a1,y1},{a1}} is non empty finite V49() set
the multF of p . [a1,y1] is set
(a1 * n) + (a1 * y1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a1 * n),(a1 * y1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a1 * n),(a1 * y1)] is V26() set
{(a1 * n),(a1 * y1)} is non empty finite set
{(a1 * n)} is non empty trivial finite 1 -element set
{{(a1 * n),(a1 * y1)},{(a1 * n)}} is non empty finite V49() set
the addF of p . [(a1 * n),(a1 * y1)] is set
the multF of p . (X,n) is set
[X,n] is V26() set
{X,n} is non empty finite set
{{X,n},{X}} is non empty finite V49() set
the multF of p . [X,n] is set
X * n1 is Element of the carrier of a
the multF of a . (X,n1) is Element of the carrier of a
[X,n1] is V26() set
{X,n1} is non empty finite set
{{X,n1},{X}} is non empty finite V49() set
the multF of a . [X,n1] is set
the addF of p . (( the multF of p . (X,n)),(X * n1)) is set
[( the multF of p . (X,n)),(X * n1)] is V26() set
{( the multF of p . (X,n)),(X * n1)} is non empty finite set
{( the multF of p . (X,n))} is non empty trivial finite 1 -element set
{{( the multF of p . (X,n)),(X * n1)},{( the multF of p . (X,n))}} is non empty finite V49() set
the addF of p . [( the multF of p . (X,n)),(X * n1)] is set
X * Y is Element of the carrier of a
the multF of a . (X,Y) is Element of the carrier of a
[X,Y] is V26() set
{X,Y} is non empty finite set
{{X,Y},{X}} is non empty finite V49() set
the multF of a . [X,Y] is set
the addF of p . ((X * Y),(X * n1)) is set
[(X * Y),(X * n1)] is V26() set
{(X * Y),(X * n1)} is non empty finite set
{(X * Y)} is non empty trivial finite 1 -element set
{{(X * Y),(X * n1)},{(X * Y)}} is non empty finite V49() set
the addF of p . [(X * Y),(X * n1)] is set
(X * Y) + (X * n1) is Element of the carrier of a
the addF of a . ((X * Y),(X * n1)) is Element of the carrier of a
the addF of a . [(X * Y),(X * n1)] is set
(Y * X) + (n1 * X) is Element of the carrier of a
the addF of a . ((Y * X),(n1 * X)) is Element of the carrier of a
the addF of a . [(Y * X),(n1 * X)] is set
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
[#] p is non empty non proper Element of bool the carrier of p
the carrier of p is non empty non trivial set
bool the carrier of p is non empty set
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the addF of p || ([#] p) is set
[:([#] p),([#] p):] is non empty set
the addF of p | [:([#] p),([#] p):] is Relation-like set
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
the multF of p || ([#] p) is set
the multF of p | [:([#] p),([#] p):] is Relation-like set
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is non empty non trivial strict doubleLoopStr
0. doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is V61( doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)) Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is non empty non trivial set
the ZeroF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
1. doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
the OneF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
L is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
F + pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (F,pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[F,pp] is V26() set
{F,pp} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,pp},{F}} is non empty finite V49() set
the addF of p . [F,pp] is set
FF is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
L + FF is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
the addF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is Relation-like [: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] -defined the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) -valued Function-like quasi_total Element of bool [:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):]
[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
[:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
bool [:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
the addF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . (L,FF) is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
[L,FF] is V26() set
{L,FF} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,FF},{L}} is non empty finite V49() set
the addF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . [L,FF] is set
L is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
F is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
L * F is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is Relation-like [: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] -defined the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) -valued Function-like quasi_total Element of bool [:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):]
[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
[:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
bool [:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . (L,F) is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
[L,F] is V26() set
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . [L,F] is set
F * L is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . (F,L) is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
[F,L] is V26() set
{F,L} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,L},{F}} is non empty finite V49() set
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . [F,L] is set
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
pp * FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (pp,FF) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[pp,FF] is V26() set
{pp,FF} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,FF},{pp}} is non empty finite V49() set
the multF of p . [pp,FF] is set
FF * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (FF,pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[FF,pp] is V26() set
{FF,pp} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,pp},{FF}} is non empty finite V49() set
the multF of p . [FF,pp] is set
L is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
pp * F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (pp,F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[pp,F] is V26() set
{pp,F} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,F},{pp}} is non empty finite V49() set
the multF of p . [pp,F] is set
FF is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
FF * L is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) is Relation-like [: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] -defined the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) -valued Function-like quasi_total Element of bool [:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):]
[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
[:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
bool [:[: the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #), the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):], the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #):] is non empty set
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . (FF,L) is Element of the carrier of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #)
[FF,L] is V26() set
{FF,L} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,L},{FF}} is non empty finite V49() set
the multF of doubleLoopStr(# the carrier of p, the addF of p, the multF of p,(1. p),(0. p) #) . [FF,L] is set
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of p is non empty non trivial set
the carrier of a is non empty non trivial set
b is set
b is set
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of p is non empty non trivial set
the carrier of a is non empty non trivial set
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total 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 || the carrier of p is set
[: the carrier of p, the carrier of p:] is non empty set
the addF of a | [: the carrier of p, the carrier of p:] is Relation-like set
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
the multF of a || the carrier of p is set
the multF of a | [: the carrier of p, the carrier of p:] is Relation-like set
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
1. a is V61(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the OneF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
0. a is V61(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the ZeroF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
b is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of p is non empty non trivial set
the carrier of a is non empty non trivial set
the carrier of b is non empty non trivial set
the addF of b is Relation-like [: the carrier of b, the carrier of b:] -defined the carrier of b -valued Function-like quasi_total Element of bool [:[: the carrier of b, the carrier of b:], the carrier of b:]
[: the carrier of b, the carrier of b:] is non empty set
[:[: the carrier of b, the carrier of b:], the carrier of b:] is non empty set
bool [:[: the carrier of b, the carrier of b:], the carrier of b:] is non empty set
the multF of b is Relation-like [: the carrier of b, the carrier of b:] -defined the carrier of b -valued Function-like quasi_total Element of bool [:[: the carrier of b, the carrier of b:], the carrier of b:]
[: the carrier of p, the carrier of p:] is non empty set
[: the carrier of a, the carrier of a:] is non empty set
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: 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 b || the carrier of a is set
the addF of b | [: the carrier of a, the carrier of a:] is Relation-like set
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the addF of a || the carrier of p is set
the addF of a | [: the carrier of p, the carrier of p:] is Relation-like set
the addF of b || the carrier of p is set
the addF of b | [: the carrier of p, the carrier of p:] is Relation-like set
the multF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
the multF of b || the carrier of a is set
the multF of b | [: the carrier of a, the carrier of a:] is Relation-like set
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
the multF of a || the carrier of p is set
the multF of a | [: the carrier of p, the carrier of p:] is Relation-like set
the multF of b || the carrier of p is set
the multF of b | [: the carrier of p, the carrier of p:] is Relation-like set
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
1. a is V61(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the OneF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
0. a is V61(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the ZeroF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
1. b is V61(b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
the OneF of b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
0. b is V61(b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
the ZeroF of b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
the carrier of a is non empty non trivial set
b is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
the carrier of b is non empty non trivial set
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
the carrier of p is non empty non trivial set
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of a, the carrier of a:] is non empty set
[: the carrier of b, the carrier of b:] is non empty set
the addF of b is Relation-like [: the carrier of b, the carrier of b:] -defined the carrier of b -valued Function-like quasi_total Element of bool [:[: the carrier of b, the carrier of b:], the carrier of b:]
[:[: the carrier of b, the carrier of b:], the carrier of b:] is non empty set
bool [:[: the carrier of b, the carrier of b:], the carrier of b:] is non empty set
the addF of p || the carrier of b is set
the addF of p | [: the carrier of b, the carrier of b:] is Relation-like set
the addF of b || the carrier of a is set
the addF of b | [: the carrier of a, the carrier of a:] is Relation-like set
the addF of p || the carrier of a is set
the addF of p | [: the carrier of a, the carrier of a:] is Relation-like set
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: 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 multF of b is Relation-like [: the carrier of b, the carrier of b:] -defined the carrier of b -valued Function-like quasi_total Element of bool [:[: the carrier of b, the carrier of b:], the carrier of b:]
the multF of p || the carrier of b is set
the multF of p | [: the carrier of b, the carrier of b:] is Relation-like set
the multF of b || the carrier of a is set
the multF of b | [: the carrier of a, the carrier of a:] is Relation-like set
the multF of p || the carrier of a is set
the multF of p | [: the carrier of a, the carrier of a:] is Relation-like set
the multF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like quasi_total Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
1. a is V61(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the OneF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
0. a is V61(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the ZeroF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
1. b is V61(b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
the OneF of b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
0. b is V61(b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
the ZeroF of b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
b is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
L is set
the carrier of a is non empty non trivial set
the carrier of b is non empty non trivial set
L is set
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
b is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
the carrier of a is non empty non trivial set
the carrier of b is non empty non trivial set
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
b is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
L is set
F is set
p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
card p is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal set
the carrier of p is non empty non trivial finite set
card the carrier of p is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal set
card the carrier of p is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
(p) is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
the carrier of p is non empty non trivial finite set
card the carrier of p is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal set
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed (p)
card a is V4() V5() V6() cardinal set
the carrier of a is non empty non trivial set
card the carrier of a is non empty V4() V5() V6() cardinal set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
b is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed ( INT.Ring p)
the carrier of b is non empty non trivial set
p - 1 is V11() V12() integer ext-real set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
0. b is V61(b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
the ZeroF of b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
F1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
1. b is V61(b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
the OneF of b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of b
1. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[1,F1] is V26() Element of [:NAT,NAT:]
{1,F1} is non empty finite V49() V117() V118() V119() V120() V121() V122() set
{1} is non empty trivial finite V49() 1 -element V117() V118() V119() V120() V121() V122() set
{{1,F1},{1}} is non empty finite V49() set
[: the carrier of b, the carrier of b:] is non empty set
the addF of b is Relation-like [: the carrier of b, the carrier of b:] -defined the carrier of b -valued Function-like quasi_total Element of bool [:[: the carrier of b, the carrier of b:], the carrier of b:]
[:[: the carrier of b, the carrier of b:], the carrier of b:] is non empty set
bool [:[: the carrier of b, the carrier of b:], the carrier of b:] is non empty set
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the addF of (INT.Ring p) || the carrier of b is set
the addF of (INT.Ring p) | [: the carrier of b, the carrier of b:] is Relation-like finite set
FF + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
1 + F1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
the addF of b . (1,F1) is set
[1,F1] is V26() set
the addF of b . [1,F1] is set
(addint p) . (1,F1) is set
(addint p) . [1,F1] is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(1 + F1) mod p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F1 is set
b is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set is Relation-like [:(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):] -defined Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):],(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):]
[:(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):],(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):],(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):] is non empty set
multint the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set is Relation-like [:(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):] -defined Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):],(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ):]
K633(1,(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set )) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
K633(0,(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set )) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
doubleLoopStr(# (Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(addint the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),(multint the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set ),K633(1,(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set )),K633(0,(Segm the non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set )) #) is strict doubleLoopStr
p is non empty multMagma
the carrier of p is non empty set
power p is Relation-like [: the carrier of p,NAT:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p,NAT:], the carrier of p:]
[: the carrier of p,NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
bool [:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
a is Element of the carrier of p
(power p) . (a,0) is Element of the carrier of p
[a,0] is V26() set
{a,0} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,0},{a}} is non empty finite V49() set
(power p) . [a,0] is set
1_ p is Element of the carrier of p
(power p) . (a,0) is set
b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(power p) . (a,b) is set
[a,b] is V26() set
{a,b} is non empty finite set
{{a,b},{a}} is non empty finite V49() set
(power p) . [a,b] is set
b - 0 is V11() V12() integer ext-real non negative set
b + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(power p) . (a,(b + 1)) is Element of the carrier of p
[a,(b + 1)] is V26() set
{a,(b + 1)} is non empty finite set
{{a,(b + 1)},{a}} is non empty finite V49() set
(power p) . [a,(b + 1)] is set
L is Element of the carrier of p
L * a is Element of the carrier of p
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p . (L,a) is Element of the carrier of p
[L,a] is V26() set
{L,a} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,a},{L}} is non empty finite V49() set
the multF of p . [L,a] is set
(power p) . (a,(b + 1)) is set
b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(power p) . (a,b) is set
[a,b] is V26() set
{a,b} is non empty finite set
{{a,b},{a}} is non empty finite V49() set
(power p) . [a,b] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the carrier of (INT.Ring p) is non empty non trivial finite set
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
1. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the carrier of (INT.Ring p) is non empty non trivial finite set
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
b mod p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p is V11() V12() integer ext-real set
a is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
p mod a is V11() V12() integer ext-real set
INT.Ring a is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm a is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
[:(Segm a),(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm a),(Segm a):],(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm a),(Segm a):],(Segm a):] is non empty set
multint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
K633(1,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
K633(0,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
doubleLoopStr(# (Segm a),(addint a),(multint a),K633(1,(Segm a)),K633(0,(Segm a)) #) is strict doubleLoopStr
the carrier of (INT.Ring a) is non empty non trivial finite set
b is V11() V12() integer ext-real set
L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
p is V11() V12() integer ext-real set
a is V11() V12() integer ext-real set
p + a is V11() V12() integer ext-real set
b is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring b is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm b is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
[:(Segm b),(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm b),(Segm b):],(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm b),(Segm b):],(Segm b):] is non empty set
multint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
K633(1,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
K633(0,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
doubleLoopStr(# (Segm b),(addint b),(multint b),K633(1,(Segm b)),K633(0,(Segm b)) #) is strict doubleLoopStr
the carrier of (INT.Ring b) is non empty non trivial finite set
p mod b is V11() V12() integer ext-real set
a mod b is V11() V12() integer ext-real set
(p + a) mod b is V11() V12() integer ext-real set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
L + F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the addF of (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] is non empty finite set
[:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite set
bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite V49() set
the addF of (INT.Ring b) . (L,F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
[L,F] is V26() set
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
the addF of (INT.Ring b) . [L,F] is set
(p mod b) + (a mod b) is V11() V12() integer ext-real set
((p mod b) + (a mod b)) mod b is V11() V12() integer ext-real set
p is V11() V12() integer ext-real set
a is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring a is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm a is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
[:(Segm a),(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm a),(Segm a):],(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm a),(Segm a):],(Segm a):] is non empty set
multint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
K633(1,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
K633(0,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
doubleLoopStr(# (Segm a),(addint a),(multint a),K633(1,(Segm a)),K633(0,(Segm a)) #) is strict doubleLoopStr
the carrier of (INT.Ring a) is non empty non trivial finite set
p mod a is V11() V12() integer ext-real set
a - p is V11() V12() integer ext-real set
(a - p) mod a is V11() V12() integer ext-real set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
- b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
b + L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the addF of (INT.Ring a) is Relation-like [: the carrier of (INT.Ring a), the carrier of (INT.Ring a):] -defined the carrier of (INT.Ring a) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):]
[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):] is non empty finite set
[:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):] is non empty finite set
bool [:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):] is non empty finite V49() set
the addF of (INT.Ring a) . (b,L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
[b,L] is V26() set
{b,L} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,L},{b}} is non empty finite V49() set
the addF of (INT.Ring a) . [b,L] is set
p + (a - p) is V11() V12() integer ext-real set
(p + (a - p)) mod a is V11() V12() integer ext-real set
0. (INT.Ring a) is V61( INT.Ring a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the ZeroF of (INT.Ring a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
p is V11() V12() integer ext-real set
a is V11() V12() integer ext-real set
p - a is V11() V12() integer ext-real set
b is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring b is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm b is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
[:(Segm b),(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm b),(Segm b):],(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm b),(Segm b):],(Segm b):] is non empty set
multint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
K633(1,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
K633(0,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
doubleLoopStr(# (Segm b),(addint b),(multint b),K633(1,(Segm b)),K633(0,(Segm b)) #) is strict doubleLoopStr
the carrier of (INT.Ring b) is non empty non trivial finite set
p mod b is V11() V12() integer ext-real set
a mod b is V11() V12() integer ext-real set
(p - a) mod b is V11() V12() integer ext-real set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
L - F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
- F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
L + (- F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the addF of (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] is non empty finite set
[:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite set
bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite V49() set
the addF of (INT.Ring b) . (L,(- F)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
[L,(- F)] is V26() set
{L,(- F)} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,(- F)},{L}} is non empty finite V49() set
the addF of (INT.Ring b) . [L,(- F)] is set
b - a is V11() V12() integer ext-real set
(b - a) mod b is V11() V12() integer ext-real set
p + (b - a) is V11() V12() integer ext-real set
(p + (b - a)) mod b is V11() V12() integer ext-real set
1 * b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(p - a) + (1 * b) is V11() V12() integer ext-real set
((p - a) + (1 * b)) mod b is V11() V12() integer ext-real set
p is V11() V12() integer ext-real set
a is V11() V12() integer ext-real set
p * a is V11() V12() integer ext-real set
b is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring b is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm b is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
[:(Segm b),(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm b),(Segm b):],(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm b),(Segm b):],(Segm b):] is non empty set
multint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
K633(1,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
K633(0,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
doubleLoopStr(# (Segm b),(addint b),(multint b),K633(1,(Segm b)),K633(0,(Segm b)) #) is strict doubleLoopStr
the carrier of (INT.Ring b) is non empty non trivial finite set
p mod b is V11() V12() integer ext-real set
a mod b is V11() V12() integer ext-real set
(p * a) mod b is V11() V12() integer ext-real set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
L * F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the multF of (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] is non empty finite set
[:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite set
bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite V49() set
the multF of (INT.Ring b) . (L,F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
[L,F] is V26() set
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
the multF of (INT.Ring b) . [L,F] is set
(p mod b) * (a mod b) is V11() V12() integer ext-real set
((p mod b) * (a mod b)) mod b is V11() V12() integer ext-real set
p is V11() V12() integer ext-real set
a is V11() V12() integer ext-real set
p * a is V11() V12() integer ext-real set
b is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring b is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm b is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
[:(Segm b),(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm b),(Segm b):],(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm b),(Segm b):],(Segm b):] is non empty set
multint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
K633(1,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
K633(0,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
doubleLoopStr(# (Segm b),(addint b),(multint b),K633(1,(Segm b)),K633(0,(Segm b)) #) is strict doubleLoopStr
the carrier of (INT.Ring b) is non empty non trivial finite set
p mod b is V11() V12() integer ext-real set
(p * a) mod b is V11() V12() integer ext-real set
a mod b is V11() V12() integer ext-real set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
L " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
F * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the multF of (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] is non empty finite set
[:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite set
bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite V49() set
the multF of (INT.Ring b) . (F,L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
[F,L] is V26() set
{F,L} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,L},{F}} is non empty finite V49() set
the multF of (INT.Ring b) . [F,L] is set
1. (INT.Ring b) is V61( INT.Ring b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the OneF of (INT.Ring b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
0. (INT.Ring b) is V61( INT.Ring b) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the ZeroF of (INT.Ring b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,b] is V26() set
{a,b} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,b},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,b] is set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a |^ 0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (a,0) is set
[a,0] is V26() set
{a,0} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,0},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,0] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (a,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,1] is V26() set
{a,1} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,1},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,1] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (a,2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,2] is V26() set
{a,2} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,2},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,2] is set
a * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,a] is V26() set
{a,a} is non empty finite set
{{a,a},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,a] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (a,2) is set
[a,2] is V26() set
{a,2} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,2},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,2] is set
a * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,a] is V26() set
{a,a} is non empty finite set
{{a,a},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,a] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
p |^ a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
b is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring b is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm b is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
[:(Segm b),(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm b),(Segm b):],(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm b),(Segm b):],(Segm b):] is non empty set
multint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
K633(1,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
K633(0,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
doubleLoopStr(# (Segm b),(addint b),(multint b),K633(1,(Segm b)),K633(0,(Segm b)) #) is strict doubleLoopStr
the carrier of (INT.Ring b) is non empty non trivial finite set
p mod b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(p |^ a) mod b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
L |^ a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
power (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b),NAT:] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):] is non empty non trivial non finite set
(power (INT.Ring b)) . (L,a) is set
[L,a] is V26() set
{L,a} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,a},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,a] is set
L |^ 0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
(power (INT.Ring b)) . (L,0) is set
[L,0] is V26() set
{L,0} is non empty finite set
{{L,0},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,0] is set
1 mod b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p |^ 0 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(p |^ 0) mod b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(power (INT.Ring b)) . (L,F) is set
[L,F] is V26() set
{L,F} is non empty finite set
{{L,F},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,F] is set
p |^ F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(p |^ F) mod b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F - 0 is V11() V12() integer ext-real non negative set
F + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(power (INT.Ring b)) . (L,(F + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
[L,(F + 1)] is V26() set
{L,(F + 1)} is non empty finite set
{{L,(F + 1)},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,(F + 1)] is set
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
pp * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the multF of (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] is non empty finite set
[:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite set
bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite V49() set
the multF of (INT.Ring b) . (pp,L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
[pp,L] is V26() set
{pp,L} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,L},{pp}} is non empty finite V49() set
the multF of (INT.Ring b) . [pp,L] is set
(p |^ F) * p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
((p |^ F) * p) mod b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p |^ (F + 1) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(p |^ (F + 1)) mod b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(power (INT.Ring b)) . (L,(F + 1)) is set
p is non empty unital associative multMagma
the carrier of p is non empty set
a is Element of the carrier of p
b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
b + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a |^ (b + 1) is Element of the carrier of p
power p is Relation-like [: the carrier of p,NAT:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p,NAT:], the carrier of p:]
[: the carrier of p,NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
bool [:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
(power p) . (a,(b + 1)) is set
[a,(b + 1)] is V26() set
{a,(b + 1)} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,(b + 1)},{a}} is non empty finite V49() set
(power p) . [a,(b + 1)] is set
a |^ b is Element of the carrier of p
(power p) . (a,b) is set
[a,b] is V26() set
{a,b} is non empty finite set
{{a,b},{a}} is non empty finite V49() set
(power p) . [a,b] is set
(a |^ b) * a is Element of the carrier of p
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p . ((a |^ b),a) is Element of the carrier of p
[(a |^ b),a] is V26() set
{(a |^ b),a} is non empty finite set
{(a |^ b)} is non empty trivial finite 1 -element set
{{(a |^ b),a},{(a |^ b)}} is non empty finite V49() set
the multF of p . [(a |^ b),a] is set
a |^ 1 is Element of the carrier of p
(power p) . (a,1) is set
[a,1] is V26() set
{a,1} is non empty finite set
{{a,1},{a}} is non empty finite V49() set
(power p) . [a,1] is set
(a |^ b) * (a |^ 1) is Element of the carrier of p
the multF of p . ((a |^ b),(a |^ 1)) is Element of the carrier of p
[(a |^ b),(a |^ 1)] is V26() set
{(a |^ b),(a |^ 1)} is non empty finite set
{{(a |^ b),(a |^ 1)},{(a |^ b)}} is non empty finite V49() set
the multF of p . [(a |^ b),(a |^ 1)] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
a is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring a is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm a is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
[:(Segm a),(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm a),(Segm a):],(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm a),(Segm a):],(Segm a):] is non empty set
multint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
K633(1,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
K633(0,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
doubleLoopStr(# (Segm a),(addint a),(multint a),K633(1,(Segm a)),K633(0,(Segm a)) #) is strict doubleLoopStr
the carrier of (INT.Ring a) is non empty non trivial finite set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
b |^ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
power (INT.Ring a) is Relation-like [: the carrier of (INT.Ring a),NAT:] -defined the carrier of (INT.Ring a) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):]
[: the carrier of (INT.Ring a),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
(power (INT.Ring a)) . (b,p) is set
[b,p] is V26() set
{b,p} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,p},{b}} is non empty finite V49() set
(power (INT.Ring a)) . [b,p] is set
L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L |^ p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(L |^ p) mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of p is non empty set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p . (a,a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a,a] is V26() set
{a,a} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,a},{a}} is non empty finite V49() set
the multF of p . [a,a] is set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
b * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (b,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[b,b] is V26() set
{b,b} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,b},{b}} is non empty finite V49() set
the multF of p . [b,b] is set
- b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a - b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a + (- b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
the addF of p . (a,(- b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a,(- b)] is V26() set
{a,(- b)} is non empty finite set
{{a,(- b)},{a}} is non empty finite V49() set
the addF of p . [a,(- b)] is set
a + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a,b] is V26() set
{a,b} is non empty finite set
{{a,b},{a}} is non empty finite V49() set
the addF of p . [a,b] is set
(a - b) * (a + b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((a - b),(a + b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a - b),(a + b)] is V26() set
{(a - b),(a + b)} is non empty finite set
{(a - b)} is non empty trivial finite 1 -element set
{{(a - b),(a + b)},{(a - b)}} is non empty finite V49() set
the multF of p . [(a - b),(a + b)] is set
(a - b) * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((a - b),a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a - b),a] is V26() set
{(a - b),a} is non empty finite set
{{(a - b),a},{(a - b)}} is non empty finite V49() set
the multF of p . [(a - b),a] is set
(a - b) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((a - b),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a - b),b] is V26() set
{(a - b),b} is non empty finite set
{{(a - b),b},{(a - b)}} is non empty finite V49() set
the multF of p . [(a - b),b] is set
((a - b) * a) + ((a - b) * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a - b) * a),((a - b) * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a - b) * a),((a - b) * b)] is V26() set
{((a - b) * a),((a - b) * b)} is non empty finite set
{((a - b) * a)} is non empty trivial finite 1 -element set
{{((a - b) * a),((a - b) * b)},{((a - b) * a)}} is non empty finite V49() set
the addF of p . [((a - b) * a),((a - b) * b)] is set
a * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . [a,b] is set
(a * a) - (a * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
- (a * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(a * a) + (- (a * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a * a),(- (a * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a * a),(- (a * b))] is V26() set
{(a * a),(- (a * b))} is non empty finite set
{(a * a)} is non empty trivial finite 1 -element set
{{(a * a),(- (a * b))},{(a * a)}} is non empty finite V49() set
the addF of p . [(a * a),(- (a * b))] is set
((a * a) - (a * b)) + ((a - b) * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) - (a * b)),((a - b) * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) - (a * b)),((a - b) * b)] is V26() set
{((a * a) - (a * b)),((a - b) * b)} is non empty finite set
{((a * a) - (a * b))} is non empty trivial finite 1 -element set
{{((a * a) - (a * b)),((a - b) * b)},{((a * a) - (a * b))}} is non empty finite V49() set
the addF of p . [((a * a) - (a * b)),((a - b) * b)] is set
b * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . (b,a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[b,a] is V26() set
{b,a} is non empty finite set
{{b,a},{b}} is non empty finite V49() set
the multF of p . [b,a] is set
(b * a) - (b * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
- (b * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(b * a) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((b * a),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(b * a),(- (b * b))] is V26() set
{(b * a),(- (b * b))} is non empty finite set
{(b * a)} is non empty trivial finite 1 -element set
{{(b * a),(- (b * b))},{(b * a)}} is non empty finite V49() set
the addF of p . [(b * a),(- (b * b))] is set
((a * a) - (a * b)) + ((b * a) - (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) - (a * b)),((b * a) - (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) - (a * b)),((b * a) - (b * b))] is V26() set
{((a * a) - (a * b)),((b * a) - (b * b))} is non empty finite set
{{((a * a) - (a * b)),((b * a) - (b * b))},{((a * a) - (a * b))}} is non empty finite V49() set
the addF of p . [((a * a) - (a * b)),((b * a) - (b * b))] is set
((a * a) - (a * b)) + (b * a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) - (a * b)),(b * a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) - (a * b)),(b * a)] is V26() set
{((a * a) - (a * b)),(b * a)} is non empty finite set
{{((a * a) - (a * b)),(b * a)},{((a * a) - (a * b))}} is non empty finite V49() set
the addF of p . [((a * a) - (a * b)),(b * a)] is set
(((a * a) - (a * b)) + (b * a)) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((((a * a) - (a * b)) + (b * a)),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(((a * a) - (a * b)) + (b * a)),(- (b * b))] is V26() set
{(((a * a) - (a * b)) + (b * a)),(- (b * b))} is non empty finite set
{(((a * a) - (a * b)) + (b * a))} is non empty trivial finite 1 -element set
{{(((a * a) - (a * b)) + (b * a)),(- (b * b))},{(((a * a) - (a * b)) + (b * a))}} is non empty finite V49() set
the addF of p . [(((a * a) - (a * b)) + (b * a)),(- (b * b))] is set
(- (a * b)) + (b * a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((- (a * b)),(b * a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(- (a * b)),(b * a)] is V26() set
{(- (a * b)),(b * a)} is non empty finite set
{(- (a * b))} is non empty trivial finite 1 -element set
{{(- (a * b)),(b * a)},{(- (a * b))}} is non empty finite V49() set
the addF of p . [(- (a * b)),(b * a)] is set
(a * a) + ((- (a * b)) + (b * a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a * a),((- (a * b)) + (b * a))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a * a),((- (a * b)) + (b * a))] is V26() set
{(a * a),((- (a * b)) + (b * a))} is non empty finite set
{{(a * a),((- (a * b)) + (b * a))},{(a * a)}} is non empty finite V49() set
the addF of p . [(a * a),((- (a * b)) + (b * a))] is set
((a * a) + ((- (a * b)) + (b * a))) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) + ((- (a * b)) + (b * a))),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) + ((- (a * b)) + (b * a))),(- (b * b))] is V26() set
{((a * a) + ((- (a * b)) + (b * a))),(- (b * b))} is non empty finite set
{((a * a) + ((- (a * b)) + (b * a)))} is non empty trivial finite 1 -element set
{{((a * a) + ((- (a * b)) + (b * a))),(- (b * b))},{((a * a) + ((- (a * b)) + (b * a)))}} is non empty finite V49() set
the addF of p . [((a * a) + ((- (a * b)) + (b * a))),(- (b * b))] is set
(b * a) - (a * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(b * a) + (- (a * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((b * a),(- (a * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(b * a),(- (a * b))] is V26() set
{(b * a),(- (a * b))} is non empty finite set
{{(b * a),(- (a * b))},{(b * a)}} is non empty finite V49() set
the addF of p . [(b * a),(- (a * b))] is set
(a * a) + ((b * a) - (a * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a * a),((b * a) - (a * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a * a),((b * a) - (a * b))] is V26() set
{(a * a),((b * a) - (a * b))} is non empty finite set
{{(a * a),((b * a) - (a * b))},{(a * a)}} is non empty finite V49() set
the addF of p . [(a * a),((b * a) - (a * b))] is set
((a * a) + ((b * a) - (a * b))) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) + ((b * a) - (a * b))),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) + ((b * a) - (a * b))),(- (b * b))] is V26() set
{((a * a) + ((b * a) - (a * b))),(- (b * b))} is non empty finite set
{((a * a) + ((b * a) - (a * b)))} is non empty trivial finite 1 -element set
{{((a * a) + ((b * a) - (a * b))),(- (b * b))},{((a * a) + ((b * a) - (a * b)))}} is non empty finite V49() set
the addF of p . [((a * a) + ((b * a) - (a * b))),(- (b * b))] is set
a - a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
- a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
a + (- a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (a,(- a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[a,(- a)] is V26() set
{a,(- a)} is non empty finite set
{{a,(- a)},{a}} is non empty finite V49() set
the addF of p . [a,(- a)] is set
(a - a) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((a - a),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a - a),b] is V26() set
{(a - a),b} is non empty finite set
{(a - a)} is non empty trivial finite 1 -element set
{{(a - a),b},{(a - a)}} is non empty finite V49() set
the multF of p . [(a - a),b] is set
(a * a) + ((a - a) * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a * a),((a - a) * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a * a),((a - a) * b)] is V26() set
{(a * a),((a - a) * b)} is non empty finite set
{{(a * a),((a - a) * b)},{(a * a)}} is non empty finite V49() set
the addF of p . [(a * a),((a - a) * b)] is set
((a * a) + ((a - a) * b)) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) + ((a - a) * b)),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) + ((a - a) * b)),(- (b * b))] is V26() set
{((a * a) + ((a - a) * b)),(- (b * b))} is non empty finite set
{((a * a) + ((a - a) * b))} is non empty trivial finite 1 -element set
{{((a * a) + ((a - a) * b)),(- (b * b))},{((a * a) + ((a - a) * b))}} is non empty finite V49() set
the addF of p . [((a * a) + ((a - a) * b)),(- (b * b))] is set
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(0. p) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((0. p),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(0. p),b] is V26() set
{(0. p),b} is non empty finite set
{(0. p)} is non empty trivial finite 1 -element set
{{(0. p),b},{(0. p)}} is non empty finite V49() set
the multF of p . [(0. p),b] is set
(a * a) + ((0. p) * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a * a),((0. p) * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a * a),((0. p) * b)] is V26() set
{(a * a),((0. p) * b)} is non empty finite set
{{(a * a),((0. p) * b)},{(a * a)}} is non empty finite V49() set
the addF of p . [(a * a),((0. p) * b)] is set
((a * a) + ((0. p) * b)) - (b * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
((a * a) + ((0. p) * b)) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) + ((0. p) * b)),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) + ((0. p) * b)),(- (b * b))] is V26() set
{((a * a) + ((0. p) * b)),(- (b * b))} is non empty finite set
{((a * a) + ((0. p) * b))} is non empty trivial finite 1 -element set
{{((a * a) + ((0. p) * b)),(- (b * b))},{((a * a) + ((0. p) * b))}} is non empty finite V49() set
the addF of p . [((a * a) + ((0. p) * b)),(- (b * b))] is set
(a * a) + (0. p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a * a),(0. p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a * a),(0. p)] is V26() set
{(a * a),(0. p)} is non empty finite set
{{(a * a),(0. p)},{(a * a)}} is non empty finite V49() set
the addF of p . [(a * a),(0. p)] is set
((a * a) + (0. p)) - (b * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
((a * a) + (0. p)) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . (((a * a) + (0. p)),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[((a * a) + (0. p)),(- (b * b))] is V26() set
{((a * a) + (0. p)),(- (b * b))} is non empty finite set
{((a * a) + (0. p))} is non empty trivial finite 1 -element set
{{((a * a) + (0. p)),(- (b * b))},{((a * a) + (0. p))}} is non empty finite V49() set
the addF of p . [((a * a) + (0. p)),(- (b * b))] is set
(a * a) - (b * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(a * a) + (- (b * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p . ((a * a),(- (b * b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(a * a),(- (b * b))] is V26() set
{(a * a),(- (b * b))} is non empty finite set
{{(a * a),(- (b * b))},{(a * a)}} is non empty finite V49() set
the addF of p . [(a * a),(- (b * b))] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a + a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the addF of (INT.Ring p) . (a,a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,a] is V26() set
{a,a} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,a},{a}} is non empty finite V49() set
the addF of (INT.Ring p) . [a,a] is set
1. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(1. (INT.Ring p)) + (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((1. (INT.Ring p)),(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),(1. (INT.Ring p))] is V26() set
{(1. (INT.Ring p)),(1. (INT.Ring p))} is non empty finite set
{(1. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(1. (INT.Ring p)),(1. (INT.Ring p))},{(1. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(1. (INT.Ring p)),(1. (INT.Ring p))] is set
((1. (INT.Ring p)) + (1. (INT.Ring p))) * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the multF of (INT.Ring p) . (((1. (INT.Ring p)) + (1. (INT.Ring p))),a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((1. (INT.Ring p)) + (1. (INT.Ring p))),a] is V26() set
{((1. (INT.Ring p)) + (1. (INT.Ring p))),a} is non empty finite set
{((1. (INT.Ring p)) + (1. (INT.Ring p)))} is non empty trivial finite 1 -element set
{{((1. (INT.Ring p)) + (1. (INT.Ring p))),a},{((1. (INT.Ring p)) + (1. (INT.Ring p)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [((1. (INT.Ring p)) + (1. (INT.Ring p))),a] is set
b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
2 * b is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(2 * b) mod p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(1. (INT.Ring p)) * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1. (INT.Ring p)),a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),a] is V26() set
{(1. (INT.Ring p)),a} is non empty finite set
{{(1. (INT.Ring p)),a},{(1. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(1. (INT.Ring p)),a] is set
((1. (INT.Ring p)) * a) + a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((1. (INT.Ring p)) * a),a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((1. (INT.Ring p)) * a),a] is V26() set
{((1. (INT.Ring p)) * a),a} is non empty finite set
{((1. (INT.Ring p)) * a)} is non empty trivial finite 1 -element set
{{((1. (INT.Ring p)) * a),a},{((1. (INT.Ring p)) * a)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((1. (INT.Ring p)) * a),a] is set
((1. (INT.Ring p)) * a) + ((1. (INT.Ring p)) * a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((1. (INT.Ring p)) * a),((1. (INT.Ring p)) * a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((1. (INT.Ring p)) * a),((1. (INT.Ring p)) * a)] is V26() set
{((1. (INT.Ring p)) * a),((1. (INT.Ring p)) * a)} is non empty finite set
{{((1. (INT.Ring p)) * a),((1. (INT.Ring p)) * a)},{((1. (INT.Ring p)) * a)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((1. (INT.Ring p)) * a),((1. (INT.Ring p)) * a)] is set
(2 * b) div p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((2 * b) div p) * p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(2 * b) - (((2 * b) div p) * p) is V11() V12() integer ext-real set
b div p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p * (b div p) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(b div p) * p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
b - ((b div p) * p) is V11() V12() integer ext-real set
b mod p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
a is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring a is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm a is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
[:(Segm a),(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm a),(Segm a):],(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm a),(Segm a):],(Segm a):] is non empty set
multint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
K633(1,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
K633(0,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
doubleLoopStr(# (Segm a),(addint a),(multint a),K633(1,(Segm a)),K633(0,(Segm a)) #) is strict doubleLoopStr
the carrier of (INT.Ring a) is non empty non trivial finite set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
b " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(b ") |^ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
power (INT.Ring a) is Relation-like [: the carrier of (INT.Ring a),NAT:] -defined the carrier of (INT.Ring a) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):]
[: the carrier of (INT.Ring a),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
(power (INT.Ring a)) . ((b "),p) is set
[(b "),p] is V26() set
{(b "),p} is non empty finite set
{(b ")} is non empty trivial finite 1 -element set
{{(b "),p},{(b ")}} is non empty finite V49() set
(power (INT.Ring a)) . [(b "),p] is set
b |^ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(power (INT.Ring a)) . (b,p) is set
[b,p] is V26() set
{b,p} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,p},{b}} is non empty finite V49() set
(power (INT.Ring a)) . [b,p] is set
(b |^ p) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
F mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L |^ p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(L |^ p) mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F |^ p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(F |^ p) mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L * F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(L * F) |^ p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
((L * F) |^ p) mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(L |^ p) * (F |^ p) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
((L |^ p) * (F |^ p)) mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(b |^ p) * ((b ") |^ p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the multF of (INT.Ring a) is Relation-like [: the carrier of (INT.Ring a), the carrier of (INT.Ring a):] -defined the carrier of (INT.Ring a) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):]
[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):] is non empty finite set
[:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):] is non empty finite set
bool [:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):] is non empty finite V49() set
the multF of (INT.Ring a) . ((b |^ p),((b ") |^ p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
[(b |^ p),((b ") |^ p)] is V26() set
{(b |^ p),((b ") |^ p)} is non empty finite set
{(b |^ p)} is non empty trivial finite 1 -element set
{{(b |^ p),((b ") |^ p)},{(b |^ p)}} is non empty finite V49() set
the multF of (INT.Ring a) . [(b |^ p),((b ") |^ p)] is set
0. (INT.Ring a) is V61( INT.Ring a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the ZeroF of (INT.Ring a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(b ") * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the multF of (INT.Ring a) . ((b "),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
[(b "),b] is V26() set
{(b "),b} is non empty finite set
{{(b "),b},{(b ")}} is non empty finite V49() set
the multF of (INT.Ring a) . [(b "),b] is set
1. (INT.Ring a) is V61( INT.Ring a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the OneF of (INT.Ring a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(L * F) mod a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((b ") |^ p) * (b |^ p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the multF of (INT.Ring a) . (((b ") |^ p),(b |^ p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
[((b ") |^ p),(b |^ p)] is V26() set
{((b ") |^ p),(b |^ p)} is non empty finite set
{((b ") |^ p)} is non empty trivial finite 1 -element set
{{((b ") |^ p),(b |^ p)},{((b ") |^ p)}} is non empty finite V49() set
the multF of (INT.Ring a) . [((b ") |^ p),(b |^ p)] is set
b is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring b is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm b is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
[:(Segm b),(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm b),(Segm b):],(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm b),(Segm b):],(Segm b):] is non empty set
multint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
K633(1,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
K633(0,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
doubleLoopStr(# (Segm b),(addint b),(multint b),K633(1,(Segm b)),K633(0,(Segm b)) #) is strict doubleLoopStr
the carrier of (INT.Ring b) is non empty non trivial finite set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L |^ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
power (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b),NAT:] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):] is non empty non trivial non finite set
(power (INT.Ring b)) . (L,p) is set
[L,p] is V26() set
{L,p} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,p},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,p] is set
a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L |^ a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
(power (INT.Ring b)) . (L,a) is set
[L,a] is V26() set
{L,a} is non empty finite set
{{L,a},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,a] is set
(L |^ p) * (L |^ a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
the multF of (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):] is non empty finite set
[:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite set
bool [:[: the carrier of (INT.Ring b), the carrier of (INT.Ring b):], the carrier of (INT.Ring b):] is non empty finite V49() set
the multF of (INT.Ring b) . ((L |^ p),(L |^ a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
[(L |^ p),(L |^ a)] is V26() set
{(L |^ p),(L |^ a)} is non empty finite set
{(L |^ p)} is non empty trivial finite 1 -element set
{{(L |^ p),(L |^ a)},{(L |^ p)}} is non empty finite V49() set
the multF of (INT.Ring b) . [(L |^ p),(L |^ a)] is set
p + a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L |^ (p + a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
(power (INT.Ring b)) . (L,(p + a)) is set
[L,(p + a)] is V26() set
{L,(p + a)} is non empty finite set
{{L,(p + a)},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,(p + a)] is set
b is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring b is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm b is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
[:(Segm b),(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm b),(Segm b):],(Segm b):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm b),(Segm b):],(Segm b):] is non empty set
multint b is Relation-like [:(Segm b),(Segm b):] -defined Segm b -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm b),(Segm b):],(Segm b):]
K633(1,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
K633(0,(Segm b)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm b
doubleLoopStr(# (Segm b),(addint b),(multint b),K633(1,(Segm b)),K633(0,(Segm b)) #) is strict doubleLoopStr
the carrier of (INT.Ring b) is non empty non trivial finite set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L |^ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
power (INT.Ring b) is Relation-like [: the carrier of (INT.Ring b),NAT:] -defined the carrier of (INT.Ring b) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):]
[: the carrier of (INT.Ring b),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring b),NAT:], the carrier of (INT.Ring b):] is non empty non trivial non finite set
(power (INT.Ring b)) . (L,p) is set
[L,p] is V26() set
{L,p} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,p},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,p] is set
a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
(L |^ p) |^ a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
(power (INT.Ring b)) . ((L |^ p),a) is set
[(L |^ p),a] is V26() set
{(L |^ p),a} is non empty finite set
{(L |^ p)} is non empty trivial finite 1 -element set
{{(L |^ p),a},{(L |^ p)}} is non empty finite V49() set
(power (INT.Ring b)) . [(L |^ p),a] is set
p * a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L |^ (p * a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring b)
(power (INT.Ring b)) . (L,(p * a)) is set
[L,(p * a)] is V26() set
{L,(p * a)} is non empty finite set
{{L,(p * a)},{L}} is non empty finite V49() set
(power (INT.Ring b)) . [L,(p * a)] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
MultGroup (INT.Ring p) is non empty finite strict Group-like associative multMagma
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
MultGroup (INT.Ring p) is non empty finite strict Group-like associative cyclic multMagma
the carrier of (MultGroup (INT.Ring p)) is non empty finite set
the carrier of (INT.Ring p) is non empty non trivial finite set
a is Element of the carrier of (MultGroup (INT.Ring p))
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
a |^ L is Element of the carrier of (MultGroup (INT.Ring p))
power (MultGroup (INT.Ring p)) is Relation-like [: the carrier of (MultGroup (INT.Ring p)),NAT:] -defined the carrier of (MultGroup (INT.Ring p)) -valued Function-like quasi_total Element of bool [:[: the carrier of (MultGroup (INT.Ring p)),NAT:], the carrier of (MultGroup (INT.Ring p)):]
[: the carrier of (MultGroup (INT.Ring p)),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (MultGroup (INT.Ring p)),NAT:], the carrier of (MultGroup (INT.Ring p)):] is non empty non trivial non finite set
bool [:[: the carrier of (MultGroup (INT.Ring p)),NAT:], the carrier of (MultGroup (INT.Ring p)):] is non empty non trivial non finite set
(power (MultGroup (INT.Ring p))) . (a,L) is set
[a,L] is V26() set
{a,L} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,L},{a}} is non empty finite V49() set
(power (MultGroup (INT.Ring p))) . [a,L] is set
b |^ L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (b,L) is set
[b,L] is V26() set
{b,L} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,L},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,L] is set
F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
a |^ F is Element of the carrier of (MultGroup (INT.Ring p))
(power (MultGroup (INT.Ring p))) . (a,F) is set
[a,F] is V26() set
{a,F} is non empty finite set
{{a,F},{a}} is non empty finite V49() set
(power (MultGroup (INT.Ring p))) . [a,F] is set
b |^ F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (b,F) is set
[b,F] is V26() set
{b,F} is non empty finite set
{{b,F},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,F] is set
F + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a |^ (F + 1) is Element of the carrier of (MultGroup (INT.Ring p))
(power (MultGroup (INT.Ring p))) . (a,(F + 1)) is set
[a,(F + 1)] is V26() set
{a,(F + 1)} is non empty finite set
{{a,(F + 1)},{a}} is non empty finite V49() set
(power (MultGroup (INT.Ring p))) . [a,(F + 1)] is set
b |^ (F + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (b,(F + 1)) is set
[b,(F + 1)] is V26() set
{b,(F + 1)} is non empty finite set
{{b,(F + 1)},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,(F + 1)] is set
(a |^ F) * a is Element of the carrier of (MultGroup (INT.Ring p))
the multF of (MultGroup (INT.Ring p)) is Relation-like [: the carrier of (MultGroup (INT.Ring p)), the carrier of (MultGroup (INT.Ring p)):] -defined the carrier of (MultGroup (INT.Ring p)) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (MultGroup (INT.Ring p)), the carrier of (MultGroup (INT.Ring p)):], the carrier of (MultGroup (INT.Ring p)):]
[: the carrier of (MultGroup (INT.Ring p)), the carrier of (MultGroup (INT.Ring p)):] is non empty finite set
[:[: the carrier of (MultGroup (INT.Ring p)), the carrier of (MultGroup (INT.Ring p)):], the carrier of (MultGroup (INT.Ring p)):] is non empty finite set
bool [:[: the carrier of (MultGroup (INT.Ring p)), the carrier of (MultGroup (INT.Ring p)):], the carrier of (MultGroup (INT.Ring p)):] is non empty finite V49() set
the multF of (MultGroup (INT.Ring p)) . ((a |^ F),a) is Element of the carrier of (MultGroup (INT.Ring p))
[(a |^ F),a] is V26() set
{(a |^ F),a} is non empty finite set
{(a |^ F)} is non empty trivial finite 1 -element set
{{(a |^ F),a},{(a |^ F)}} is non empty finite V49() set
the multF of (MultGroup (INT.Ring p)) . [(a |^ F),a] is set
(b |^ F) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . ((b |^ F),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(b |^ F),b] is V26() set
{(b |^ F),b} is non empty finite set
{(b |^ F)} is non empty trivial finite 1 -element set
{{(b |^ F),b},{(b |^ F)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(b |^ F),b] is set
a |^ 0 is Element of the carrier of (MultGroup (INT.Ring p))
(power (MultGroup (INT.Ring p))) . (a,0) is set
[a,0] is V26() set
{a,0} is non empty finite set
{{a,0},{a}} is non empty finite V49() set
(power (MultGroup (INT.Ring p))) . [a,0] is set
1_ (MultGroup (INT.Ring p)) is Element of the carrier of (MultGroup (INT.Ring p))
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b |^ 0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (b,0) is set
[b,0] is V26() set
{b,0} is non empty finite set
{{b,0},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,0] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
MultGroup (INT.Ring p) is non empty finite strict Group-like associative cyclic multMagma
the carrier of (MultGroup (INT.Ring p)) is non empty finite set
a is Element of the carrier of (MultGroup (INT.Ring p))
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
{(0. (INT.Ring p))} is non empty trivial finite 1 -element Element of bool the carrier of (INT.Ring p)
bool the carrier of (INT.Ring p) is non empty finite V49() set
the carrier of (MultGroup (INT.Ring p)) \/ {(0. (INT.Ring p))} is non empty finite set
F is Element of the carrier of (MultGroup (INT.Ring p))
pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
a |^ pp is Element of the carrier of (MultGroup (INT.Ring p))
power (MultGroup (INT.Ring p)) is Relation-like [: the carrier of (MultGroup (INT.Ring p)),NAT:] -defined the carrier of (MultGroup (INT.Ring p)) -valued Function-like quasi_total Element of bool [:[: the carrier of (MultGroup (INT.Ring p)),NAT:], the carrier of (MultGroup (INT.Ring p)):]
[: the carrier of (MultGroup (INT.Ring p)),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (MultGroup (INT.Ring p)),NAT:], the carrier of (MultGroup (INT.Ring p)):] is non empty non trivial non finite set
bool [:[: the carrier of (MultGroup (INT.Ring p)),NAT:], the carrier of (MultGroup (INT.Ring p)):] is non empty non trivial non finite set
(power (MultGroup (INT.Ring p))) . (a,pp) is set
[a,pp] is V26() set
{a,pp} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,pp},{a}} is non empty finite V49() set
(power (MultGroup (INT.Ring p))) . [a,pp] is set
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
b |^ FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (b,FF) is set
[b,FF] is V26() set
{b,FF} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,FF},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,FF] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (a,2) is set
[a,2] is V26() set
{a,2} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,2},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,2] is set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
1. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the carrier of (INT.Ring p) is non empty non trivial finite set
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (a,2) is set
[a,2] is V26() set
{a,2} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,2},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,2] is set
(1. (INT.Ring p)) * (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . ((1. (INT.Ring p)),(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),(1. (INT.Ring p))] is V26() set
{(1. (INT.Ring p)),(1. (INT.Ring p))} is non empty finite set
{(1. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(1. (INT.Ring p)),(1. (INT.Ring p))},{(1. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(1. (INT.Ring p)),(1. (INT.Ring p))] is set
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- 1 is V11() V12() integer ext-real non positive set
b is V11() V12() integer ext-real set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a) is V11() V12() integer ext-real set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (b,2) is set
[b,2] is V26() set
{b,2} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,2},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,2] is set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (b,2) is set
[b,2] is V26() set
{b,2} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,2},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,2] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a) is V11() V12() integer ext-real set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a) is V11() V12() integer ext-real set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (a,2) is set
[a,2] is V26() set
{a,2} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,2},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,2] is set
(p,(a |^ 2)) is V11() V12() integer ext-real set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a) is V11() V12() integer ext-real set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,b] is V26() set
{a,b} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,b},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,b] is set
(p,(a * b)) is V11() V12() integer ext-real set
(p,b) is V11() V12() integer ext-real set
(p,a) * (p,b) is V11() V12() integer ext-real set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F,2) is set
[F,2] is V26() set
{F,2} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,2},{F}} is non empty finite V49() set
(power (INT.Ring p)) . [F,2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F,2) is set
[F,2] is V26() set
{F,2} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,2},{F}} is non empty finite V49() set
(power (INT.Ring p)) . [F,2] is set
(L |^ 2) * (F |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((L |^ 2),(F |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(L |^ 2),(F |^ 2)] is V26() set
{(L |^ 2),(F |^ 2)} is non empty finite set
{(L |^ 2)} is non empty trivial finite 1 -element set
{{(L |^ 2),(F |^ 2)},{(L |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(L |^ 2),(F |^ 2)] is set
L * F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (L,F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[L,F] is V26() set
{L,F} is non empty finite set
{{L,F},{L}} is non empty finite V49() set
the multF of (INT.Ring p) . [L,F] is set
(L * F) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L * F),2) is set
[(L * F),2] is V26() set
{(L * F),2} is non empty finite set
{(L * F)} is non empty trivial finite 1 -element set
{{(L * F),2},{(L * F)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L * F),2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F,2) is set
[F,2] is V26() set
{F,2} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,2},{F}} is non empty finite V49() set
(power (INT.Ring p)) . [F,2] is set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,2) is set
[pp,2] is V26() set
{pp,2} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,2},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,2] is set
F * F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,F] is V26() set
{F,F} is non empty finite set
{{F,F},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,F] is set
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,2) is set
[pp,2] is V26() set
{pp,2} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,2},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,2] is set
F " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F ") * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((F "),L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F "),L] is V26() set
{(F "),L} is non empty finite set
{(F ")} is non empty trivial finite 1 -element set
{{(F "),L},{(F ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [(F "),L] is set
((F ") * L) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (((F ") * L),2) is set
[((F ") * L),2] is V26() set
{((F ") * L),2} is non empty finite set
{((F ") * L)} is non empty trivial finite 1 -element set
{{((F ") * L),2},{((F ") * L)}} is non empty finite V49() set
(power (INT.Ring p)) . [((F ") * L),2] is set
(F ") |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F "),2) is set
[(F "),2] is V26() set
{(F "),2} is non empty finite set
{{(F "),2},{(F ")}} is non empty finite V49() set
(power (INT.Ring p)) . [(F "),2] is set
((F ") |^ 2) * (a * b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((F ") |^ 2),(a * b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F ") |^ 2),(a * b)] is V26() set
{((F ") |^ 2),(a * b)} is non empty finite set
{((F ") |^ 2)} is non empty trivial finite 1 -element set
{{((F ") |^ 2),(a * b)},{((F ") |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((F ") |^ 2),(a * b)] is set
((F ") |^ 2) * (F |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((F ") |^ 2),(F |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F ") |^ 2),(F |^ 2)] is V26() set
{((F ") |^ 2),(F |^ 2)} is non empty finite set
{{((F ") |^ 2),(F |^ 2)},{((F ") |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((F ") |^ 2),(F |^ 2)] is set
(((F ") |^ 2) * (F |^ 2)) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((((F ") |^ 2) * (F |^ 2)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((F ") |^ 2) * (F |^ 2)),b] is V26() set
{(((F ") |^ 2) * (F |^ 2)),b} is non empty finite set
{(((F ") |^ 2) * (F |^ 2))} is non empty trivial finite 1 -element set
{{(((F ") |^ 2) * (F |^ 2)),b},{(((F ") |^ 2) * (F |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(((F ") |^ 2) * (F |^ 2)),b] is set
(F |^ 2) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((F |^ 2) ") * (F |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((F |^ 2) "),(F |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F |^ 2) "),(F |^ 2)] is V26() set
{((F |^ 2) "),(F |^ 2)} is non empty finite set
{((F |^ 2) ")} is non empty trivial finite 1 -element set
{{((F |^ 2) "),(F |^ 2)},{((F |^ 2) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((F |^ 2) "),(F |^ 2)] is set
(((F |^ 2) ") * (F |^ 2)) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((((F |^ 2) ") * (F |^ 2)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((F |^ 2) ") * (F |^ 2)),b] is V26() set
{(((F |^ 2) ") * (F |^ 2)),b} is non empty finite set
{(((F |^ 2) ") * (F |^ 2))} is non empty trivial finite 1 -element set
{{(((F |^ 2) ") * (F |^ 2)),b},{(((F |^ 2) ") * (F |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(((F |^ 2) ") * (F |^ 2)),b] is set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(1. (INT.Ring p)) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1. (INT.Ring p)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),b] is V26() set
{(1. (INT.Ring p)),b} is non empty finite set
{(1. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(1. (INT.Ring p)),b},{(1. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(1. (INT.Ring p)),b] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F,2) is set
[F,2] is V26() set
{F,2} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,2},{F}} is non empty finite V49() set
(power (INT.Ring p)) . [F,2] is set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,2) is set
[pp,2] is V26() set
{pp,2} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,2},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,2] is set
F * F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,F] is V26() set
{F,F} is non empty finite set
{{F,F},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,F] is set
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,2) is set
[pp,2] is V26() set
{pp,2} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,2},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,2] is set
F " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L * (F ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (L,(F ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[L,(F ")] is V26() set
{L,(F ")} is non empty finite set
{{L,(F ")},{L}} is non empty finite V49() set
the multF of (INT.Ring p) . [L,(F ")] is set
(L * (F ")) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L * (F ")),2) is set
[(L * (F ")),2] is V26() set
{(L * (F ")),2} is non empty finite set
{(L * (F "))} is non empty trivial finite 1 -element set
{{(L * (F ")),2},{(L * (F "))}} is non empty finite V49() set
(power (INT.Ring p)) . [(L * (F ")),2] is set
(F ") |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F "),2) is set
[(F "),2] is V26() set
{(F "),2} is non empty finite set
{(F ")} is non empty trivial finite 1 -element set
{{(F "),2},{(F ")}} is non empty finite V49() set
(power (INT.Ring p)) . [(F "),2] is set
(a * b) * ((F ") |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * b),((F ") |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * b),((F ") |^ 2)] is V26() set
{(a * b),((F ") |^ 2)} is non empty finite set
{(a * b)} is non empty trivial finite 1 -element set
{{(a * b),((F ") |^ 2)},{(a * b)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * b),((F ") |^ 2)] is set
(F |^ 2) * ((F ") |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((F |^ 2),((F ") |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F |^ 2),((F ") |^ 2)] is V26() set
{(F |^ 2),((F ") |^ 2)} is non empty finite set
{(F |^ 2)} is non empty trivial finite 1 -element set
{{(F |^ 2),((F ") |^ 2)},{(F |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(F |^ 2),((F ") |^ 2)] is set
a * ((F |^ 2) * ((F ") |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,((F |^ 2) * ((F ") |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,((F |^ 2) * ((F ") |^ 2))] is V26() set
{a,((F |^ 2) * ((F ") |^ 2))} is non empty finite set
{{a,((F |^ 2) * ((F ") |^ 2))},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,((F |^ 2) * ((F ") |^ 2))] is set
(F |^ 2) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F |^ 2) * ((F |^ 2) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((F |^ 2),((F |^ 2) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F |^ 2),((F |^ 2) ")] is V26() set
{(F |^ 2),((F |^ 2) ")} is non empty finite set
{{(F |^ 2),((F |^ 2) ")},{(F |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(F |^ 2),((F |^ 2) ")] is set
a * ((F |^ 2) * ((F |^ 2) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,((F |^ 2) * ((F |^ 2) "))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,((F |^ 2) * ((F |^ 2) "))] is V26() set
{a,((F |^ 2) * ((F |^ 2) "))} is non empty finite set
{{a,((F |^ 2) * ((F |^ 2) "))},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,((F |^ 2) * ((F |^ 2) "))] is set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a * (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(1. (INT.Ring p))] is V26() set
{a,(1. (INT.Ring p))} is non empty finite set
{{a,(1. (INT.Ring p))},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(1. (INT.Ring p))] is set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L |^ F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,F) is set
[L,F] is V26() set
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,F] is set
pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L |^ pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (L,pp) is set
[L,pp] is V26() set
{L,pp} is non empty finite set
{{L,pp},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,pp] is set
F div 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(F div 2) * 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F mod 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((F div 2) * 2) + (F mod 2) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
pp div 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(pp div 2) * 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
pp mod 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((pp div 2) * 2) + (pp mod 2) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L |^ FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (L,FF) is set
[L,FF] is V26() set
{L,FF} is non empty finite set
{{L,FF},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,FF] is set
(L |^ FF) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L |^ FF),2) is set
[(L |^ FF),2] is V26() set
{(L |^ FF),2} is non empty finite set
{(L |^ FF)} is non empty trivial finite 1 -element set
{{(L |^ FF),2},{(L |^ FF)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L |^ FF),2] is set
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L |^ FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (L,FF) is set
[L,FF] is V26() set
{L,FF} is non empty finite set
{{L,FF},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,FF] is set
(L |^ FF) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L |^ FF),2) is set
[(L |^ FF),2] is V26() set
{(L |^ FF),2} is non empty finite set
{(L |^ FF)} is non empty trivial finite 1 -element set
{{(L |^ FF),2},{(L |^ FF)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L |^ FF),2] is set
(F div 2) + (pp div 2) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((F div 2) + (pp div 2)) + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F + pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
((F div 2) * 2) + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(((F div 2) * 2) + 1) + pp is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((pp div 2) * 2) + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(((F div 2) * 2) + 1) + (((pp div 2) * 2) + 1) is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
FF * 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L |^ (F + pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (L,(F + pp)) is set
[L,(F + pp)] is V26() set
{L,(F + pp)} is non empty finite set
{{L,(F + pp)},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,(F + pp)] is set
L |^ FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (L,FF) is set
[L,FF] is V26() set
{L,FF} is non empty finite set
{{L,FF},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,FF] is set
(L |^ FF) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L |^ FF),2) is set
[(L |^ FF),2] is V26() set
{(L |^ FF),2} is non empty finite set
{(L |^ FF)} is non empty trivial finite 1 -element set
{{(L |^ FF),2},{(L |^ FF)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L |^ FF),2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
p mod 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring a is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm a is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
[:(Segm a),(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm a),(Segm a):],(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm a),(Segm a):],(Segm a):] is non empty set
multint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
K633(1,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
K633(0,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
doubleLoopStr(# (Segm a),(addint a),(multint a),K633(1,(Segm a)),K633(0,(Segm a)) #) is strict doubleLoopStr
the carrier of (INT.Ring a) is non empty non trivial finite set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
b |^ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
power (INT.Ring a) is Relation-like [: the carrier of (INT.Ring a),NAT:] -defined the carrier of (INT.Ring a) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):]
[: the carrier of (INT.Ring a),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
(power (INT.Ring a)) . (b,p) is set
[b,p] is V26() set
{b,p} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,p},{b}} is non empty finite V49() set
(power (INT.Ring a)) . [b,p] is set
(a,(b |^ p)) is V11() V12() integer ext-real set
p div 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(p div 2) * 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((p div 2) * 2) + (p mod 2) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
b |^ L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(power (INT.Ring a)) . (b,L) is set
[b,L] is V26() set
{b,L} is non empty finite set
{{b,L},{b}} is non empty finite V49() set
(power (INT.Ring a)) . [b,L] is set
(b |^ L) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(power (INT.Ring a)) . ((b |^ L),2) is set
[(b |^ L),2] is V26() set
{(b |^ L),2} is non empty finite set
{(b |^ L)} is non empty trivial finite 1 -element set
{{(b |^ L),2},{(b |^ L)}} is non empty finite V49() set
(power (INT.Ring a)) . [(b |^ L),2] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
p mod 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring a is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm a is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
[:(Segm a),(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm a),(Segm a):],(Segm a):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm a),(Segm a):],(Segm a):] is non empty set
multint a is Relation-like [:(Segm a),(Segm a):] -defined Segm a -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm a),(Segm a):],(Segm a):]
K633(1,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
K633(0,(Segm a)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm a
doubleLoopStr(# (Segm a),(addint a),(multint a),K633(1,(Segm a)),K633(0,(Segm a)) #) is strict doubleLoopStr
the carrier of (INT.Ring a) is non empty non trivial finite set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
b |^ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
power (INT.Ring a) is Relation-like [: the carrier of (INT.Ring a),NAT:] -defined the carrier of (INT.Ring a) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):]
[: the carrier of (INT.Ring a),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring a),NAT:], the carrier of (INT.Ring a):] is non empty non trivial non finite set
(power (INT.Ring a)) . (b,p) is set
[b,p] is V26() set
{b,p} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,p},{b}} is non empty finite V49() set
(power (INT.Ring a)) . [b,p] is set
(a,(b |^ p)) is V11() V12() integer ext-real set
(a,b) is V11() V12() integer ext-real set
p div 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(p div 2) * 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
((p div 2) * 2) + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p - 1 is V11() V12() integer ext-real set
L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
b |^ (L + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(power (INT.Ring a)) . (b,(L + 1)) is set
[b,(L + 1)] is V26() set
{b,(L + 1)} is non empty finite set
{{b,(L + 1)},{b}} is non empty finite V49() set
(power (INT.Ring a)) . [b,(L + 1)] is set
b |^ L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
(power (INT.Ring a)) . (b,L) is set
[b,L] is V26() set
{b,L} is non empty finite set
{{b,L},{b}} is non empty finite V49() set
(power (INT.Ring a)) . [b,L] is set
(b |^ L) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
the multF of (INT.Ring a) is Relation-like [: the carrier of (INT.Ring a), the carrier of (INT.Ring a):] -defined the carrier of (INT.Ring a) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):]
[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):] is non empty finite set
[:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):] is non empty finite set
bool [:[: the carrier of (INT.Ring a), the carrier of (INT.Ring a):], the carrier of (INT.Ring a):] is non empty finite V49() set
the multF of (INT.Ring a) . ((b |^ L),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring a)
[(b |^ L),b] is V26() set
{(b |^ L),b} is non empty finite set
{(b |^ L)} is non empty trivial finite 1 -element set
{{(b |^ L),b},{(b |^ L)}} is non empty finite V49() set
the multF of (INT.Ring a) . [(b |^ L),b] is set
(a,(b |^ L)) is V11() V12() integer ext-real set
(a,(b |^ L)) * (a,b) is V11() V12() integer ext-real set
(p - 1) mod 2 is V11() V12() integer ext-real set
0 + ((p div 2) * 2) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(0 + ((p div 2) * 2)) mod 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
0 mod 2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
{ b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = a } is set
card { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = a } is V4() V5() V6() cardinal set
(p,a) is V11() V12() integer ext-real set
1 + (p,a) is V11() V12() integer ext-real set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (b,2) is set
[b,2] is V26() set
{b,2} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,2},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,2] is set
- b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(- b) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((- b),2) is set
[(- b),2] is V26() set
{(- b),2} is non empty finite set
{(- b)} is non empty trivial finite 1 -element set
{{(- b),2},{(- b)}} is non empty finite V49() set
(power (INT.Ring p)) . [(- b),2] is set
(- b) * (- b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . ((- b),(- b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(- b),(- b)] is V26() set
{(- b),(- b)} is non empty finite set
{{(- b),(- b)},{(- b)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(- b),(- b)] is set
b * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,b] is V26() set
{b,b} is non empty finite set
{{b,b},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,b] is set
{b,(- b)} is non empty finite Element of bool the carrier of (INT.Ring p)
bool the carrier of (INT.Ring p) is non empty finite V49() set
b + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . (b,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . [b,b] is set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) * (0. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((0. (INT.Ring p)),(0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(0. (INT.Ring p)),(0. (INT.Ring p))] is set
L is set
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F,2) is set
[F,2] is V26() set
{F,2} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,2},{F}} is non empty finite V49() set
(power (INT.Ring p)) . [F,2] is set
F * F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,F) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,F] is V26() set
{F,F} is non empty finite set
{{F,F},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,F] is set
card {b,(- b)} is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
b is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
{(0. (INT.Ring p))} is non empty trivial finite 1 -element Element of bool the carrier of (INT.Ring p)
bool the carrier of (INT.Ring p) is non empty finite V49() set
(0. (INT.Ring p)) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((0. (INT.Ring p)),2) is set
[(0. (INT.Ring p)),2] is V26() set
{(0. (INT.Ring p)),2} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),2},{(0. (INT.Ring p))}} is non empty finite V49() set
(power (INT.Ring p)) . [(0. (INT.Ring p)),2] is set
(0. (INT.Ring p)) * (0. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . ((0. (INT.Ring p)),(0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(0. (INT.Ring p)),(0. (INT.Ring p))] is set
1 + 0 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
b is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,2) is set
[L,2] is V26() set
{L,2} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,2},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,2] is set
1 + (- 1) is V11() V12() integer ext-real set
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of p is non empty non trivial set
[: the carrier of p, the carrier of p, the carrier of p:] is non empty set
0. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(0. p),(0. p),(0. p)] is V26() V27() Element of [: the carrier of p, the carrier of p, the carrier of p:]
[(0. p),(0. p)] is V26() set
{(0. p),(0. p)} is non empty finite set
{(0. p)} is non empty trivial finite 1 -element set
{{(0. p),(0. p)},{(0. p)}} is non empty finite V49() set
[[(0. p),(0. p)],(0. p)] is V26() set
{[(0. p),(0. p)],(0. p)} is non empty finite set
{[(0. p),(0. p)]} is non empty trivial finite 1 -element set
{{[(0. p),(0. p)],(0. p)},{[(0. p),(0. p)]}} is non empty finite V49() set
{[(0. p),(0. p),(0. p)]} is non empty trivial finite 1 -element Element of bool [: the carrier of p, the carrier of p, the carrier of p:]
bool [: the carrier of p, the carrier of p, the carrier of p:] is non empty set
[: the carrier of p, the carrier of p, the carrier of p:] \ {[(0. p),(0. p),(0. p)]} is Element of bool [: the carrier of p, the carrier of p, the carrier of p:]
1. p is V61(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(1. p),(1. p),(1. p)] is V26() V27() Element of [: the carrier of p, the carrier of p, the carrier of p:]
[(1. p),(1. p)] is V26() set
{(1. p),(1. p)} is non empty finite set
{(1. p)} is non empty trivial finite 1 -element set
{{(1. p),(1. p)},{(1. p)}} is non empty finite V49() set
[[(1. p),(1. p)],(1. p)] is V26() set
{[(1. p),(1. p)],(1. p)} is non empty finite set
{[(1. p),(1. p)]} is non empty trivial finite 1 -element set
{{[(1. p),(1. p)],(1. p)},{[(1. p),(1. p)]}} is non empty finite V49() set
[:NAT,NAT,NAT:] is non empty set
[0,0,0] is V26() V27() Element of [:NAT,NAT,NAT:]
[0,0] is V26() set
{0,0} is non empty finite V49() V117() V118() V119() V120() V121() V122() set
{0} is non empty trivial finite V49() 1 -element V117() V118() V119() V120() V121() V122() set
{{0,0},{0}} is non empty finite V49() set
[[0,0],0] is V26() set
{[0,0],0} is non empty finite set
{[0,0]} is non empty trivial finite 1 -element set
{{[0,0],0},{[0,0]}} is non empty finite V49() set
{[0,0,0]} is non empty trivial finite 1 -element Element of bool [:NAT,NAT,NAT:]
bool [:NAT,NAT,NAT:] is non empty set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[0,0,0]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
4 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
4 mod p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
27 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
27 mod p is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
3 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (a,3) is set
[a,3] is V26() set
{a,3} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,3},{a}} is non empty finite V49() set
(power (INT.Ring p)) . [a,3] is set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (b,2) is set
[b,2] is V26() set
{b,2} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,2},{b}} is non empty finite V49() set
(power (INT.Ring p)) . [b,2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L * (a |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (L,(a |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[L,(a |^ 3)] is V26() set
{L,(a |^ 3)} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,(a |^ 3)},{L}} is non empty finite V49() set
the multF of (INT.Ring p) . [L,(a |^ 3)] is set
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F * (b |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,(b |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,(b |^ 2)] is V26() set
{F,(b |^ 2)} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,(b |^ 2)},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,(b |^ 2)] is set
(L * (a |^ 3)) + (F * (b |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((L * (a |^ 3)),(F * (b |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(L * (a |^ 3)),(F * (b |^ 2))] is V26() set
{(L * (a |^ 3)),(F * (b |^ 2))} is non empty finite set
{(L * (a |^ 3))} is non empty trivial finite 1 -element set
{{(L * (a |^ 3)),(F * (b |^ 2))},{(L * (a |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(L * (a |^ 3)),(F * (b |^ 2))] is set
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF * (a |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(a |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(a |^ 3)] is V26() set
{FF,(a |^ 3)} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,(a |^ 3)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(a |^ 3)] is set
F1 * (b |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F1,(b |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F1,(b |^ 2)] is V26() set
{F1,(b |^ 2)} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,(b |^ 2)},{F1}} is non empty finite V49() set
the multF of (INT.Ring p) . [F1,(b |^ 2)] is set
(FF * (a |^ 3)) + (F1 * (b |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((FF * (a |^ 3)),(F1 * (b |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(FF * (a |^ 3)),(F1 * (b |^ 2))] is V26() set
{(FF * (a |^ 3)),(F1 * (b |^ 2))} is non empty finite set
{(FF * (a |^ 3))} is non empty trivial finite 1 -element set
{{(FF * (a |^ 3)),(F1 * (b |^ 2))},{(FF * (a |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(FF * (a |^ 3)),(F1 * (b |^ 2))] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp * (a |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (pp,(a |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(a |^ 3)] is V26() set
{pp,(a |^ 3)} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,(a |^ 3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(a |^ 3)] is set
FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF * (b |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(b |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(b |^ 2)] is V26() set
{FF,(b |^ 2)} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,(b |^ 2)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(b |^ 2)] is set
(pp * (a |^ 3)) + (FF * (b |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((pp * (a |^ 3)),(FF * (b |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp * (a |^ 3)),(FF * (b |^ 2))] is V26() set
{(pp * (a |^ 3)),(FF * (b |^ 2))} is non empty finite set
{(pp * (a |^ 3))} is non empty trivial finite 1 -element set
{{(pp * (a |^ 3)),(FF * (b |^ 2))},{(pp * (a |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(pp * (a |^ 3)),(FF * (b |^ 2))] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
pp is Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
F . pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp `1 is set
(pp `1) `2 is set
(pp `2_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . ((pp `2_3),2) is set
[(pp `2_3),2] is V26() set
{(pp `2_3),2} is non empty finite set
{(pp `2_3)} is non empty trivial finite 1 -element set
{{(pp `2_3),2},{(pp `2_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp `2_3),2] is set
pp `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((pp `2_3) |^ 2) * (pp `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (((pp `2_3) |^ 2),(pp `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp `2_3) |^ 2),(pp `3_3)] is V26() set
{((pp `2_3) |^ 2),(pp `3_3)} is non empty finite set
{((pp `2_3) |^ 2)} is non empty trivial finite 1 -element set
{{((pp `2_3) |^ 2),(pp `3_3)},{((pp `2_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp `2_3) |^ 2),(pp `3_3)] is set
pp `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(pp `1) `1 is set
(pp `1_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((pp `1_3),3) is set
[(pp `1_3),3] is V26() set
{(pp `1_3),3} is non empty finite set
{(pp `1_3)} is non empty trivial finite 1 -element set
{{(pp `1_3),3},{(pp `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp `1_3),3] is set
a * (pp `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(pp `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(pp `1_3)] is V26() set
{a,(pp `1_3)} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,(pp `1_3)},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(pp `1_3)] is set
(pp `3_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((pp `3_3),2) is set
[(pp `3_3),2] is V26() set
{(pp `3_3),2} is non empty finite set
{(pp `3_3)} is non empty trivial finite 1 -element set
{{(pp `3_3),2},{(pp `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp `3_3),2] is set
(a * (pp `1_3)) * ((pp `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (pp `1_3)),((pp `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (pp `1_3)),((pp `3_3) |^ 2)] is V26() set
{(a * (pp `1_3)),((pp `3_3) |^ 2)} is non empty finite set
{(a * (pp `1_3))} is non empty trivial finite 1 -element set
{{(a * (pp `1_3)),((pp `3_3) |^ 2)},{(a * (pp `1_3))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (pp `1_3)),((pp `3_3) |^ 2)] is set
((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . (((pp `1_3) |^ 3),((a * (pp `1_3)) * ((pp `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp `1_3) |^ 3),((a * (pp `1_3)) * ((pp `3_3) |^ 2))] is V26() set
{((pp `1_3) |^ 3),((a * (pp `1_3)) * ((pp `3_3) |^ 2))} is non empty finite set
{((pp `1_3) |^ 3)} is non empty trivial finite 1 -element set
{{((pp `1_3) |^ 3),((a * (pp `1_3)) * ((pp `3_3) |^ 2))},{((pp `1_3) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp `1_3) |^ 3),((a * (pp `1_3)) * ((pp `3_3) |^ 2))] is set
(pp `3_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((pp `3_3),3) is set
[(pp `3_3),3] is V26() set
{(pp `3_3),3} is non empty finite set
{{(pp `3_3),3},{(pp `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp `3_3),3] is set
b * ((pp `3_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((pp `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((pp `3_3) |^ 3)] is V26() set
{b,((pp `3_3) |^ 3)} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,((pp `3_3) |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((pp `3_3) |^ 3)] is set
(((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))),(b * ((pp `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))),(b * ((pp `3_3) |^ 3))] is V26() set
{(((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))),(b * ((pp `3_3) |^ 3))} is non empty finite set
{(((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))),(b * ((pp `3_3) |^ 3))},{(((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))),(b * ((pp `3_3) |^ 3))] is set
(((pp `2_3) |^ 2) * (pp `3_3)) - ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp `2_3) |^ 2) * (pp `3_3)) + (- ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp `2_3) |^ 2) * (pp `3_3)),(- ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp `2_3) |^ 2) * (pp `3_3)),(- ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3))))] is V26() set
{(((pp `2_3) |^ 2) * (pp `3_3)),(- ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3))))} is non empty finite set
{(((pp `2_3) |^ 2) * (pp `3_3))} is non empty trivial finite 1 -element set
{{(((pp `2_3) |^ 2) * (pp `3_3)),(- ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3))))},{(((pp `2_3) |^ 2) * (pp `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp `2_3) |^ 2) * (pp `3_3)),(- ((((pp `1_3) |^ 3) + ((a * (pp `1_3)) * ((pp `3_3) |^ 2))) + (b * ((pp `3_3) |^ 3))))] is set
F is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
pp is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
FF is Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
F . FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF `1 is set
(FF `1) `2 is set
(FF `2_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . ((FF `2_3),2) is set
[(FF `2_3),2] is V26() set
{(FF `2_3),2} is non empty finite set
{(FF `2_3)} is non empty trivial finite 1 -element set
{{(FF `2_3),2},{(FF `2_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(FF `2_3),2] is set
FF `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((FF `2_3) |^ 2) * (FF `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (((FF `2_3) |^ 2),(FF `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((FF `2_3) |^ 2),(FF `3_3)] is V26() set
{((FF `2_3) |^ 2),(FF `3_3)} is non empty finite set
{((FF `2_3) |^ 2)} is non empty trivial finite 1 -element set
{{((FF `2_3) |^ 2),(FF `3_3)},{((FF `2_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((FF `2_3) |^ 2),(FF `3_3)] is set
FF `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(FF `1) `1 is set
(FF `1_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((FF `1_3),3) is set
[(FF `1_3),3] is V26() set
{(FF `1_3),3} is non empty finite set
{(FF `1_3)} is non empty trivial finite 1 -element set
{{(FF `1_3),3},{(FF `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(FF `1_3),3] is set
a * (FF `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(FF `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(FF `1_3)] is V26() set
{a,(FF `1_3)} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,(FF `1_3)},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(FF `1_3)] is set
(FF `3_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((FF `3_3),2) is set
[(FF `3_3),2] is V26() set
{(FF `3_3),2} is non empty finite set
{(FF `3_3)} is non empty trivial finite 1 -element set
{{(FF `3_3),2},{(FF `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(FF `3_3),2] is set
(a * (FF `1_3)) * ((FF `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (FF `1_3)),((FF `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (FF `1_3)),((FF `3_3) |^ 2)] is V26() set
{(a * (FF `1_3)),((FF `3_3) |^ 2)} is non empty finite set
{(a * (FF `1_3))} is non empty trivial finite 1 -element set
{{(a * (FF `1_3)),((FF `3_3) |^ 2)},{(a * (FF `1_3))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (FF `1_3)),((FF `3_3) |^ 2)] is set
((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . (((FF `1_3) |^ 3),((a * (FF `1_3)) * ((FF `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((FF `1_3) |^ 3),((a * (FF `1_3)) * ((FF `3_3) |^ 2))] is V26() set
{((FF `1_3) |^ 3),((a * (FF `1_3)) * ((FF `3_3) |^ 2))} is non empty finite set
{((FF `1_3) |^ 3)} is non empty trivial finite 1 -element set
{{((FF `1_3) |^ 3),((a * (FF `1_3)) * ((FF `3_3) |^ 2))},{((FF `1_3) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((FF `1_3) |^ 3),((a * (FF `1_3)) * ((FF `3_3) |^ 2))] is set
(FF `3_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((FF `3_3),3) is set
[(FF `3_3),3] is V26() set
{(FF `3_3),3} is non empty finite set
{{(FF `3_3),3},{(FF `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(FF `3_3),3] is set
b * ((FF `3_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((FF `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((FF `3_3) |^ 3)] is V26() set
{b,((FF `3_3) |^ 3)} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,((FF `3_3) |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((FF `3_3) |^ 3)] is set
(((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))),(b * ((FF `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))),(b * ((FF `3_3) |^ 3))] is V26() set
{(((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))),(b * ((FF `3_3) |^ 3))} is non empty finite set
{(((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))),(b * ((FF `3_3) |^ 3))},{(((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))),(b * ((FF `3_3) |^ 3))] is set
(((FF `2_3) |^ 2) * (FF `3_3)) - ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((FF `2_3) |^ 2) * (FF `3_3)) + (- ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((FF `2_3) |^ 2) * (FF `3_3)),(- ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((FF `2_3) |^ 2) * (FF `3_3)),(- ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3))))] is V26() set
{(((FF `2_3) |^ 2) * (FF `3_3)),(- ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3))))} is non empty finite set
{(((FF `2_3) |^ 2) * (FF `3_3))} is non empty trivial finite 1 -element set
{{(((FF `2_3) |^ 2) * (FF `3_3)),(- ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3))))},{(((FF `2_3) |^ 2) * (FF `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((FF `2_3) |^ 2) * (FF `3_3)),(- ((((FF `1_3) |^ 3) + ((a * (FF `1_3)) * ((FF `3_3) |^ 2))) + (b * ((FF `3_3) |^ 3))))] is set
pp . FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[L,F,pp] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[L,F] is V26() set
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
[[L,F],pp] is V26() set
{[L,F],pp} is non empty finite set
{[L,F]} is non empty trivial finite 1 -element set
{{[L,F],pp},{[L,F]}} is non empty finite V49() set
(p,a,b) . [L,F,pp] is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (F,2) is set
[F,2] is V26() set
{F,2} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,2},{F}} is non empty finite V49() set
(power (INT.Ring p)) . [F,2] is set
(F |^ 2) * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . ((F |^ 2),pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F |^ 2),pp] is V26() set
{(F |^ 2),pp} is non empty finite set
{(F |^ 2)} is non empty trivial finite 1 -element set
{{(F |^ 2),pp},{(F |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(F |^ 2),pp] is set
L |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (L,3) is set
[L,3] is V26() set
{L,3} is non empty finite set
{{L,3},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,3] is set
a * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,L] is V26() set
{a,L} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,L},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,L] is set
pp |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,2) is set
[pp,2] is V26() set
{pp,2} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,2},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,2] is set
(a * L) * (pp |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * L),(pp |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * L),(pp |^ 2)] is V26() set
{(a * L),(pp |^ 2)} is non empty finite set
{(a * L)} is non empty trivial finite 1 -element set
{{(a * L),(pp |^ 2)},{(a * L)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * L),(pp |^ 2)] is set
(L |^ 3) + ((a * L) * (pp |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((L |^ 3),((a * L) * (pp |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(L |^ 3),((a * L) * (pp |^ 2))] is V26() set
{(L |^ 3),((a * L) * (pp |^ 2))} is non empty finite set
{(L |^ 3)} is non empty trivial finite 1 -element set
{{(L |^ 3),((a * L) * (pp |^ 2))},{(L |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(L |^ 3),((a * L) * (pp |^ 2))] is set
pp |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,3) is set
[pp,3] is V26() set
{pp,3} is non empty finite set
{{pp,3},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,3] is set
b * (pp |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,(pp |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,(pp |^ 3)] is V26() set
{b,(pp |^ 3)} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,(pp |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,(pp |^ 3)] is set
((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((L |^ 3) + ((a * L) * (pp |^ 2))),(b * (pp |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L |^ 3) + ((a * L) * (pp |^ 2))),(b * (pp |^ 3))] is V26() set
{((L |^ 3) + ((a * L) * (pp |^ 2))),(b * (pp |^ 3))} is non empty finite set
{((L |^ 3) + ((a * L) * (pp |^ 2)))} is non empty trivial finite 1 -element set
{{((L |^ 3) + ((a * L) * (pp |^ 2))),(b * (pp |^ 3))},{((L |^ 3) + ((a * L) * (pp |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L |^ 3) + ((a * L) * (pp |^ 2))),(b * (pp |^ 3))] is set
((F |^ 2) * pp) - (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((F |^ 2) * pp) + (- (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((F |^ 2) * pp),(- (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F |^ 2) * pp),(- (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3))))] is V26() set
{((F |^ 2) * pp),(- (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3))))} is non empty finite set
{((F |^ 2) * pp)} is non empty trivial finite 1 -element set
{{((F |^ 2) * pp),(- (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3))))},{((F |^ 2) * pp)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((F |^ 2) * pp),(- (((L |^ 3) + ((a * L) * (pp |^ 2))) + (b * (pp |^ 3))))] is set
F1 is Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
F1 `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 `1 is set
(F1 `1) `1 is set
F1 `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F1 `1) `2 is set
F1 `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[0,1,0] is V26() V27() Element of [:NAT,NAT,NAT:]
[0,1] is V26() set
{0,1} is non empty finite V49() V117() V118() V119() V120() V121() V122() set
{{0,1},{0}} is non empty finite V49() set
[[0,1],0] is V26() set
{[0,1],0} is non empty finite set
{[0,1]} is non empty trivial finite 1 -element set
{{[0,1],0},{[0,1]}} is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
(p,a,b) . [0,1,0] is set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[0,0,0]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
F is Element of ((INT.Ring p))
F `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F `1 is set
(F `1) `1 is set
F `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F `1) `2 is set
F `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),1,0] is V26() V27() Element of [: the carrier of (INT.Ring p),NAT,NAT:]
[: the carrier of (INT.Ring p),NAT,NAT:] is non empty set
[(0. (INT.Ring p)),1] is V26() set
{(0. (INT.Ring p)),1} is non empty finite set
{{(0. (INT.Ring p)),1},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),1],0] is V26() set
{[(0. (INT.Ring p)),1],0} is non empty finite set
{[(0. (INT.Ring p)),1]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),1],0},{[(0. (INT.Ring p)),1]}} is non empty finite V49() set
[(0. (INT.Ring p)),(1. (INT.Ring p)),0] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[(0. (INT.Ring p)),(1. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(1. (INT.Ring p))} is non empty finite set
{{(0. (INT.Ring p)),(1. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(1. (INT.Ring p))],0] is V26() set
{[(0. (INT.Ring p)),(1. (INT.Ring p))],0} is non empty finite set
{[(0. (INT.Ring p)),(1. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(1. (INT.Ring p))],0},{[(0. (INT.Ring p)),(1. (INT.Ring p))]}} is non empty finite V49() set
[(0. (INT.Ring p)),(1. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[[(0. (INT.Ring p)),(1. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(1. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{{[(0. (INT.Ring p)),(1. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(1. (INT.Ring p))]}} is non empty finite V49() set
(F `1_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . ((F `1_3),3) is set
[(F `1_3),3] is V26() set
{(F `1_3),3} is non empty finite set
{(F `1_3)} is non empty trivial finite 1 -element set
{{(F `1_3),3},{(F `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `1_3),3] is set
2 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(F `1_3) |^ (2 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `1_3),(2 + 1)) is set
[(F `1_3),(2 + 1)] is V26() set
{(F `1_3),(2 + 1)} is non empty finite set
{{(F `1_3),(2 + 1)},{(F `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `1_3),(2 + 1)] is set
(F `1_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `1_3),2) is set
[(F `1_3),2] is V26() set
{(F `1_3),2} is non empty finite set
{{(F `1_3),2},{(F `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `1_3),2] is set
((F `1_3) |^ 2) * (F `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (((F `1_3) |^ 2),(F `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F `1_3) |^ 2),(F `1_3)] is V26() set
{((F `1_3) |^ 2),(F `1_3)} is non empty finite set
{((F `1_3) |^ 2)} is non empty trivial finite 1 -element set
{{((F `1_3) |^ 2),(F `1_3)},{((F `1_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((F `1_3) |^ 2),(F `1_3)] is set
(F `3_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `3_3),3) is set
[(F `3_3),3] is V26() set
{(F `3_3),3} is non empty finite set
{(F `3_3)} is non empty trivial finite 1 -element set
{{(F `3_3),3},{(F `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `3_3),3] is set
(F `3_3) |^ (2 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `3_3),(2 + 1)) is set
[(F `3_3),(2 + 1)] is V26() set
{(F `3_3),(2 + 1)} is non empty finite set
{{(F `3_3),(2 + 1)},{(F `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `3_3),(2 + 1)] is set
(F `3_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `3_3),2) is set
[(F `3_3),2] is V26() set
{(F `3_3),2} is non empty finite set
{{(F `3_3),2},{(F `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `3_3),2] is set
((F `3_3) |^ 2) * (F `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((F `3_3) |^ 2),(F `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F `3_3) |^ 2),(F `3_3)] is V26() set
{((F `3_3) |^ 2),(F `3_3)} is non empty finite set
{((F `3_3) |^ 2)} is non empty trivial finite 1 -element set
{{((F `3_3) |^ 2),(F `3_3)},{((F `3_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((F `3_3) |^ 2),(F `3_3)] is set
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(F `3_3) |^ (1 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `3_3),(1 + 1)) is set
[(F `3_3),(1 + 1)] is V26() set
{(F `3_3),(1 + 1)} is non empty finite set
{{(F `3_3),(1 + 1)},{(F `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `3_3),(1 + 1)] is set
(F `3_3) |^ 1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `3_3),1) is set
[(F `3_3),1] is V26() set
{(F `3_3),1} is non empty finite set
{{(F `3_3),1},{(F `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `3_3),1] is set
((F `3_3) |^ 1) * (F `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((F `3_3) |^ 1),(F `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F `3_3) |^ 1),(F `3_3)] is V26() set
{((F `3_3) |^ 1),(F `3_3)} is non empty finite set
{((F `3_3) |^ 1)} is non empty trivial finite 1 -element set
{{((F `3_3) |^ 1),(F `3_3)},{((F `3_3) |^ 1)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((F `3_3) |^ 1),(F `3_3)] is set
(p,a,b) . F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F `2_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((F `2_3),2) is set
[(F `2_3),2] is V26() set
{(F `2_3),2} is non empty finite set
{(F `2_3)} is non empty trivial finite 1 -element set
{{(F `2_3),2},{(F `2_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(F `2_3),2] is set
((F `2_3) |^ 2) * (F `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((F `2_3) |^ 2),(F `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F `2_3) |^ 2),(F `3_3)] is V26() set
{((F `2_3) |^ 2),(F `3_3)} is non empty finite set
{((F `2_3) |^ 2)} is non empty trivial finite 1 -element set
{{((F `2_3) |^ 2),(F `3_3)},{((F `2_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((F `2_3) |^ 2),(F `3_3)] is set
a * (F `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(F `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(F `1_3)] is V26() set
{a,(F `1_3)} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,(F `1_3)},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(F `1_3)] is set
(a * (F `1_3)) * ((F `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (F `1_3)),((F `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (F `1_3)),((F `3_3) |^ 2)] is V26() set
{(a * (F `1_3)),((F `3_3) |^ 2)} is non empty finite set
{(a * (F `1_3))} is non empty trivial finite 1 -element set
{{(a * (F `1_3)),((F `3_3) |^ 2)},{(a * (F `1_3))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (F `1_3)),((F `3_3) |^ 2)] is set
((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . (((F `1_3) |^ 3),((a * (F `1_3)) * ((F `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F `1_3) |^ 3),((a * (F `1_3)) * ((F `3_3) |^ 2))] is V26() set
{((F `1_3) |^ 3),((a * (F `1_3)) * ((F `3_3) |^ 2))} is non empty finite set
{((F `1_3) |^ 3)} is non empty trivial finite 1 -element set
{{((F `1_3) |^ 3),((a * (F `1_3)) * ((F `3_3) |^ 2))},{((F `1_3) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((F `1_3) |^ 3),((a * (F `1_3)) * ((F `3_3) |^ 2))] is set
b * ((F `3_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((F `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((F `3_3) |^ 3)] is V26() set
{b,((F `3_3) |^ 3)} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,((F `3_3) |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((F `3_3) |^ 3)] is set
(((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))] is V26() set
{(((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))} is non empty finite set
{(((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))},{(((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))] is set
(((F `2_3) |^ 2) * (F `3_3)) - ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((F `2_3) |^ 2) * (F `3_3)) + (- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((F `2_3) |^ 2) * (F `3_3)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((F `2_3) |^ 2) * (F `3_3)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))] is V26() set
{(((F `2_3) |^ 2) * (F `3_3)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))} is non empty finite set
{(((F `2_3) |^ 2) * (F `3_3))} is non empty trivial finite 1 -element set
{{(((F `2_3) |^ 2) * (F `3_3)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))},{(((F `2_3) |^ 2) * (F `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((F `2_3) |^ 2) * (F `3_3)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))] is set
(0. (INT.Ring p)) - ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))] is V26() set
{(0. (INT.Ring p)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))} is non empty finite set
{{(0. (INT.Ring p)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(- ((((F `1_3) |^ 3) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))))] is set
(0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),((a * (F `1_3)) * ((F `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),((a * (F `1_3)) * ((F `3_3) |^ 2))] is V26() set
{(0. (INT.Ring p)),((a * (F `1_3)) * ((F `3_3) |^ 2))} is non empty finite set
{{(0. (INT.Ring p)),((a * (F `1_3)) * ((F `3_3) |^ 2))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),((a * (F `1_3)) * ((F `3_3) |^ 2))] is set
((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))] is V26() set
{((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))} is non empty finite set
{((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))},{((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2))),(b * ((F `3_3) |^ 3))] is set
- (((0. (INT.Ring p)) + ((a * (F `1_3)) * ((F `3_3) |^ 2))) + (b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((a * (F `1_3)) * ((F `3_3) |^ 2)) + (b * ((F `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((a * (F `1_3)) * ((F `3_3) |^ 2)),(b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((a * (F `1_3)) * ((F `3_3) |^ 2)),(b * ((F `3_3) |^ 3))] is V26() set
{((a * (F `1_3)) * ((F `3_3) |^ 2)),(b * ((F `3_3) |^ 3))} is non empty finite set
{((a * (F `1_3)) * ((F `3_3) |^ 2))} is non empty trivial finite 1 -element set
{{((a * (F `1_3)) * ((F `3_3) |^ 2)),(b * ((F `3_3) |^ 3))},{((a * (F `1_3)) * ((F `3_3) |^ 2))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((a * (F `1_3)) * ((F `3_3) |^ 2)),(b * ((F `3_3) |^ 3))] is set
- (((a * (F `1_3)) * ((F `3_3) |^ 2)) + (b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (b * ((F `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(b * ((F `3_3) |^ 3))] is V26() set
{(0. (INT.Ring p)),(b * ((F `3_3) |^ 3))} is non empty finite set
{{(0. (INT.Ring p)),(b * ((F `3_3) |^ 3))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(b * ((F `3_3) |^ 3))] is set
- ((0. (INT.Ring p)) + (b * ((F `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (b * ((F `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (0. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) - (0. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (- (0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(- (0. (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(- (0. (INT.Ring p)))] is V26() set
{(0. (INT.Ring p)),(- (0. (INT.Ring p)))} is non empty finite set
{{(0. (INT.Ring p)),(- (0. (INT.Ring p)))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(- (0. (INT.Ring p)))] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
bool ((INT.Ring p)) is non empty finite V49() set
L is set
F is Element of ((INT.Ring p))
(p,a,b) . F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L is Element of ((INT.Ring p))
(p,a,b) . L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,b,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[a,b] is V26() set
{a,b} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,b},{a}} is non empty finite V49() set
[[a,b],1] is V26() set
{[a,b],1} is non empty finite set
{[a,b]} is non empty trivial finite 1 -element set
{{[a,b],1},{[a,b]}} is non empty finite V49() set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[0,0,0]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) . [0,1,0] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (F,2) is set
[F,2] is V26() set
{F,2} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,2},{F}} is non empty finite V49() set
(power (INT.Ring p)) . [F,2] is set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (L,3) is set
[L,3] is V26() set
{L,3} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,3},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,3] is set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,L] is V26() set
{a,L} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,L},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,L] is set
(L |^ 3) + (a * L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((L |^ 3),(a * L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(L |^ 3),(a * L)] is V26() set
{(L |^ 3),(a * L)} is non empty finite set
{(L |^ 3)} is non empty trivial finite 1 -element set
{{(L |^ 3),(a * L)},{(L |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(L |^ 3),(a * L)] is set
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((L |^ 3) + (a * L)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((L |^ 3) + (a * L)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L |^ 3) + (a * L)),b] is V26() set
{((L |^ 3) + (a * L)),b} is non empty finite set
{((L |^ 3) + (a * L))} is non empty trivial finite 1 -element set
{{((L |^ 3) + (a * L)),b},{((L |^ 3) + (a * L))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L |^ 3) + (a * L)),b] is set
[L,F,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[L,F] is V26() set
{L,F} is non empty finite set
{{L,F},{L}} is non empty finite V49() set
[[L,F],1] is V26() set
{[L,F],1} is non empty finite set
{[L,F]} is non empty trivial finite 1 -element set
{{[L,F],1},{[L,F]}} is non empty finite V49() set
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F |^ 2) * (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((F |^ 2),(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F |^ 2),(1. (INT.Ring p))] is V26() set
{(F |^ 2),(1. (INT.Ring p))} is non empty finite set
{(F |^ 2)} is non empty trivial finite 1 -element set
{{(F |^ 2),(1. (INT.Ring p))},{(F |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(F |^ 2),(1. (INT.Ring p))] is set
(a * L) * (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * L),(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * L),(1. (INT.Ring p))] is V26() set
{(a * L),(1. (INT.Ring p))} is non empty finite set
{(a * L)} is non empty trivial finite 1 -element set
{{(a * L),(1. (INT.Ring p))},{(a * L)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * L),(1. (INT.Ring p))] is set
(1. (INT.Ring p)) * (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1. (INT.Ring p)),(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),(1. (INT.Ring p))] is V26() set
{(1. (INT.Ring p)),(1. (INT.Ring p))} is non empty finite set
{(1. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(1. (INT.Ring p)),(1. (INT.Ring p))},{(1. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(1. (INT.Ring p)),(1. (INT.Ring p))] is set
(a * L) * ((1. (INT.Ring p)) * (1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * L),((1. (INT.Ring p)) * (1. (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * L),((1. (INT.Ring p)) * (1. (INT.Ring p)))] is V26() set
{(a * L),((1. (INT.Ring p)) * (1. (INT.Ring p)))} is non empty finite set
{{(a * L),((1. (INT.Ring p)) * (1. (INT.Ring p)))},{(a * L)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * L),((1. (INT.Ring p)) * (1. (INT.Ring p)))] is set
(1. (INT.Ring p)) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((1. (INT.Ring p)),2) is set
[(1. (INT.Ring p)),2] is V26() set
{(1. (INT.Ring p)),2} is non empty finite set
{{(1. (INT.Ring p)),2},{(1. (INT.Ring p))}} is non empty finite V49() set
(power (INT.Ring p)) . [(1. (INT.Ring p)),2] is set
(a * L) * ((1. (INT.Ring p)) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * L),((1. (INT.Ring p)) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * L),((1. (INT.Ring p)) |^ 2)] is V26() set
{(a * L),((1. (INT.Ring p)) |^ 2)} is non empty finite set
{{(a * L),((1. (INT.Ring p)) |^ 2)},{(a * L)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * L),((1. (INT.Ring p)) |^ 2)] is set
b * (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,(1. (INT.Ring p))] is V26() set
{b,(1. (INT.Ring p))} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,(1. (INT.Ring p))},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,(1. (INT.Ring p))] is set
b * ((1. (INT.Ring p)) * (1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((1. (INT.Ring p)) * (1. (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((1. (INT.Ring p)) * (1. (INT.Ring p)))] is V26() set
{b,((1. (INT.Ring p)) * (1. (INT.Ring p)))} is non empty finite set
{{b,((1. (INT.Ring p)) * (1. (INT.Ring p)))},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((1. (INT.Ring p)) * (1. (INT.Ring p)))] is set
b * ((1. (INT.Ring p)) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((1. (INT.Ring p)) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((1. (INT.Ring p)) |^ 2)] is V26() set
{b,((1. (INT.Ring p)) |^ 2)} is non empty finite set
{{b,((1. (INT.Ring p)) |^ 2)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((1. (INT.Ring p)) |^ 2)] is set
((1. (INT.Ring p)) |^ 2) * (1. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((1. (INT.Ring p)) |^ 2),(1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((1. (INT.Ring p)) |^ 2),(1. (INT.Ring p))] is V26() set
{((1. (INT.Ring p)) |^ 2),(1. (INT.Ring p))} is non empty finite set
{((1. (INT.Ring p)) |^ 2)} is non empty trivial finite 1 -element set
{{((1. (INT.Ring p)) |^ 2),(1. (INT.Ring p))},{((1. (INT.Ring p)) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((1. (INT.Ring p)) |^ 2),(1. (INT.Ring p))] is set
b * (((1. (INT.Ring p)) |^ 2) * (1. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,(((1. (INT.Ring p)) |^ 2) * (1. (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,(((1. (INT.Ring p)) |^ 2) * (1. (INT.Ring p)))] is V26() set
{b,(((1. (INT.Ring p)) |^ 2) * (1. (INT.Ring p)))} is non empty finite set
{{b,(((1. (INT.Ring p)) |^ 2) * (1. (INT.Ring p)))},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,(((1. (INT.Ring p)) |^ 2) * (1. (INT.Ring p)))] is set
2 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(1. (INT.Ring p)) |^ (2 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((1. (INT.Ring p)),(2 + 1)) is set
[(1. (INT.Ring p)),(2 + 1)] is V26() set
{(1. (INT.Ring p)),(2 + 1)} is non empty finite set
{{(1. (INT.Ring p)),(2 + 1)},{(1. (INT.Ring p))}} is non empty finite V49() set
(power (INT.Ring p)) . [(1. (INT.Ring p)),(2 + 1)] is set
b * ((1. (INT.Ring p)) |^ (2 + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((1. (INT.Ring p)) |^ (2 + 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((1. (INT.Ring p)) |^ (2 + 1))] is V26() set
{b,((1. (INT.Ring p)) |^ (2 + 1))} is non empty finite set
{{b,((1. (INT.Ring p)) |^ (2 + 1))},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((1. (INT.Ring p)) |^ (2 + 1))] is set
(1. (INT.Ring p)) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((1. (INT.Ring p)),3) is set
[(1. (INT.Ring p)),3] is V26() set
{(1. (INT.Ring p)),3} is non empty finite set
{{(1. (INT.Ring p)),3},{(1. (INT.Ring p))}} is non empty finite V49() set
(power (INT.Ring p)) . [(1. (INT.Ring p)),3] is set
b * ((1. (INT.Ring p)) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((1. (INT.Ring p)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((1. (INT.Ring p)) |^ 3)] is V26() set
{b,((1. (INT.Ring p)) |^ 3)} is non empty finite set
{{b,((1. (INT.Ring p)) |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((1. (INT.Ring p)) |^ 3)] is set
(F |^ 2) - (((L |^ 3) + (a * L)) + b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (((L |^ 3) + (a * L)) + b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F |^ 2) + (- (((L |^ 3) + (a * L)) + b)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((F |^ 2),(- (((L |^ 3) + (a * L)) + b))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F |^ 2),(- (((L |^ 3) + (a * L)) + b))] is V26() set
{(F |^ 2),(- (((L |^ 3) + (a * L)) + b))} is non empty finite set
{{(F |^ 2),(- (((L |^ 3) + (a * L)) + b))},{(F |^ 2)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(F |^ 2),(- (((L |^ 3) + (a * L)) + b))] is set
pp is Element of ((INT.Ring p))
(p,a,b) . pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is Element of ((INT.Ring p))
(p,a,b) . FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
L is Element of ((INT.Ring p))
L `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1 is set
(L `1) `1 is set
L `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `1) `2 is set
L `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (F,(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,(L `1_3)] is V26() set
{F,(L `1_3)} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,(L `1_3)},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,(L `1_3)] is set
F * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,(L `2_3)] is V26() set
{F,(L `2_3)} is non empty finite set
{{F,(L `2_3)},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,(L `2_3)] is set
F * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,(L `3_3)] is V26() set
{F,(L `3_3)} is non empty finite set
{{F,(L `3_3)},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,(L `3_3)] is set
L is Element of ((INT.Ring p))
L `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1 is set
(L `1) `1 is set
L `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `1) `2 is set
L `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L is Element of ((INT.Ring p))
L `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1 is set
(L `1) `1 is set
F is Element of ((INT.Ring p))
F `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F `1 is set
(F `1) `1 is set
L `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `1) `2 is set
F `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F `1) `2 is set
L `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp * (F `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (pp,(F `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(F `1_3)] is V26() set
{pp,(F `1_3)} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,(F `1_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(F `1_3)] is set
pp * (F `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (pp,(F `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(F `2_3)] is V26() set
{pp,(F `2_3)} is non empty finite set
{{pp,(F `2_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(F `2_3)] is set
pp * (F `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (pp,(F `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(F `3_3)] is V26() set
{pp,(F `3_3)} is non empty finite set
{{pp,(F `3_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(F `3_3)] is set
pp " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(L `1_3)] is V26() set
{FF,(L `1_3)} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,(L `1_3)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(L `1_3)] is set
FF * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(L `2_3)] is V26() set
{FF,(L `2_3)} is non empty finite set
{{FF,(L `2_3)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(L `2_3)] is set
FF * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(L `3_3)] is V26() set
{FF,(L `3_3)} is non empty finite set
{{FF,(L `3_3)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(L `3_3)] is set
FF * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,pp] is V26() set
{FF,pp} is non empty finite set
{{FF,pp},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,pp] is set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(1. (INT.Ring p)) * (F `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1. (INT.Ring p)),(F `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),(F `1_3)] is V26() set
{(1. (INT.Ring p)),(F `1_3)} is non empty finite set
{(1. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(1. (INT.Ring p)),(F `1_3)},{(1. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(1. (INT.Ring p)),(F `1_3)] is set
FF * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,pp] is V26() set
{FF,pp} is non empty finite set
{{FF,pp},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,pp] is set
(FF * pp) * (F `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((FF * pp),(F `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(FF * pp),(F `1_3)] is V26() set
{(FF * pp),(F `1_3)} is non empty finite set
{(FF * pp)} is non empty trivial finite 1 -element set
{{(FF * pp),(F `1_3)},{(FF * pp)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(FF * pp),(F `1_3)] is set
(1. (INT.Ring p)) * (F `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1. (INT.Ring p)),(F `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),(F `2_3)] is V26() set
{(1. (INT.Ring p)),(F `2_3)} is non empty finite set
{{(1. (INT.Ring p)),(F `2_3)},{(1. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(1. (INT.Ring p)),(F `2_3)] is set
(FF * pp) * (F `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((FF * pp),(F `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(FF * pp),(F `2_3)] is V26() set
{(FF * pp),(F `2_3)} is non empty finite set
{{(FF * pp),(F `2_3)},{(FF * pp)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(FF * pp),(F `2_3)] is set
(1. (INT.Ring p)) * (F `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1. (INT.Ring p)),(F `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1. (INT.Ring p)),(F `3_3)] is V26() set
{(1. (INT.Ring p)),(F `3_3)} is non empty finite set
{{(1. (INT.Ring p)),(F `3_3)},{(1. (INT.Ring p))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(1. (INT.Ring p)),(F `3_3)] is set
(FF * pp) * (F `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((FF * pp),(F `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(FF * pp),(F `3_3)] is V26() set
{(FF * pp),(F `3_3)} is non empty finite set
{{(FF * pp),(F `3_3)},{(FF * pp)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(FF * pp),(F `3_3)] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is Element of ((INT.Ring p))
b is Element of ((INT.Ring p))
L is Element of ((INT.Ring p))
a `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a `1 is set
(a `1) `1 is set
b `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b `1 is set
(b `1) `1 is set
a `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(a `1) `2 is set
b `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(b `1) `2 is set
a `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F * (b `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (F,(b `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,(b `1_3)] is V26() set
{F,(b `1_3)} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,(b `1_3)},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,(b `1_3)] is set
F * (b `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,(b `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,(b `2_3)] is V26() set
{F,(b `2_3)} is non empty finite set
{{F,(b `2_3)},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,(b `2_3)] is set
F * (b `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,(b `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,(b `3_3)] is V26() set
{F,(b `3_3)} is non empty finite set
{{F,(b `3_3)},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,(b `3_3)] is set
L `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1 is set
(L `1) `1 is set
L `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `1) `2 is set
L `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (pp,(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(L `1_3)] is V26() set
{pp,(L `1_3)} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,(L `1_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(L `1_3)] is set
pp * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (pp,(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(L `2_3)] is V26() set
{pp,(L `2_3)} is non empty finite set
{{pp,(L `2_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(L `2_3)] is set
pp * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (pp,(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(L `3_3)] is V26() set
{pp,(L `3_3)} is non empty finite set
{{pp,(L `3_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(L `3_3)] is set
F * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (F,pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F,pp] is V26() set
{F,pp} is non empty finite set
{{F,pp},{F}} is non empty finite V49() set
the multF of (INT.Ring p) . [F,pp] is set
FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(L `1_3)] is V26() set
{FF,(L `1_3)} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,(L `1_3)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(L `1_3)] is set
FF * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(L `2_3)] is V26() set
{FF,(L `2_3)} is non empty finite set
{{FF,(L `2_3)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(L `2_3)] is set
FF * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (FF,(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,(L `3_3)] is V26() set
{FF,(L `3_3)} is non empty finite set
{{FF,(L `3_3)},{FF}} is non empty finite V49() set
the multF of (INT.Ring p) . [FF,(L `3_3)] is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
L is Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
F is Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
F `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F `1 is set
(F `1) `1 is set
L `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1 is set
(L `1) `1 is set
F `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F `1) `2 is set
L `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `1) `2 is set
F `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (pp,(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(L `1_3)] is V26() set
{pp,(L `1_3)} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,(L `1_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(L `1_3)] is set
pp * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (pp,(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(L `2_3)] is V26() set
{pp,(L `2_3)} is non empty finite set
{{pp,(L `2_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(L `2_3)] is set
pp * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (pp,(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,(L `3_3)] is V26() set
{pp,(L `3_3)} is non empty finite set
{{pp,(L `3_3)},{pp}} is non empty finite V49() set
the multF of (INT.Ring p) . [pp,(L `3_3)] is set
F1 is Element of ((INT.Ring p))
(p,a,b) . F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) . L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `2_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . ((L `2_3),2) is set
[(L `2_3),2] is V26() set
{(L `2_3),2} is non empty finite set
{(L `2_3)} is non empty trivial finite 1 -element set
{{(L `2_3),2},{(L `2_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `2_3),2] is set
((L `2_3) |^ 2) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `2_3) |^ 2),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `2_3) |^ 2),(L `3_3)] is V26() set
{((L `2_3) |^ 2),(L `3_3)} is non empty finite set
{((L `2_3) |^ 2)} is non empty trivial finite 1 -element set
{{((L `2_3) |^ 2),(L `3_3)},{((L `2_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `2_3) |^ 2),(L `3_3)] is set
(L `1_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `1_3),3) is set
[(L `1_3),3] is V26() set
{(L `1_3),3} is non empty finite set
{(L `1_3)} is non empty trivial finite 1 -element set
{{(L `1_3),3},{(L `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `1_3),3] is set
a * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(L `1_3)] is V26() set
{a,(L `1_3)} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,(L `1_3)},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(L `1_3)] is set
(L `3_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `3_3),2) is set
[(L `3_3),2] is V26() set
{(L `3_3),2} is non empty finite set
{(L `3_3)} is non empty trivial finite 1 -element set
{{(L `3_3),2},{(L `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `3_3),2] is set
(a * (L `1_3)) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (L `1_3)),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (L `1_3)),((L `3_3) |^ 2)] is V26() set
{(a * (L `1_3)),((L `3_3) |^ 2)} is non empty finite set
{(a * (L `1_3))} is non empty trivial finite 1 -element set
{{(a * (L `1_3)),((L `3_3) |^ 2)},{(a * (L `1_3))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (L `1_3)),((L `3_3) |^ 2)] is set
((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . (((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))] is V26() set
{((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))} is non empty finite set
{((L `1_3) |^ 3)} is non empty trivial finite 1 -element set
{{((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))},{((L `1_3) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))] is set
(L `3_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `3_3),3) is set
[(L `3_3),3] is V26() set
{(L `3_3),3} is non empty finite set
{{(L `3_3),3},{(L `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `3_3),3] is set
b * ((L `3_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((L `3_3) |^ 3)] is V26() set
{b,((L `3_3) |^ 3)} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,((L `3_3) |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((L `3_3) |^ 3)] is set
(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))] is V26() set
{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))} is non empty finite set
{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))},{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))] is set
(((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((L `2_3) |^ 2) * (L `3_3)) + (- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is V26() set
{(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))} is non empty finite set
{(((L `2_3) |^ 2) * (L `3_3))} is non empty trivial finite 1 -element set
{{(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))},{(((L `2_3) |^ 2) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is set
(p,a,b) . F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(pp * (L `2_3)) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((pp * (L `2_3)),2) is set
[(pp * (L `2_3)),2] is V26() set
{(pp * (L `2_3)),2} is non empty finite set
{(pp * (L `2_3))} is non empty trivial finite 1 -element set
{{(pp * (L `2_3)),2},{(pp * (L `2_3))}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp * (L `2_3)),2] is set
((pp * (L `2_3)) |^ 2) * (pp * (L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp * (L `2_3)) |^ 2),(pp * (L `3_3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp * (L `2_3)) |^ 2),(pp * (L `3_3))] is V26() set
{((pp * (L `2_3)) |^ 2),(pp * (L `3_3))} is non empty finite set
{((pp * (L `2_3)) |^ 2)} is non empty trivial finite 1 -element set
{{((pp * (L `2_3)) |^ 2),(pp * (L `3_3))},{((pp * (L `2_3)) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp * (L `2_3)) |^ 2),(pp * (L `3_3))] is set
(pp * (L `1_3)) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((pp * (L `1_3)),3) is set
[(pp * (L `1_3)),3] is V26() set
{(pp * (L `1_3)),3} is non empty finite set
{(pp * (L `1_3))} is non empty trivial finite 1 -element set
{{(pp * (L `1_3)),3},{(pp * (L `1_3))}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp * (L `1_3)),3] is set
a * (pp * (L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(pp * (L `1_3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(pp * (L `1_3))] is V26() set
{a,(pp * (L `1_3))} is non empty finite set
{{a,(pp * (L `1_3))},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(pp * (L `1_3))] is set
(pp * (L `3_3)) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((pp * (L `3_3)),2) is set
[(pp * (L `3_3)),2] is V26() set
{(pp * (L `3_3)),2} is non empty finite set
{(pp * (L `3_3))} is non empty trivial finite 1 -element set
{{(pp * (L `3_3)),2},{(pp * (L `3_3))}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp * (L `3_3)),2] is set
(a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (pp * (L `1_3))),((pp * (L `3_3)) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (pp * (L `1_3))),((pp * (L `3_3)) |^ 2)] is V26() set
{(a * (pp * (L `1_3))),((pp * (L `3_3)) |^ 2)} is non empty finite set
{(a * (pp * (L `1_3)))} is non empty trivial finite 1 -element set
{{(a * (pp * (L `1_3))),((pp * (L `3_3)) |^ 2)},{(a * (pp * (L `1_3)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (pp * (L `1_3))),((pp * (L `3_3)) |^ 2)] is set
((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp * (L `1_3)) |^ 3),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp * (L `1_3)) |^ 3),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))] is V26() set
{((pp * (L `1_3)) |^ 3),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))} is non empty finite set
{((pp * (L `1_3)) |^ 3)} is non empty trivial finite 1 -element set
{{((pp * (L `1_3)) |^ 3),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))},{((pp * (L `1_3)) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp * (L `1_3)) |^ 3),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))] is set
(pp * (L `3_3)) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((pp * (L `3_3)),3) is set
[(pp * (L `3_3)),3] is V26() set
{(pp * (L `3_3)),3} is non empty finite set
{{(pp * (L `3_3)),3},{(pp * (L `3_3))}} is non empty finite V49() set
(power (INT.Ring p)) . [(pp * (L `3_3)),3] is set
b * ((pp * (L `3_3)) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((pp * (L `3_3)) |^ 3)] is V26() set
{b,((pp * (L `3_3)) |^ 3)} is non empty finite set
{{b,((pp * (L `3_3)) |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((pp * (L `3_3)) |^ 3)] is set
(((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3))) - ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3))) + (- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp * (L `2_3)) |^ 2) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3)))} is non empty trivial finite 1 -element set
{{(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp * (L `2_3)) |^ 2) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
pp |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,2) is set
[pp,2] is V26() set
{pp,2} is non empty finite set
{{pp,2},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,2] is set
(pp |^ 2) * ((L `2_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 2),((L `2_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 2),((L `2_3) |^ 2)] is V26() set
{(pp |^ 2),((L `2_3) |^ 2)} is non empty finite set
{(pp |^ 2)} is non empty trivial finite 1 -element set
{{(pp |^ 2),((L `2_3) |^ 2)},{(pp |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 2),((L `2_3) |^ 2)] is set
((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ 2) * ((L `2_3) |^ 2)),(pp * (L `3_3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 2) * ((L `2_3) |^ 2)),(pp * (L `3_3))] is V26() set
{((pp |^ 2) * ((L `2_3) |^ 2)),(pp * (L `3_3))} is non empty finite set
{((pp |^ 2) * ((L `2_3) |^ 2))} is non empty trivial finite 1 -element set
{{((pp |^ 2) * ((L `2_3) |^ 2)),(pp * (L `3_3))},{((pp |^ 2) * ((L `2_3) |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ 2) * ((L `2_3) |^ 2)),(pp * (L `3_3))] is set
(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3))) - ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3))) + (- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3)))} is non empty trivial finite 1 -element set
{{(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 2) * ((L `2_3) |^ 2)) * (pp * (L `3_3))),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
((pp |^ 2) * ((L `2_3) |^ 2)) * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ 2) * ((L `2_3) |^ 2)),pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 2) * ((L `2_3) |^ 2)),pp] is V26() set
{((pp |^ 2) * ((L `2_3) |^ 2)),pp} is non empty finite set
{{((pp |^ 2) * ((L `2_3) |^ 2)),pp},{((pp |^ 2) * ((L `2_3) |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ 2) * ((L `2_3) |^ 2)),pp] is set
(((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((((pp |^ 2) * ((L `2_3) |^ 2)) * pp),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 2) * ((L `2_3) |^ 2)) * pp),(L `3_3)] is V26() set
{(((pp |^ 2) * ((L `2_3) |^ 2)) * pp),(L `3_3)} is non empty finite set
{(((pp |^ 2) * ((L `2_3) |^ 2)) * pp)} is non empty trivial finite 1 -element set
{{(((pp |^ 2) * ((L `2_3) |^ 2)) * pp),(L `3_3)},{(((pp |^ 2) * ((L `2_3) |^ 2)) * pp)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(((pp |^ 2) * ((L `2_3) |^ 2)) * pp),(L `3_3)] is set
((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3)) - ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3)) + (- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3))} is non empty trivial finite 1 -element set
{{((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((((pp |^ 2) * ((L `2_3) |^ 2)) * pp) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
(pp |^ 2) * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 2),pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 2),pp] is V26() set
{(pp |^ 2),pp} is non empty finite set
{{(pp |^ 2),pp},{(pp |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 2),pp] is set
((pp |^ 2) * pp) * ((L `2_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ 2) * pp),((L `2_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 2) * pp),((L `2_3) |^ 2)] is V26() set
{((pp |^ 2) * pp),((L `2_3) |^ 2)} is non empty finite set
{((pp |^ 2) * pp)} is non empty trivial finite 1 -element set
{{((pp |^ 2) * pp),((L `2_3) |^ 2)},{((pp |^ 2) * pp)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ 2) * pp),((L `2_3) |^ 2)] is set
(((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((((pp |^ 2) * pp) * ((L `2_3) |^ 2)),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 2) * pp) * ((L `2_3) |^ 2)),(L `3_3)] is V26() set
{(((pp |^ 2) * pp) * ((L `2_3) |^ 2)),(L `3_3)} is non empty finite set
{(((pp |^ 2) * pp) * ((L `2_3) |^ 2))} is non empty trivial finite 1 -element set
{{(((pp |^ 2) * pp) * ((L `2_3) |^ 2)),(L `3_3)},{(((pp |^ 2) * pp) * ((L `2_3) |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(((pp |^ 2) * pp) * ((L `2_3) |^ 2)),(L `3_3)] is set
((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3))} is non empty trivial finite 1 -element set
{{((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((((pp |^ 2) * pp) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
2 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
pp |^ (2 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,(2 + 1)) is set
[pp,(2 + 1)] is V26() set
{pp,(2 + 1)} is non empty finite set
{{pp,(2 + 1)},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,(2 + 1)] is set
(pp |^ (2 + 1)) * ((L `2_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ (2 + 1)),((L `2_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ (2 + 1)),((L `2_3) |^ 2)] is V26() set
{(pp |^ (2 + 1)),((L `2_3) |^ 2)} is non empty finite set
{(pp |^ (2 + 1))} is non empty trivial finite 1 -element set
{{(pp |^ (2 + 1)),((L `2_3) |^ 2)},{(pp |^ (2 + 1))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ (2 + 1)),((L `2_3) |^ 2)] is set
((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ (2 + 1)) * ((L `2_3) |^ 2)),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ (2 + 1)) * ((L `2_3) |^ 2)),(L `3_3)] is V26() set
{((pp |^ (2 + 1)) * ((L `2_3) |^ 2)),(L `3_3)} is non empty finite set
{((pp |^ (2 + 1)) * ((L `2_3) |^ 2))} is non empty trivial finite 1 -element set
{{((pp |^ (2 + 1)) * ((L `2_3) |^ 2)),(L `3_3)},{((pp |^ (2 + 1)) * ((L `2_3) |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ (2 + 1)) * ((L `2_3) |^ 2)),(L `3_3)] is set
(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3))} is non empty trivial finite 1 -element set
{{(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ (2 + 1)) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp * (L `1_3)) |^ 3) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
pp |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (pp,3) is set
[pp,3] is V26() set
{pp,3} is non empty finite set
{{pp,3},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,3] is set
(pp |^ 3) * ((L `2_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),((L `2_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),((L `2_3) |^ 2)] is V26() set
{(pp |^ 3),((L `2_3) |^ 2)} is non empty finite set
{(pp |^ 3)} is non empty trivial finite 1 -element set
{{(pp |^ 3),((L `2_3) |^ 2)},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),((L `2_3) |^ 2)] is set
((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ 3) * ((L `2_3) |^ 2)),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `2_3) |^ 2)),(L `3_3)] is V26() set
{((pp |^ 3) * ((L `2_3) |^ 2)),(L `3_3)} is non empty finite set
{((pp |^ 3) * ((L `2_3) |^ 2))} is non empty trivial finite 1 -element set
{{((pp |^ 3) * ((L `2_3) |^ 2)),(L `3_3)},{((pp |^ 3) * ((L `2_3) |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ 3) * ((L `2_3) |^ 2)),(L `3_3)] is set
(pp |^ 3) * ((L `1_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),((L `1_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),((L `1_3) |^ 3)] is V26() set
{(pp |^ 3),((L `1_3) |^ 3)} is non empty finite set
{{(pp |^ 3),((L `1_3) |^ 3)},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),((L `1_3) |^ 3)] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))} is non empty finite set
{((pp |^ 3) * ((L `1_3) |^ 3))} is non empty trivial finite 1 -element set
{{((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp * (L `3_3)) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
(pp |^ 2) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 2),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 2),((L `3_3) |^ 2)] is V26() set
{(pp |^ 2),((L `3_3) |^ 2)} is non empty finite set
{{(pp |^ 2),((L `3_3) |^ 2)},{(pp |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 2),((L `3_3) |^ 2)] is set
(a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (pp * (L `1_3))),((pp |^ 2) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (pp * (L `1_3))),((pp |^ 2) * ((L `3_3) |^ 2))] is V26() set
{(a * (pp * (L `1_3))),((pp |^ 2) * ((L `3_3) |^ 2))} is non empty finite set
{{(a * (pp * (L `1_3))),((pp |^ 2) * ((L `3_3) |^ 2))},{(a * (pp * (L `1_3)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (pp * (L `1_3))),((pp |^ 2) * ((L `3_3) |^ 2))] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))} is non empty finite set
{{((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2))))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2))))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (pp * (L `1_3))) * ((pp |^ 2) * ((L `3_3) |^ 2)))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
(a * (pp * (L `1_3))) * (pp |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (pp * (L `1_3))),(pp |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (pp * (L `1_3))),(pp |^ 2)] is V26() set
{(a * (pp * (L `1_3))),(pp |^ 2)} is non empty finite set
{{(a * (pp * (L `1_3))),(pp |^ 2)},{(a * (pp * (L `1_3)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (pp * (L `1_3))),(pp |^ 2)] is set
((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((a * (pp * (L `1_3))) * (pp |^ 2)),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((a * (pp * (L `1_3))) * (pp |^ 2)),((L `3_3) |^ 2)] is V26() set
{((a * (pp * (L `1_3))) * (pp |^ 2)),((L `3_3) |^ 2)} is non empty finite set
{((a * (pp * (L `1_3))) * (pp |^ 2))} is non empty trivial finite 1 -element set
{{((a * (pp * (L `1_3))) * (pp |^ 2)),((L `3_3) |^ 2)},{((a * (pp * (L `1_3))) * (pp |^ 2))}} is non empty finite V49() set
the multF of (INT.Ring p) . [((a * (pp * (L `1_3))) * (pp |^ 2)),((L `3_3) |^ 2)] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),(((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),(((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),(((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))} is non empty finite set
{{((pp |^ 3) * ((L `1_3) |^ 3)),(((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),(((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((a * (pp * (L `1_3))) * (pp |^ 2)) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
(pp * (L `1_3)) * (pp |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp * (L `1_3)),(pp |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp * (L `1_3)),(pp |^ 2)] is V26() set
{(pp * (L `1_3)),(pp |^ 2)} is non empty finite set
{{(pp * (L `1_3)),(pp |^ 2)},{(pp * (L `1_3))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp * (L `1_3)),(pp |^ 2)] is set
a * ((pp * (L `1_3)) * (pp |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,((pp * (L `1_3)) * (pp |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,((pp * (L `1_3)) * (pp |^ 2))] is V26() set
{a,((pp * (L `1_3)) * (pp |^ 2))} is non empty finite set
{{a,((pp * (L `1_3)) * (pp |^ 2))},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,((pp * (L `1_3)) * (pp |^ 2))] is set
(a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * ((pp * (L `1_3)) * (pp |^ 2))),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * ((pp * (L `1_3)) * (pp |^ 2))),((L `3_3) |^ 2)] is V26() set
{(a * ((pp * (L `1_3)) * (pp |^ 2))),((L `3_3) |^ 2)} is non empty finite set
{(a * ((pp * (L `1_3)) * (pp |^ 2)))} is non empty trivial finite 1 -element set
{{(a * ((pp * (L `1_3)) * (pp |^ 2))),((L `3_3) |^ 2)},{(a * ((pp * (L `1_3)) * (pp |^ 2)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * ((pp * (L `1_3)) * (pp |^ 2))),((L `3_3) |^ 2)] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))} is non empty finite set
{{((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp * (L `1_3)) * (pp |^ 2))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
((pp |^ 2) * pp) * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ 2) * pp),(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 2) * pp),(L `1_3)] is V26() set
{((pp |^ 2) * pp),(L `1_3)} is non empty finite set
{{((pp |^ 2) * pp),(L `1_3)},{((pp |^ 2) * pp)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ 2) * pp),(L `1_3)] is set
a * (((pp |^ 2) * pp) * (L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(((pp |^ 2) * pp) * (L `1_3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(((pp |^ 2) * pp) * (L `1_3))] is V26() set
{a,(((pp |^ 2) * pp) * (L `1_3))} is non empty finite set
{{a,(((pp |^ 2) * pp) * (L `1_3))},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(((pp |^ 2) * pp) * (L `1_3))] is set
(a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (((pp |^ 2) * pp) * (L `1_3))),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (((pp |^ 2) * pp) * (L `1_3))),((L `3_3) |^ 2)] is V26() set
{(a * (((pp |^ 2) * pp) * (L `1_3))),((L `3_3) |^ 2)} is non empty finite set
{(a * (((pp |^ 2) * pp) * (L `1_3)))} is non empty trivial finite 1 -element set
{{(a * (((pp |^ 2) * pp) * (L `1_3))),((L `3_3) |^ 2)},{(a * (((pp |^ 2) * pp) * (L `1_3)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (((pp |^ 2) * pp) * (L `1_3))),((L `3_3) |^ 2)] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))} is non empty finite set
{{((pp |^ 3) * ((L `1_3) |^ 3)),((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * (((pp |^ 2) * pp) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
(pp |^ (2 + 1)) * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ (2 + 1)),(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ (2 + 1)),(L `1_3)] is V26() set
{(pp |^ (2 + 1)),(L `1_3)} is non empty finite set
{{(pp |^ (2 + 1)),(L `1_3)},{(pp |^ (2 + 1))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ (2 + 1)),(L `1_3)] is set
a * ((pp |^ (2 + 1)) * (L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,((pp |^ (2 + 1)) * (L `1_3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,((pp |^ (2 + 1)) * (L `1_3))] is V26() set
{a,((pp |^ (2 + 1)) * (L `1_3))} is non empty finite set
{{a,((pp |^ (2 + 1)) * (L `1_3))},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,((pp |^ (2 + 1)) * (L `1_3))] is set
(a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * ((pp |^ (2 + 1)) * (L `1_3))),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * ((pp |^ (2 + 1)) * (L `1_3))),((L `3_3) |^ 2)] is V26() set
{(a * ((pp |^ (2 + 1)) * (L `1_3))),((L `3_3) |^ 2)} is non empty finite set
{(a * ((pp |^ (2 + 1)) * (L `1_3)))} is non empty trivial finite 1 -element set
{{(a * ((pp |^ (2 + 1)) * (L `1_3))),((L `3_3) |^ 2)},{(a * ((pp |^ (2 + 1)) * (L `1_3)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * ((pp |^ (2 + 1)) * (L `1_3))),((L `3_3) |^ 2)] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))} is non empty finite set
{{((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((a * ((pp |^ (2 + 1)) * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
(pp |^ 3) * (a * (L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),(a * (L `1_3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),(a * (L `1_3))] is V26() set
{(pp |^ 3),(a * (L `1_3))} is non empty finite set
{{(pp |^ 3),(a * (L `1_3))},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),(a * (L `1_3))] is set
((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ 3) * (a * (L `1_3))),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * (a * (L `1_3))),((L `3_3) |^ 2)] is V26() set
{((pp |^ 3) * (a * (L `1_3))),((L `3_3) |^ 2)} is non empty finite set
{((pp |^ 3) * (a * (L `1_3)))} is non empty trivial finite 1 -element set
{{((pp |^ 3) * (a * (L `1_3))),((L `3_3) |^ 2)},{((pp |^ 3) * (a * (L `1_3)))}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ 3) * (a * (L `1_3))),((L `3_3) |^ 2)] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),(((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),(((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),(((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))} is non empty finite set
{{((pp |^ 3) * ((L `1_3) |^ 3)),(((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),(((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp * (L `3_3)) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp * (L `3_3)) |^ 3))))] is set
(pp |^ 3) * ((L `3_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),((L `3_3) |^ 3)] is V26() set
{(pp |^ 3),((L `3_3) |^ 3)} is non empty finite set
{{(pp |^ 3),((L `3_3) |^ 3)},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),((L `3_3) |^ 3)] is set
b * ((pp |^ 3) * ((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((pp |^ 3) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((pp |^ 3) * ((L `3_3) |^ 3))] is V26() set
{b,((pp |^ 3) * ((L `3_3) |^ 3))} is non empty finite set
{{b,((pp |^ 3) * ((L `3_3) |^ 3))},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((pp |^ 3) * ((L `3_3) |^ 3))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp |^ 3) * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp |^ 3) * ((L `3_3) |^ 3)))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp |^ 3) * ((L `3_3) |^ 3)))} is non empty finite set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp |^ 3) * ((L `3_3) |^ 3)))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(b * ((pp |^ 3) * ((L `3_3) |^ 3)))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3)))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3)))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3)))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3)))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (b * ((pp |^ 3) * ((L `3_3) |^ 3)))))] is set
(pp |^ 3) * b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),b] is V26() set
{(pp |^ 3),b} is non empty finite set
{{(pp |^ 3),b},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),b] is set
((pp |^ 3) * b) * ((L `3_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((pp |^ 3) * b),((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * b),((L `3_3) |^ 3)] is V26() set
{((pp |^ 3) * b),((L `3_3) |^ 3)} is non empty finite set
{((pp |^ 3) * b)} is non empty trivial finite 1 -element set
{{((pp |^ 3) * b),((L `3_3) |^ 3)},{((pp |^ 3) * b)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((pp |^ 3) * b),((L `3_3) |^ 3)] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))} is non empty finite set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))] is set
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))] is V26() set
{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))} is non empty finite set
{{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))},{(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `2_3) |^ 2)) * (L `3_3)),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))] is set
(pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),(((L `2_3) |^ 2) * (L `3_3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),(((L `2_3) |^ 2) * (L `3_3))] is V26() set
{(pp |^ 3),(((L `2_3) |^ 2) * (L `3_3))} is non empty finite set
{{(pp |^ 3),(((L `2_3) |^ 2) * (L `3_3))},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),(((L `2_3) |^ 2) * (L `3_3))] is set
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))] is V26() set
{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))} is non empty finite set
{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3)))} is non empty trivial finite 1 -element set
{{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))},{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + (((pp |^ 3) * (a * (L `1_3))) * ((L `3_3) |^ 2))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))] is set
(pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))] is V26() set
{(pp |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))} is non empty finite set
{{(pp |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))] is set
((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * ((L `1_3) |^ 3)),((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * ((L `1_3) |^ 3)),((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))] is V26() set
{((pp |^ 3) * ((L `1_3) |^ 3)),((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))} is non empty finite set
{{((pp |^ 3) * ((L `1_3) |^ 3)),((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))},{((pp |^ 3) * ((L `1_3) |^ 3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * ((L `1_3) |^ 3)),((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))} is non empty finite set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2))))} is non empty trivial finite 1 -element set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2))))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),(((pp |^ 3) * b) * ((L `3_3) |^ 3))] is set
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))] is V26() set
{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))} is non empty finite set
{{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))},{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + (((pp |^ 3) * b) * ((L `3_3) |^ 3))))] is set
(pp |^ 3) * (b * ((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),(b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),(b * ((L `3_3) |^ 3))] is V26() set
{(pp |^ 3),(b * ((L `3_3) |^ 3))} is non empty finite set
{{(pp |^ 3),(b * ((L `3_3) |^ 3))},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),(b * ((L `3_3) |^ 3))] is set
(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))] is V26() set
{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))} is non empty finite set
{{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))},{(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2))))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))] is set
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) - ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) + (- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))] is V26() set
{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))} is non empty finite set
{{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))},{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((((pp |^ 3) * ((L `1_3) |^ 3)) + ((pp |^ 3) * ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))] is set
(pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))] is V26() set
{(pp |^ 3),(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))} is non empty finite set
{{(pp |^ 3),(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))] is set
((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))] is V26() set
{((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))} is non empty finite set
{((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))))} is non empty trivial finite 1 -element set
{{((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))},{((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))),((pp |^ 3) * (b * ((L `3_3) |^ 3)))] is set
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) - (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) + (- (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))] is V26() set
{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))} is non empty finite set
{{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))},{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- (((pp |^ 3) * (((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))) + ((pp |^ 3) * (b * ((L `3_3) |^ 3)))))] is set
(pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))] is V26() set
{(pp |^ 3),((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))} is non empty finite set
{{(pp |^ 3),((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))] is set
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) - ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))) + (- ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))))] is V26() set
{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))))} is non empty finite set
{{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))))},{((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) * (((L `2_3) |^ 2) * (L `3_3))),(- ((pp |^ 3) * ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))))] is set
(pp |^ 3) * ((((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((pp |^ 3),((((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),((((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is V26() set
{(pp |^ 3),((((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))} is non empty finite set
{{(pp |^ 3),((((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))},{(pp |^ 3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(pp |^ 3),((((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[0,0,0]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(F `1_3),(F `2_3),(F `3_3)] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(F `1_3),(F `2_3)] is V26() set
{(F `1_3),(F `2_3)} is non empty finite set
{(F `1_3)} is non empty trivial finite 1 -element set
{{(F `1_3),(F `2_3)},{(F `1_3)}} is non empty finite V49() set
[[(F `1_3),(F `2_3)],(F `3_3)] is V26() set
{[(F `1_3),(F `2_3)],(F `3_3)} is non empty finite set
{[(F `1_3),(F `2_3)]} is non empty trivial finite 1 -element set
{{[(F `1_3),(F `2_3)],(F `3_3)},{[(F `1_3),(F `2_3)]}} is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
b is set
L is Element of ((INT.Ring p))
F is Element of ((INT.Ring p))
[L,F] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
[:((INT.Ring p)),((INT.Ring p)):] is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -valued finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):],[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]:]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):],[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]:] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):],[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]:] is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued finite Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
a is Element of ((INT.Ring p))
b is Element of ((INT.Ring p))
[a,b] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{a,b} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,b},{a}} is non empty finite V49() set
L is Element of ((INT.Ring p))
F is Element of ((INT.Ring p))
[L,F] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued finite Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
b is set
L is Element of ((INT.Ring p))
[b,b] is V26() set
{b,b} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,b},{b}} is non empty finite V49() set
L is set
[b,L] is V26() set
{b,L} is non empty finite set
{{b,L},{b}} is non empty finite V49() set
F is Element of ((INT.Ring p))
pp is Element of ((INT.Ring p))
[F,pp] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{F,pp} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,pp},{F}} is non empty finite V49() set
dom (p) is finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
field (p) is finite set
b is set
L is set
[b,L] is V26() set
{b,L} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,L},{b}} is non empty finite V49() set
[L,b] is V26() set
{L,b} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,b},{L}} is non empty finite V49() set
F is Element of ((INT.Ring p))
pp is Element of ((INT.Ring p))
[F,pp] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{F,pp} is non empty finite set
{F} is non empty trivial finite 1 -element set
{{F,pp},{F}} is non empty finite V49() set
b is set
L is set
F is set
[b,L] is V26() set
{b,L} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,L},{b}} is non empty finite V49() set
[L,F] is V26() set
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
[b,F] is V26() set
{b,F} is non empty finite set
{{b,F},{b}} is non empty finite V49() set
pp is Element of ((INT.Ring p))
FF is Element of ((INT.Ring p))
[pp,FF] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{pp,FF} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,FF},{pp}} is non empty finite V49() set
F1 is Element of ((INT.Ring p))
F2 is Element of ((INT.Ring p))
[F1,F2] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{F1,F2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,F2},{F1}} is non empty finite V49() set
[pp,F2] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{pp,F2} is non empty finite set
{{pp,F2},{pp}} is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
[:(p,a,b),(p,a,b):] is non empty finite set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) /\ (nabla (p,a,b)) is Relation-like (p,a,b) -defined ((INT.Ring p)) -defined (p,a,b) -valued ((INT.Ring p)) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
pp is Relation-like (p,a,b) -defined (p,a,b) -valued finite Element of bool [:(p,a,b),(p,a,b):]
FF is set
F1 is Element of ((INT.Ring p))
[FF,FF] is V26() set
{FF,FF} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,FF},{FF}} is non empty finite V49() set
[:(p,a,b),(p,a,b):] is non empty Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued finite Element of bool [:((INT.Ring p)),((INT.Ring p)):]
F1 is set
[FF,F1] is V26() set
{FF,F1} is non empty finite set
{{FF,F1},{FF}} is non empty finite V49() set
dom pp is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like ((INT.Ring p)) -defined (p,a,b) -defined ((INT.Ring p)) -valued (p,a,b) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
L is Element of ((INT.Ring p))
F is Element of ((INT.Ring p))
[L,F] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
[:(p,a,b),(p,a,b):] is non empty Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued finite Element of bool [:((INT.Ring p)),((INT.Ring p)):]
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
L is Element of ((INT.Ring p))
L `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `3_3) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((L `3_3) ") * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (((L `3_3) "),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `3_3) "),(L `3_3)] is V26() set
{((L `3_3) "),(L `3_3)} is non empty finite set
{((L `3_3) ")} is non empty trivial finite 1 -element set
{{((L `3_3) "),(L `3_3)},{((L `3_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `3_3) "),(L `3_3)] is set
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1 is set
(L `1) `1 is set
((L `3_3) ") * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (((L `3_3) "),(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `3_3) "),(L `1_3)] is V26() set
{((L `3_3) "),(L `1_3)} is non empty finite set
{((L `3_3) ")} is non empty trivial finite 1 -element set
{{((L `3_3) "),(L `1_3)},{((L `3_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `3_3) "),(L `1_3)] is set
L `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `1) `2 is set
((L `3_3) ") * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `3_3) "),(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `3_3) "),(L `2_3)] is V26() set
{((L `3_3) "),(L `2_3)} is non empty finite set
{{((L `3_3) "),(L `2_3)},{((L `3_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `3_3) "),(L `2_3)] is set
((L `3_3) ") * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `3_3) "),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `3_3) "),(L `3_3)] is V26() set
{((L `3_3) "),(L `3_3)} is non empty finite set
{{((L `3_3) "),(L `3_3)},{((L `3_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `3_3) "),(L `3_3)] is set
[(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3)),(((L `3_3) ") * (L `3_3))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))] is V26() set
{(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))} is non empty finite set
{(((L `3_3) ") * (L `1_3))} is non empty trivial finite 1 -element set
{{(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))},{(((L `3_3) ") * (L `1_3))}} is non empty finite V49() set
[[(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))],(((L `3_3) ") * (L `3_3))] is V26() set
{[(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))],(((L `3_3) ") * (L `3_3))} is non empty finite set
{[(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))]} is non empty trivial finite 1 -element set
{{[(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))],(((L `3_3) ") * (L `3_3))},{[(((L `3_3) ") * (L `1_3)),(((L `3_3) ") * (L `2_3))]}} is non empty finite V49() set
pp is Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
pp `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp `1 is set
(pp `1) `1 is set
pp `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(pp `1) `2 is set
pp `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is Element of ((INT.Ring p))
(p,a,b) . FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 is Element of ((INT.Ring p))
F1 `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
L is Element of ((INT.Ring p))
L `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L `1 is set
(L `1) `2 is set
(L `2_3) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `3_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . ((L `3_3),3) is set
[(L `3_3),3] is V26() set
{(L `3_3),3} is non empty finite set
{(L `3_3)} is non empty trivial finite 1 -element set
{{(L `3_3),3},{(L `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `3_3),3] is set
2 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(L `3_3) |^ (2 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `3_3),(2 + 1)) is set
[(L `3_3),(2 + 1)] is V26() set
{(L `3_3),(2 + 1)} is non empty finite set
{{(L `3_3),(2 + 1)},{(L `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `3_3),(2 + 1)] is set
(L `3_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `3_3),2) is set
[(L `3_3),2] is V26() set
{(L `3_3),2} is non empty finite set
{{(L `3_3),2},{(L `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `3_3),2] is set
((L `3_3) |^ 2) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (((L `3_3) |^ 2),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `3_3) |^ 2),(L `3_3)] is V26() set
{((L `3_3) |^ 2),(L `3_3)} is non empty finite set
{((L `3_3) |^ 2)} is non empty trivial finite 1 -element set
{{((L `3_3) |^ 2),(L `3_3)},{((L `3_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `3_3) |^ 2),(L `3_3)] is set
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(L `3_3) |^ (1 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `3_3),(1 + 1)) is set
[(L `3_3),(1 + 1)] is V26() set
{(L `3_3),(1 + 1)} is non empty finite set
{{(L `3_3),(1 + 1)},{(L `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `3_3),(1 + 1)] is set
(L `3_3) |^ 1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `3_3),1) is set
[(L `3_3),1] is V26() set
{(L `3_3),1} is non empty finite set
{{(L `3_3),1},{(L `3_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `3_3),1] is set
((L `3_3) |^ 1) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `3_3) |^ 1),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `3_3) |^ 1),(L `3_3)] is V26() set
{((L `3_3) |^ 1),(L `3_3)} is non empty finite set
{((L `3_3) |^ 1)} is non empty trivial finite 1 -element set
{{((L `3_3) |^ 1),(L `3_3)},{((L `3_3) |^ 1)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `3_3) |^ 1),(L `3_3)] is set
(L `2_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `2_3),2) is set
[(L `2_3),2] is V26() set
{(L `2_3),2} is non empty finite set
{(L `2_3)} is non empty trivial finite 1 -element set
{{(L `2_3),2},{(L `2_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `2_3),2] is set
((L `2_3) |^ 2) * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `2_3) |^ 2),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `2_3) |^ 2),(L `3_3)] is V26() set
{((L `2_3) |^ 2),(L `3_3)} is non empty finite set
{((L `2_3) |^ 2)} is non empty trivial finite 1 -element set
{{((L `2_3) |^ 2),(L `3_3)},{((L `2_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `2_3) |^ 2),(L `3_3)] is set
L `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(L `1) `1 is set
(L `1_3) |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `1_3),3) is set
[(L `1_3),3] is V26() set
{(L `1_3),3} is non empty finite set
{(L `1_3)} is non empty trivial finite 1 -element set
{{(L `1_3),3},{(L `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `1_3),3] is set
a * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,(L `1_3)] is V26() set
{a,(L `1_3)} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,(L `1_3)},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,(L `1_3)] is set
(a * (L `1_3)) * ((L `3_3) |^ 2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((a * (L `1_3)),((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(a * (L `1_3)),((L `3_3) |^ 2)] is V26() set
{(a * (L `1_3)),((L `3_3) |^ 2)} is non empty finite set
{(a * (L `1_3))} is non empty trivial finite 1 -element set
{{(a * (L `1_3)),((L `3_3) |^ 2)},{(a * (L `1_3))}} is non empty finite V49() set
the multF of (INT.Ring p) . [(a * (L `1_3)),((L `3_3) |^ 2)] is set
((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . (((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))] is V26() set
{((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))} is non empty finite set
{((L `1_3) |^ 3)} is non empty trivial finite 1 -element set
{{((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))},{((L `1_3) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L `1_3) |^ 3),((a * (L `1_3)) * ((L `3_3) |^ 2))] is set
b * ((L `3_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (b,((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[b,((L `3_3) |^ 3)] is V26() set
{b,((L `3_3) |^ 3)} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,((L `3_3) |^ 3)},{b}} is non empty finite V49() set
the multF of (INT.Ring p) . [b,((L `3_3) |^ 3)] is set
(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))] is V26() set
{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))} is non empty finite set
{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))} is non empty trivial finite 1 -element set
{{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))},{(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))),(b * ((L `3_3) |^ 3))] is set
(((L `2_3) |^ 2) * (L `3_3)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(((L `2_3) |^ 2) * (L `3_3)) + (- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is V26() set
{(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))} is non empty finite set
{(((L `2_3) |^ 2) * (L `3_3))} is non empty trivial finite 1 -element set
{{(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))},{(((L `2_3) |^ 2) * (L `3_3))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((L `2_3) |^ 2) * (L `3_3)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is set
(0. (INT.Ring p)) - ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is V26() set
{(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))} is non empty finite set
{{(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + ((a * (L `1_3)) * ((L `3_3) |^ 2))) + (b * ((L `3_3) |^ 3))))] is set
((L `1_3) |^ 3) + (0. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((L `1_3) |^ 3),(0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `1_3) |^ 3),(0. (INT.Ring p))] is V26() set
{((L `1_3) |^ 3),(0. (INT.Ring p))} is non empty finite set
{{((L `1_3) |^ 3),(0. (INT.Ring p))},{((L `1_3) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L `1_3) |^ 3),(0. (INT.Ring p))] is set
(((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((L `1_3) |^ 3) + (0. (INT.Ring p))),(b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((L `1_3) |^ 3) + (0. (INT.Ring p))),(b * ((L `3_3) |^ 3))] is V26() set
{(((L `1_3) |^ 3) + (0. (INT.Ring p))),(b * ((L `3_3) |^ 3))} is non empty finite set
{(((L `1_3) |^ 3) + (0. (INT.Ring p)))} is non empty trivial finite 1 -element set
{{(((L `1_3) |^ 3) + (0. (INT.Ring p))),(b * ((L `3_3) |^ 3))},{(((L `1_3) |^ 3) + (0. (INT.Ring p)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((L `1_3) |^ 3) + (0. (INT.Ring p))),(b * ((L `3_3) |^ 3))] is set
(0. (INT.Ring p)) - ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3))))] is V26() set
{(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3))))} is non empty finite set
{{(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3))))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (b * ((L `3_3) |^ 3))))] is set
(((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((((L `1_3) |^ 3) + (0. (INT.Ring p))),(0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(((L `1_3) |^ 3) + (0. (INT.Ring p))),(0. (INT.Ring p))] is V26() set
{(((L `1_3) |^ 3) + (0. (INT.Ring p))),(0. (INT.Ring p))} is non empty finite set
{{(((L `1_3) |^ 3) + (0. (INT.Ring p))),(0. (INT.Ring p))},{(((L `1_3) |^ 3) + (0. (INT.Ring p)))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(((L `1_3) |^ 3) + (0. (INT.Ring p))),(0. (INT.Ring p))] is set
(0. (INT.Ring p)) - ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p))))] is V26() set
{(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p))))} is non empty finite set
{{(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p))))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(- ((((L `1_3) |^ 3) + (0. (INT.Ring p))) + (0. (INT.Ring p))))] is set
(0. (INT.Ring p)) - (((L `1_3) |^ 3) + (0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (((L `1_3) |^ 3) + (0. (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (- (((L `1_3) |^ 3) + (0. (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(- (((L `1_3) |^ 3) + (0. (INT.Ring p))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(- (((L `1_3) |^ 3) + (0. (INT.Ring p))))] is V26() set
{(0. (INT.Ring p)),(- (((L `1_3) |^ 3) + (0. (INT.Ring p))))} is non empty finite set
{{(0. (INT.Ring p)),(- (((L `1_3) |^ 3) + (0. (INT.Ring p))))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(- (((L `1_3) |^ 3) + (0. (INT.Ring p))))] is set
(0. (INT.Ring p)) - ((L `1_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- ((L `1_3) |^ 3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(0. (INT.Ring p)) + (- ((L `1_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((0. (INT.Ring p)),(- ((L `1_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(0. (INT.Ring p)),(- ((L `1_3) |^ 3))] is V26() set
{(0. (INT.Ring p)),(- ((L `1_3) |^ 3))} is non empty finite set
{{(0. (INT.Ring p)),(- ((L `1_3) |^ 3))},{(0. (INT.Ring p))}} is non empty finite V49() set
the addF of (INT.Ring p) . [(0. (INT.Ring p)),(- ((L `1_3) |^ 3))] is set
pp is Element of ((INT.Ring p))
(p,a,b) . pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((L `1_3) |^ 3) + (- ((L `1_3) |^ 3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((L `1_3) |^ 3),(- ((L `1_3) |^ 3))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `1_3) |^ 3),(- ((L `1_3) |^ 3))] is V26() set
{((L `1_3) |^ 3),(- ((L `1_3) |^ 3))} is non empty finite set
{{((L `1_3) |^ 3),(- ((L `1_3) |^ 3))},{((L `1_3) |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L `1_3) |^ 3),(- ((L `1_3) |^ 3))] is set
(L `1_3) * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((L `1_3),(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(L `1_3),(L `1_3)] is V26() set
{(L `1_3),(L `1_3)} is non empty finite set
{{(L `1_3),(L `1_3)},{(L `1_3)}} is non empty finite V49() set
the multF of (INT.Ring p) . [(L `1_3),(L `1_3)] is set
(L `1_3) |^ 1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `1_3),1) is set
[(L `1_3),1] is V26() set
{(L `1_3),1} is non empty finite set
{{(L `1_3),1},{(L `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `1_3),1] is set
((L `1_3) |^ 1) * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `1_3) |^ 1),(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `1_3) |^ 1),(L `1_3)] is V26() set
{((L `1_3) |^ 1),(L `1_3)} is non empty finite set
{((L `1_3) |^ 1)} is non empty trivial finite 1 -element set
{{((L `1_3) |^ 1),(L `1_3)},{((L `1_3) |^ 1)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `1_3) |^ 1),(L `1_3)] is set
(L `1_3) |^ (1 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `1_3),(1 + 1)) is set
[(L `1_3),(1 + 1)] is V26() set
{(L `1_3),(1 + 1)} is non empty finite set
{{(L `1_3),(1 + 1)},{(L `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `1_3),(1 + 1)] is set
(L `1_3) |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `1_3),2) is set
[(L `1_3),2] is V26() set
{(L `1_3),2} is non empty finite set
{{(L `1_3),2},{(L `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `1_3),2] is set
((L `1_3) |^ 2) * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `1_3) |^ 2),(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `1_3) |^ 2),(L `1_3)] is V26() set
{((L `1_3) |^ 2),(L `1_3)} is non empty finite set
{((L `1_3) |^ 2)} is non empty trivial finite 1 -element set
{{((L `1_3) |^ 2),(L `1_3)},{((L `1_3) |^ 2)}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `1_3) |^ 2),(L `1_3)] is set
(L `1_3) |^ (2 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . ((L `1_3),(2 + 1)) is set
[(L `1_3),(2 + 1)] is V26() set
{(L `1_3),(2 + 1)} is non empty finite set
{{(L `1_3),(2 + 1)},{(L `1_3)}} is non empty finite V49() set
(power (INT.Ring p)) . [(L `1_3),(2 + 1)] is set
[(L `1_3),(L `2_3),(L `3_3)] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(L `1_3),(L `2_3)] is V26() set
{(L `1_3),(L `2_3)} is non empty finite set
{{(L `1_3),(L `2_3)},{(L `1_3)}} is non empty finite V49() set
[[(L `1_3),(L `2_3)],(L `3_3)] is V26() set
{[(L `1_3),(L `2_3)],(L `3_3)} is non empty finite set
{[(L `1_3),(L `2_3)]} is non empty trivial finite 1 -element set
{{[(L `1_3),(L `2_3)],(L `3_3)},{[(L `1_3),(L `2_3)]}} is non empty finite V49() set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[0,0,0]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
((L `2_3) ") * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `2_3) "),(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `2_3) "),(L `2_3)] is V26() set
{((L `2_3) "),(L `2_3)} is non empty finite set
{((L `2_3) ")} is non empty trivial finite 1 -element set
{{((L `2_3) "),(L `2_3)},{((L `2_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `2_3) "),(L `2_3)] is set
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((L `2_3) ") * (L `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `2_3) "),(L `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `2_3) "),(L `1_3)] is V26() set
{((L `2_3) "),(L `1_3)} is non empty finite set
{((L `2_3) ")} is non empty trivial finite 1 -element set
{{((L `2_3) "),(L `1_3)},{((L `2_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `2_3) "),(L `1_3)] is set
((L `2_3) ") * (L `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `2_3) "),(L `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `2_3) "),(L `2_3)] is V26() set
{((L `2_3) "),(L `2_3)} is non empty finite set
{{((L `2_3) "),(L `2_3)},{((L `2_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `2_3) "),(L `2_3)] is set
((L `2_3) ") * (L `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (((L `2_3) "),(L `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L `2_3) "),(L `3_3)] is V26() set
{((L `2_3) "),(L `3_3)} is non empty finite set
{{((L `2_3) "),(L `3_3)},{((L `2_3) ")}} is non empty finite V49() set
the multF of (INT.Ring p) . [((L `2_3) "),(L `3_3)] is set
[(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3)),(((L `2_3) ") * (L `3_3))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))] is V26() set
{(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))} is non empty finite set
{(((L `2_3) ") * (L `1_3))} is non empty trivial finite 1 -element set
{{(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))},{(((L `2_3) ") * (L `1_3))}} is non empty finite V49() set
[[(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))],(((L `2_3) ") * (L `3_3))] is V26() set
{[(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))],(((L `2_3) ") * (L `3_3))} is non empty finite set
{[(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))]} is non empty trivial finite 1 -element set
{{[(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))],(((L `2_3) ") * (L `3_3))},{[(((L `2_3) ") * (L `1_3)),(((L `2_3) ") * (L `2_3))]}} is non empty finite V49() set
pp is Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
pp `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp `1 is set
(pp `1) `1 is set
pp `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(pp `1) `2 is set
pp `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is Element of ((INT.Ring p))
(p,a,b) . FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 is Element of ((INT.Ring p))
F1 `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 `1 is set
(F1 `1) `1 is set
F1 `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F1 `1) `2 is set
F1 `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like ((INT.Ring p)) -defined (p,a,b) -defined ((INT.Ring p)) -valued (p,a,b) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
Class (p,a,b) is non empty finite V49() V130() a_partition of (p,a,b)
L is set
F is Element of (p,a,b)
Class ((p,a,b),F) is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
pp is Element of ((INT.Ring p))
pp `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is Element of ((INT.Ring p))
FF `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF `1 is set
(FF `1) `1 is set
FF `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(FF `1) `2 is set
FF `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[FF,pp] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{FF,pp} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,pp},{FF}} is non empty finite V49() set
Class ((p,a,b),FF) is finite Element of bool (p,a,b)
pp is Element of ((INT.Ring p))
pp `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is Element of ((INT.Ring p))
FF `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF `1 is set
(FF `1) `1 is set
FF `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(FF `1) `2 is set
[(FF `1_3),(FF `2_3),1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[(FF `1_3),(FF `2_3)] is V26() set
{(FF `1_3),(FF `2_3)} is non empty finite set
{(FF `1_3)} is non empty trivial finite 1 -element set
{{(FF `1_3),(FF `2_3)},{(FF `1_3)}} is non empty finite V49() set
[[(FF `1_3),(FF `2_3)],1] is V26() set
{[(FF `1_3),(FF `2_3)],1} is non empty finite set
{[(FF `1_3),(FF `2_3)]} is non empty trivial finite 1 -element set
{{[(FF `1_3),(FF `2_3)],1},{[(FF `1_3),(FF `2_3)]}} is non empty finite V49() set
[FF,pp] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{FF,pp} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,pp},{FF}} is non empty finite V49() set
Class ((p,a,b),FF) is finite Element of bool (p,a,b)
pp is Element of ((INT.Ring p))
pp `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like ((INT.Ring p)) -defined (p,a,b) -defined ((INT.Ring p)) -valued (p,a,b) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
Class (p,a,b) is non empty finite V49() V130() a_partition of (p,a,b)
bool (p,a,b) is non empty finite V49() set
Class ((p,a,b),[0,1,0]) is finite Element of bool (p,a,b)
{(Class ((p,a,b),[0,1,0]))} is non empty trivial finite V49() 1 -element Element of bool (bool (p,a,b))
bool (bool (p,a,b)) is non empty finite V49() set
{ (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is set
{(Class ((p,a,b),[0,1,0]))} \/ { (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is non empty set
FF is set
F1 is Element of ((INT.Ring p))
Class ((p,a,b),F1) is finite Element of bool (p,a,b)
F2 is Element of ((INT.Ring p))
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,Y,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[X,Y] is V26() set
{X,Y} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,Y},{X}} is non empty finite V49() set
[[X,Y],1] is V26() set
{[X,Y],1} is non empty finite set
{[X,Y]} is non empty trivial finite 1 -element set
{{[X,Y],1},{[X,Y]}} is non empty finite V49() set
Class ((p,a,b),F2) is finite Element of bool (p,a,b)
pp is Element of (p,a,b)
EqClass ((p,a,b),pp) is finite Element of Class (p,a,b)
F1 is Element of ((INT.Ring p))
Class ((p,a,b),F1) is finite Element of bool (p,a,b)
F2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F2,X,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[F2,X] is V26() set
{F2,X} is non empty finite set
{F2} is non empty trivial finite 1 -element set
{{F2,X},{F2}} is non empty finite V49() set
[[F2,X],1] is V26() set
{[F2,X],1} is non empty finite set
{[F2,X]} is non empty trivial finite 1 -element set
{{[F2,X],1},{[F2,X]}} is non empty finite V49() set
F1 is Element of ((INT.Ring p))
Class ((p,a,b),F1) is finite Element of bool (p,a,b)
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,Y,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[X,Y] is V26() set
{X,Y} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,Y},{X}} is non empty finite V49() set
[[X,Y],1] is V26() set
{[X,Y],1} is non empty finite set
{[X,Y]} is non empty trivial finite 1 -element set
{{[X,Y],1},{[X,Y]}} is non empty finite V49() set
F2 is Element of (p,a,b)
EqClass ((p,a,b),F2) is finite Element of Class (p,a,b)
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,Y,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[X,Y] is V26() set
{X,Y} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,Y},{X}} is non empty finite V49() set
[[X,Y],1] is V26() set
{[X,Y],1} is non empty finite set
{[X,Y]} is non empty trivial finite 1 -element set
{{[X,Y],1},{[X,Y]}} is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[L,F,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[L,F] is V26() set
{L,F} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,F},{L}} is non empty finite V49() set
[[L,F],1] is V26() set
{[L,F],1} is non empty finite set
{[L,F]} is non empty trivial finite 1 -element set
{{[L,F],1},{[L,F]}} is non empty finite V49() set
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[pp,FF,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[pp,FF] is V26() set
{pp,FF} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,FF},{pp}} is non empty finite V49() set
[[pp,FF],1] is V26() set
{[pp,FF],1} is non empty finite set
{[pp,FF]} is non empty trivial finite 1 -element set
{{[pp,FF],1},{[pp,FF]}} is non empty finite V49() set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like (p,a,b) -defined ((INT.Ring p)) -defined (p,a,b) -valued ((INT.Ring p)) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
Class ((p,a,b),[L,F,1]) is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
Class ((p,a,b),[pp,FF,1]) is finite Element of bool (p,a,b)
[[L,F,1],[pp,FF,1]] is V26() Element of [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:],[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]:]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:],[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]:] is non empty set
{[L,F,1],[pp,FF,1]} is non empty finite set
{[L,F,1]} is non empty trivial finite 1 -element set
{{[L,F,1],[pp,FF,1]},{[L,F,1]}} is non empty finite V49() set
F1 is Element of ((INT.Ring p))
F2 is Element of ((INT.Ring p))
F2 `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F2 `1 is set
(F2 `1) `1 is set
F1 `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 `1 is set
(F1 `1) `1 is set
F2 `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F2 `1) `2 is set
F1 `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(F1 `1) `2 is set
F2 `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
X * (F1 `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (X,(F1 `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,(F1 `1_3)] is V26() set
{X,(F1 `1_3)} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,(F1 `1_3)},{X}} is non empty finite V49() set
the multF of (INT.Ring p) . [X,(F1 `1_3)] is set
X * (F1 `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (X,(F1 `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,(F1 `2_3)] is V26() set
{X,(F1 `2_3)} is non empty finite set
{{X,(F1 `2_3)},{X}} is non empty finite V49() set
the multF of (INT.Ring p) . [X,(F1 `2_3)] is set
X * (F1 `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (X,(F1 `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,(F1 `3_3)] is V26() set
{X,(F1 `3_3)} is non empty finite set
{{X,(F1 `3_3)},{X}} is non empty finite V49() set
the multF of (INT.Ring p) . [X,(F1 `3_3)] is set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
bool (p,a,b) is non empty finite V49() set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like ((INT.Ring p)) -defined (p,a,b) -defined ((INT.Ring p)) -valued (p,a,b) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
Class ((p,a,b),[0,1,0]) is finite Element of bool (p,a,b)
{(Class ((p,a,b),[0,1,0]))} is non empty trivial finite V49() 1 -element Element of bool (bool (p,a,b))
bool (bool (p,a,b)) is non empty finite V49() set
{ (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is set
L is set
F is set
L /\ F is set
pp is set
FF is Element of ((INT.Ring p))
Class ((p,a,b),FF) is finite Element of bool (p,a,b)
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F1,F2,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[F1,F2] is V26() set
{F1,F2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,F2},{F1}} is non empty finite V49() set
[[F1,F2],1] is V26() set
{[F1,F2],1} is non empty finite set
{[F1,F2]} is non empty trivial finite 1 -element set
{{[F1,F2],1},{[F1,F2]}} is non empty finite V49() set
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[F1,F2,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[F1,F2] is V26() set
{F1,F2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,F2},{F1}} is non empty finite V49() set
[[F1,F2],1] is V26() set
{[F1,F2],1} is non empty finite set
{[F1,F2]} is non empty trivial finite 1 -element set
{{[F1,F2],1},{[F1,F2]}} is non empty finite V49() set
X is Element of ((INT.Ring p))
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
n1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[Y,n1,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[Y,n1] is V26() set
{Y,n1} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,n1},{Y}} is non empty finite V49() set
[[Y,n1],1] is V26() set
{[Y,n1],1} is non empty finite set
{[Y,n1]} is non empty trivial finite 1 -element set
{{[Y,n1],1},{[Y,n1]}} is non empty finite V49() set
[FF,X] is V26() Element of [:((INT.Ring p)),((INT.Ring p)):]
{FF,X} is non empty finite set
{FF} is non empty trivial finite 1 -element set
{{FF,X},{FF}} is non empty finite V49() set
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
n1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[Y,n1,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[Y,n1] is V26() set
{Y,n1} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,n1},{Y}} is non empty finite V49() set
[[Y,n1],1] is V26() set
{[Y,n1],1} is non empty finite set
{[Y,n1]} is non empty trivial finite 1 -element set
{{[Y,n1],1},{[Y,n1]}} is non empty finite V49() set
X `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
X `1 is set
(X `1) `1 is set
FF `1_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF `1 is set
(FF `1) `1 is set
X `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(X `1) `2 is set
FF `2_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(FF `1) `2 is set
X `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
FF `3_3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Y * (FF `1_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (Y,(FF `1_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[Y,(FF `1_3)] is V26() set
{Y,(FF `1_3)} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,(FF `1_3)},{Y}} is non empty finite V49() set
the multF of (INT.Ring p) . [Y,(FF `1_3)] is set
Y * (FF `2_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (Y,(FF `2_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[Y,(FF `2_3)] is V26() set
{Y,(FF `2_3)} is non empty finite set
{{Y,(FF `2_3)},{Y}} is non empty finite V49() set
the multF of (INT.Ring p) . [Y,(FF `2_3)] is set
Y * (FF `3_3) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (Y,(FF `3_3)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[Y,(FF `3_3)] is V26() set
{Y,(FF `3_3)} is non empty finite set
{{Y,(FF `3_3)},{Y}} is non empty finite V49() set
the multF of (INT.Ring p) . [Y,(FF `3_3)] is set
1. (INT.Ring p) is V61( INT.Ring p) V61( INT.Ring p) left_add-cancelable left_add-cancelable right_add-cancelable right_add-cancelable add-cancelable add-cancelable right_complementable right_complementable (p) Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
p is non empty finite set
[:p,p:] is non empty finite set
bool [:p,p:] is non empty finite V49() set
bool p is non empty finite V49() set
a is Relation-like p -defined p -valued total finite reflexive symmetric transitive Element of bool [:p,p:]
Class a is non empty finite V49() V130() a_partition of p
b is Relation-like Class a -valued Function-like set
dom b is set
L is set
b . L is set
p is non empty set
[:p,p:] is non empty set
bool [:p,p:] is non empty set
a is Relation-like p -defined p -valued total reflexive symmetric transitive Element of bool [:p,p:]
Class a is non empty V130() a_partition of p
b is Relation-like Class a -valued Function-like set
L is set
F is set
dom b is set
b . L is set
b . F is set
dom b is set
b . L is set
b . F is set
dom b is set
p is non empty set
[:p,p:] is non empty set
bool [:p,p:] is non empty set
a is Relation-like p -defined p -valued total reflexive symmetric transitive Element of bool [:p,p:]
Class a is non empty V130() a_partition of p
b is Relation-like Class a -valued Function-like set
Union b is set
rng b is set
union (rng b) is set
union (Class a) is set
p is non empty finite set
[:p,p:] is non empty finite set
bool [:p,p:] is non empty finite V49() set
card p is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a is Relation-like p -defined p -valued total finite reflexive symmetric transitive Element of bool [:p,p:]
Class a is non empty finite V49() V130() a_partition of p
b is Relation-like Class a -valued Function-like set
dom b is set
L is Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() FinSequence-like FinSequence of NAT
dom L is V117() V118() V119() V120() V121() V122() Element of bool NAT
Sum L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
b . F is set
L . F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
card (b . F) is V4() V5() V6() cardinal set
Union b is set
rng b is set
union (rng b) is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
L |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,3) is set
[L,3] is V26() set
{L,3} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,3},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,3] is set
a * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,L] is V26() set
{a,L} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,L},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,L] is set
(L |^ 3) + (a * L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((L |^ 3),(a * L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(L |^ 3),(a * L)] is V26() set
{(L |^ 3),(a * L)} is non empty finite set
{(L |^ 3)} is non empty trivial finite 1 -element set
{{(L |^ 3),(a * L)},{(L |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(L |^ 3),(a * L)] is set
((L |^ 3) + (a * L)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((L |^ 3) + (a * L)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L |^ 3) + (a * L)),b] is V26() set
{((L |^ 3) + (a * L)),b} is non empty finite set
{((L |^ 3) + (a * L))} is non empty trivial finite 1 -element set
{{((L |^ 3) + (a * L)),b},{((L |^ 3) + (a * L))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L |^ 3) + (a * L)),b] is set
{ b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } is set
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like (p,a,b) -defined ((INT.Ring p)) -defined (p,a,b) -valued ((INT.Ring p)) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
{ (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } is set
F is set
pp is set
[:F,pp:] is set
bool [:F,pp:] is non empty set
FF is set
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F1,2) is set
[F1,2] is V26() set
{F1,2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,2},{F1}} is non empty finite V49() set
(power (INT.Ring p)) . [F1,2] is set
[L,F1,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[L,F1] is V26() set
{L,F1} is non empty finite set
{{L,F1},{L}} is non empty finite V49() set
[[L,F1],1] is V26() set
{[L,F1],1} is non empty finite set
{[L,F1]} is non empty trivial finite 1 -element set
{{[L,F1],1},{[L,F1]}} is non empty finite V49() set
Class ((p,a,b),[L,F1,1]) is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
F2 is set
[L,F2,1] is V26() V27() set
[L,F2] is V26() set
{L,F2} is non empty finite set
{{L,F2},{L}} is non empty finite V49() set
[[L,F2],1] is V26() set
{[L,F2],1} is non empty finite set
{[L,F2]} is non empty trivial finite 1 -element set
{{[L,F2],1},{[L,F2]}} is non empty finite V49() set
Class ((p,a,b),[L,F2,1]) is finite Element of bool (p,a,b)
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
X |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (X,2) is set
[X,2] is V26() set
{X,2} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,2},{X}} is non empty finite V49() set
(power (INT.Ring p)) . [X,2] is set
[L,X,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[L,X] is V26() set
{L,X} is non empty finite set
{{L,X},{L}} is non empty finite V49() set
[[L,X],1] is V26() set
{[L,X],1} is non empty finite set
{[L,X]} is non empty trivial finite 1 -element set
{{[L,X],1},{[L,X]}} is non empty finite V49() set
F2 is Relation-like F -defined pp -valued Function-like quasi_total Element of bool [:F,pp:]
X is set
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[L,Y,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[L,Y] is V26() set
{L,Y} is non empty finite set
{{L,Y},{L}} is non empty finite V49() set
[[L,Y],1] is V26() set
{[L,Y],1} is non empty finite set
{[L,Y]} is non empty trivial finite 1 -element set
{{[L,Y],1},{[L,Y]}} is non empty finite V49() set
Class ((p,a,b),[L,Y,1]) is finite Element of bool (p,a,b)
Y |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (Y,2) is set
[Y,2] is V26() set
{Y,2} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,2},{Y}} is non empty finite V49() set
(power (INT.Ring p)) . [Y,2] is set
F2 . Y is set
rng F2 is Element of bool pp
bool pp is non empty set
X is set
dom F2 is Element of bool F
bool F is non empty set
Y is set
F2 . X is set
F2 . Y is set
n1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
n1 |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (n1,2) is set
[n1,2] is V26() set
{n1,2} is non empty finite set
{n1} is non empty trivial finite 1 -element set
{{n1,2},{n1}} is non empty finite V49() set
(power (INT.Ring p)) . [n1,2] is set
n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
n |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (n,2) is set
[n,2] is V26() set
{n,2} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,2},{n}} is non empty finite V49() set
(power (INT.Ring p)) . [n,2] is set
[L,X,1] is V26() V27() set
[L,X] is V26() set
{L,X} is non empty finite set
{{L,X},{L}} is non empty finite V49() set
[[L,X],1] is V26() set
{[L,X],1} is non empty finite set
{[L,X]} is non empty trivial finite 1 -element set
{{[L,X],1},{[L,X]}} is non empty finite V49() set
Class ((p,a,b),[L,X,1]) is finite Element of bool (p,a,b)
[L,Y,1] is V26() V27() set
[L,Y] is V26() set
{L,Y} is non empty finite set
{{L,Y},{L}} is non empty finite V49() set
[[L,Y],1] is V26() set
{[L,Y],1} is non empty finite set
{[L,Y]} is non empty trivial finite 1 -element set
{{[L,Y],1},{[L,Y]}} is non empty finite V49() set
Class ((p,a,b),[L,Y,1]) is finite Element of bool (p,a,b)
[L,n,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[L,n] is V26() set
{L,n} is non empty finite set
{{L,n},{L}} is non empty finite V49() set
[[L,n],1] is V26() set
{[L,n],1} is non empty finite set
{[L,n]} is non empty trivial finite 1 -element set
{{[L,n],1},{[L,n]}} is non empty finite V49() set
[L,n1,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[L,n1] is V26() set
{L,n1} is non empty finite set
{{L,n1},{L}} is non empty finite V49() set
[[L,n1],1] is V26() set
{[L,n1],1} is non empty finite set
{[L,n1]} is non empty trivial finite 1 -element set
{{[L,n1],1},{[L,n1]}} is non empty finite V49() set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like (p,a,b) -defined ((INT.Ring p)) -defined (p,a,b) -valued ((INT.Ring p)) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
{ (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } is set
card { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } is V4() V5() V6() cardinal set
L |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (L,3) is set
[L,3] is V26() set
{L,3} is non empty finite set
{L} is non empty trivial finite 1 -element set
{{L,3},{L}} is non empty finite V49() set
(power (INT.Ring p)) . [L,3] is set
a * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,L] is V26() set
{a,L} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,L},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,L] is set
(L |^ 3) + (a * L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((L |^ 3),(a * L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(L |^ 3),(a * L)] is V26() set
{(L |^ 3),(a * L)} is non empty finite set
{(L |^ 3)} is non empty trivial finite 1 -element set
{{(L |^ 3),(a * L)},{(L |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(L |^ 3),(a * L)] is set
((L |^ 3) + (a * L)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((L |^ 3) + (a * L)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((L |^ 3) + (a * L)),b] is V26() set
{((L |^ 3) + (a * L)),b} is non empty finite set
{((L |^ 3) + (a * L))} is non empty trivial finite 1 -element set
{{((L |^ 3) + (a * L)),b},{((L |^ 3) + (a * L))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((L |^ 3) + (a * L)),b] is set
(p,(((L |^ 3) + (a * L)) + b)) is V11() V12() integer ext-real set
1 + (p,(((L |^ 3) + (a * L)) + b)) is V11() V12() integer ext-real set
{ b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } is set
FF is set
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[L,F1,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[L,F1] is V26() set
{L,F1} is non empty finite set
{{L,F1},{L}} is non empty finite V49() set
[[L,F1],1] is V26() set
{[L,F1],1} is non empty finite set
{[L,F1]} is non empty trivial finite 1 -element set
{{[L,F1],1},{[L,F1]}} is non empty finite V49() set
Class ((p,a,b),[L,F1,1]) is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
F1 |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F1,2) is set
[F1,2] is V26() set
{F1,2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,2},{F1}} is non empty finite V49() set
(power (INT.Ring p)) . [F1,2] is set
FF is set
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 |^ 2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F1,2) is set
[F1,2] is V26() set
{F1,2} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,2},{F1}} is non empty finite V49() set
(power (INT.Ring p)) . [F1,2] is set
[L,F1,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[L,F1] is V26() set
{L,F1} is non empty finite set
{{L,F1},{L}} is non empty finite V49() set
[[L,F1],1] is V26() set
{[L,F1],1} is non empty finite set
{[L,F1]} is non empty trivial finite 1 -element set
{{[L,F1],1},{[L,F1]}} is non empty finite V49() set
Class ((p,a,b),[L,F1,1]) is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
[: { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } , { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } :] is set
bool [: { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } , { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } :] is non empty set
F2 is Relation-like { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } -defined { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } -valued Function-like quasi_total Element of bool [: { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } , { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } :]
dom F2 is Element of bool { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b }
bool { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } is non empty set
rng F2 is Element of bool { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) }
bool { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } is non empty set
card { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } is V4() V5() V6() cardinal set
[: { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } , { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } :] is set
bool [: { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } , { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } :] is non empty set
F2 " is Relation-like Function-like set
F2 * (F2 ") is Relation-like set
id { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } is Relation-like { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } -defined { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } -valued total reflexive symmetric antisymmetric transitive Element of bool [: { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } , { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } :]
[: { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } , { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } :] is set
bool [: { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } , { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } :] is non empty set
(F2 ") * F2 is Relation-like set
id { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } is Relation-like { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } -defined { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } -valued total reflexive symmetric antisymmetric transitive Element of bool [: { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } , { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } :]
[: { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } , { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } :] is set
bool [: { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } , { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } :] is non empty set
X is Relation-like { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } -defined { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } -valued Function-like quasi_total Element of bool [: { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) } , { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b } :]
rng X is Element of bool { b1 where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : b1 |^ 2 = ((L |^ 3) + (a * L)) + b }
dom X is Element of bool { (Class ((p,a,b),[L,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [L,b1,1] in (p,a,b) }
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
Seg p is V117() V118() V119() V120() V121() V122() Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT : ( 1 <= b1 & b1 <= p ) } is set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
a is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
a - 1 is V11() V12() integer ext-real set
1 - 1 is V11() V12() integer ext-real set
p - 1 is V11() V12() integer ext-real set
p - 0 is non empty V11() V12() integer ext-real positive non negative set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Seg p is V117() V118() V119() V120() V121() V122() Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT : ( 1 <= b1 & b1 <= p ) } is set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like ((INT.Ring p)) -defined (p,a,b) -defined ((INT.Ring p)) -valued (p,a,b) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
{ (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is set
{ (Class ((p,a,b),[(a1 - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(a1 - 1),b1,1] in (p,a,b) } is set
pp is Relation-like Function-like FinSequence-like set
len pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
dom pp is V117() V118() V119() V120() V121() V122() Element of bool NAT
dom pp is set
Union pp is set
rng pp is set
union (rng pp) is set
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
pp . FF is set
FF - 1 is V11() V12() integer ext-real set
{ (Class ((p,a,b),[(FF - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(FF - 1),b1,1] in (p,a,b) } is set
FF is set
F1 is set
F2 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
F2 - 1 is V11() V12() integer ext-real set
X is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
X - 1 is V11() V12() integer ext-real set
pp . F2 is set
{ (Class ((p,a,b),[(F2 - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(F2 - 1),b1,1] in (p,a,b) } is set
pp . X is set
{ (Class ((p,a,b),[(X - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(X - 1),b1,1] in (p,a,b) } is set
pp . FF is set
pp . F1 is set
Y is set
n1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F2 - 1),n1,1] is V26() V27() set
[(F2 - 1),n1] is V26() set
{(F2 - 1),n1} is non empty finite set
{(F2 - 1)} is non empty trivial finite 1 -element V117() V118() V119() V120() V121() set
{{(F2 - 1),n1},{(F2 - 1)}} is non empty finite V49() set
[[(F2 - 1),n1],1] is V26() set
{[(F2 - 1),n1],1} is non empty finite set
{[(F2 - 1),n1]} is non empty trivial finite 1 -element set
{{[(F2 - 1),n1],1},{[(F2 - 1),n1]}} is non empty finite V49() set
Class ((p,a,b),[(F2 - 1),n1,1]) is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(X - 1),n,1] is V26() V27() set
[(X - 1),n] is V26() set
{(X - 1),n} is non empty finite set
{(X - 1)} is non empty trivial finite 1 -element V117() V118() V119() V120() V121() set
{{(X - 1),n},{(X - 1)}} is non empty finite V49() set
[[(X - 1),n],1] is V26() set
{[(X - 1),n],1} is non empty finite set
{[(X - 1),n]} is non empty trivial finite 1 -element set
{{[(X - 1),n],1},{[(X - 1),n]}} is non empty finite V49() set
Class ((p,a,b),[(X - 1),n,1]) is finite Element of bool (p,a,b)
pp . FF is set
pp . F1 is set
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
pp . FF is set
FF - 1 is V11() V12() integer ext-real set
{ (Class ((p,a,b),[(FF - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(FF - 1),b1,1] in (p,a,b) } is set
1 - 1 is V11() V12() integer ext-real set
p - 1 is V11() V12() integer ext-real set
p - 0 is non empty V11() V12() integer ext-real positive non negative set
card (pp . FF) is V4() V5() V6() cardinal set
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
{ (Class ((p,a,b),[F1,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [F1,b1,1] in (p,a,b) } is set
card { (Class ((p,a,b),[F1,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [F1,b1,1] in (p,a,b) } is V4() V5() V6() cardinal set
F1 |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (F1,3) is set
[F1,3] is V26() set
{F1,3} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,3},{F1}} is non empty finite V49() set
(power (INT.Ring p)) . [F1,3] is set
a * F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,F1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,F1] is V26() set
{a,F1} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,F1},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,F1] is set
(F1 |^ 3) + (a * F1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((F1 |^ 3),(a * F1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F1 |^ 3),(a * F1)] is V26() set
{(F1 |^ 3),(a * F1)} is non empty finite set
{(F1 |^ 3)} is non empty trivial finite 1 -element set
{{(F1 |^ 3),(a * F1)},{(F1 |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(F1 |^ 3),(a * F1)] is set
((F1 |^ 3) + (a * F1)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((F1 |^ 3) + (a * F1)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F1 |^ 3) + (a * F1)),b] is V26() set
{((F1 |^ 3) + (a * F1)),b} is non empty finite set
{((F1 |^ 3) + (a * F1))} is non empty trivial finite 1 -element set
{{((F1 |^ 3) + (a * F1)),b},{((F1 |^ 3) + (a * F1))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((F1 |^ 3) + (a * F1)),b] is set
(p,(((F1 |^ 3) + (a * F1)) + b)) is V11() V12() integer ext-real set
1 + (p,(((F1 |^ 3) + (a * F1)) + b)) is V11() V12() integer ext-real set
F1 is set
F2 is set
X is set
pp . X is set
Y is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
pp . Y is set
Y - 1 is V11() V12() integer ext-real set
{ (Class ((p,a,b),[(Y - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(Y - 1),b1,1] in (p,a,b) } is set
n1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(Y - 1),n1,1] is V26() V27() set
[(Y - 1),n1] is V26() set
{(Y - 1),n1} is non empty finite set
{(Y - 1)} is non empty trivial finite 1 -element V117() V118() V119() V120() V121() set
{{(Y - 1),n1},{(Y - 1)}} is non empty finite V49() set
[[(Y - 1),n1],1] is V26() set
{[(Y - 1),n1],1} is non empty finite set
{[(Y - 1),n1]} is non empty trivial finite 1 -element set
{{[(Y - 1),n1],1},{[(Y - 1),n1]}} is non empty finite V49() set
Class ((p,a,b),[(Y - 1),n1,1]) is finite Element of bool (p,a,b)
bool (p,a,b) is non empty finite V49() set
F2 is Element of ((INT.Ring p))
Class ((p,a,b),F2) is finite Element of bool (p,a,b)
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,Y,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[X,Y] is V26() set
{X,Y} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,Y},{X}} is non empty finite V49() set
[[X,Y],1] is V26() set
{[X,Y],1} is non empty finite set
{[X,Y]} is non empty trivial finite 1 -element set
{{[X,Y],1},{[X,Y]}} is non empty finite V49() set
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[X,Y,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:] is non empty set
[X,Y] is V26() set
{X,Y} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,Y},{X}} is non empty finite V49() set
[[X,Y],1] is V26() set
{[X,Y],1} is non empty finite set
{[X,Y]} is non empty trivial finite 1 -element set
{{[X,Y],1},{[X,Y]}} is non empty finite V49() set
n1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
0 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
n1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(n1 + 1) - 1 is V11() V12() integer ext-real set
{ (Class ((p,a,b),[((n1 + 1) - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [((n1 + 1) - 1),b1,1] in (p,a,b) } is set
y1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[y1,a1,1] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p),NAT:]
[y1,a1] is V26() set
{y1,a1} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,a1},{y1}} is non empty finite V49() set
[[y1,a1],1] is V26() set
{[y1,a1],1} is non empty finite set
{[y1,a1]} is non empty trivial finite 1 -element set
{{[y1,a1],1},{[y1,a1]}} is non empty finite V49() set
pp . (n1 + 1) is set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Seg p is V117() V118() V119() V120() V121() V122() Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT : ( 1 <= b1 & b1 <= p ) } is set
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like ((INT.Ring p)) -defined (p,a,b) -defined ((INT.Ring p)) -valued (p,a,b) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
{ (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is set
card { (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is V4() V5() V6() cardinal set
L is Relation-like Function-like set
dom L is set
Union L is set
rng L is set
union (rng L) is set
F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L . F is set
card (L . F) is V4() V5() V6() cardinal set
pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
FF is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F is Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() FinSequence-like FinSequence of NAT
dom F is V117() V118() V119() V120() V121() V122() Element of bool NAT
len F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
Sum F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
1 - 1 is V11() V12() integer ext-real set
pp - 1 is V11() V12() integer ext-real set
p - 1 is V11() V12() integer ext-real set
p - 0 is non empty V11() V12() integer ext-real positive non negative set
FF is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F . pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L . pp is set
card (L . pp) is V4() V5() V6() cardinal set
{ (Class ((p,a,b),[(pp - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(pp - 1),b1,1] in (p,a,b) } is set
card { (Class ((p,a,b),[(pp - 1),b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [(pp - 1),b1,1] in (p,a,b) } is V4() V5() V6() cardinal set
{ (Class ((p,a,b),[F1,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [F1,b1,1] in (p,a,b) } is set
card { (Class ((p,a,b),[F1,b1,1])) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) : [F1,b1,1] in (p,a,b) } is V4() V5() V6() cardinal set
F1 |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (F1,3) is set
[F1,3] is V26() set
{F1,3} is non empty finite set
{F1} is non empty trivial finite 1 -element set
{{F1,3},{F1}} is non empty finite V49() set
(power (INT.Ring p)) . [F1,3] is set
a * F1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,F1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,F1] is V26() set
{a,F1} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,F1},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,F1] is set
(F1 |^ 3) + (a * F1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((F1 |^ 3),(a * F1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F1 |^ 3),(a * F1)] is V26() set
{(F1 |^ 3),(a * F1)} is non empty finite set
{(F1 |^ 3)} is non empty trivial finite 1 -element set
{{(F1 |^ 3),(a * F1)},{(F1 |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(F1 |^ 3),(a * F1)] is set
((F1 |^ 3) + (a * F1)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((F1 |^ 3) + (a * F1)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F1 |^ 3) + (a * F1)),b] is V26() set
{((F1 |^ 3) + (a * F1)),b} is non empty finite set
{((F1 |^ 3) + (a * F1))} is non empty trivial finite 1 -element set
{{((F1 |^ 3) + (a * F1)),b},{((F1 |^ 3) + (a * F1))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((F1 |^ 3) + (a * F1)),b] is set
(p,(((F1 |^ 3) + (a * F1)) + b)) is V11() V12() integer ext-real set
1 + (p,(((F1 |^ 3) + (a * F1)) + b)) is V11() V12() integer ext-real set
pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
L . pp is set
F . pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
card (L . pp) is V4() V5() V6() cardinal set
pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
pp - 1 is V11() V12() integer ext-real set
F . pp is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
p is non empty V4() V5() V6() V10() V11() V12() integer V14() ext-real positive non negative finite cardinal set
INT.Ring p is non empty non degenerated non trivial finite left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed () doubleLoopStr
Segm p is V117() V118() V119() V120() V121() V122() Element of bool NAT
addint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
[:[:(Segm p),(Segm p):],(Segm p):] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like quasi_total V35() V36() V37() V38() Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
K633(1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
K633(0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),K633(1,(Segm p)),K633(0,(Segm p)) #) is strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial finite set
0. (INT.Ring p) is V61( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
Seg p is V117() V118() V119() V120() V121() V122() Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT : ( 1 <= b1 & b1 <= p ) } is set
1 + p is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(p,a,b) is non empty finite Element of bool ((INT.Ring p))
((INT.Ring p)) is non empty finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite V49() set
[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() V27() Element of [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[(0. (INT.Ring p)),(0. (INT.Ring p))] is V26() set
{(0. (INT.Ring p)),(0. (INT.Ring p))} is non empty finite set
{(0. (INT.Ring p))} is non empty trivial finite 1 -element set
{{(0. (INT.Ring p)),(0. (INT.Ring p))},{(0. (INT.Ring p))}} is non empty finite V49() set
[[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))] is V26() set
{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))} is non empty finite set
{[(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element set
{{[(0. (INT.Ring p)),(0. (INT.Ring p))],(0. (INT.Ring p))},{[(0. (INT.Ring p)),(0. (INT.Ring p))]}} is non empty finite V49() set
{[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is non empty trivial finite 1 -element Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] \ {[(0. (INT.Ring p)),(0. (INT.Ring p)),(0. (INT.Ring p))]} is finite Element of bool [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):]
bool ((INT.Ring p)) is non empty finite V49() set
(p,a,b) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
{ b1 where b1 is Element of ((INT.Ring p)) : (p,a,b) . b1 = 0. (INT.Ring p) } is set
(p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
[:(p,a,b),(p,a,b):] is non empty finite set
bool [:(p,a,b),(p,a,b):] is non empty finite V49() set
(p) is Relation-like ((INT.Ring p)) -defined ((INT.Ring p)) -valued total finite reflexive symmetric transitive Element of bool [:((INT.Ring p)),((INT.Ring p)):]
[:((INT.Ring p)),((INT.Ring p)):] is non empty finite set
bool [:((INT.Ring p)),((INT.Ring p)):] is non empty finite V49() set
{ [b1,b2] where b1, b2 is Element of ((INT.Ring p)) : (p,b1,b2) } is set
nabla (p,a,b) is Relation-like (p,a,b) -defined (p,a,b) -valued total finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
(p) /\ (nabla (p,a,b)) is Relation-like (p,a,b) -defined ((INT.Ring p)) -defined (p,a,b) -valued ((INT.Ring p)) -valued finite reflexive symmetric transitive Element of bool [:(p,a,b),(p,a,b):]
Class (p,a,b) is non empty finite V49() V130() a_partition of (p,a,b)
card (Class (p,a,b)) is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
{ (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is set
card { (Class ((p,a,b),b1)) where b1 is Element of ((INT.Ring p)) : ( b1 in (p,a,b) & ex b2, b3 being left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p) st b1 = [b2,b3,1] ) } is V4() V5() V6() cardinal set
L is Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() FinSequence-like FinSequence of NAT
len L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
Sum L is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
1 - 1 is V11() V12() integer ext-real set
F - 1 is V11() V12() integer ext-real set
p - 1 is V11() V12() integer ext-real set
p - 0 is non empty V11() V12() integer ext-real positive non negative set
pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
pp |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
power (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial RAT -valued INT -valued V35() V36() V37() V38() non finite set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
(power (INT.Ring p)) . (pp,3) is set
[pp,3] is V26() set
{pp,3} is non empty finite set
{pp} is non empty trivial finite 1 -element set
{{pp,3},{pp}} is non empty finite V49() set
(power (INT.Ring p)) . [pp,3] is set
a * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty finite set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty finite V49() set
the multF of (INT.Ring p) . (a,pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,pp] is V26() set
{a,pp} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,pp},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,pp] is set
(pp |^ 3) + (a * pp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
the addF of (INT.Ring p) . ((pp |^ 3),(a * pp)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(pp |^ 3),(a * pp)] is V26() set
{(pp |^ 3),(a * pp)} is non empty finite set
{(pp |^ 3)} is non empty trivial finite 1 -element set
{{(pp |^ 3),(a * pp)},{(pp |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(pp |^ 3),(a * pp)] is set
((pp |^ 3) + (a * pp)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((pp |^ 3) + (a * pp)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((pp |^ 3) + (a * pp)),b] is V26() set
{((pp |^ 3) + (a * pp)),b} is non empty finite set
{((pp |^ 3) + (a * pp))} is non empty trivial finite 1 -element set
{{((pp |^ 3) + (a * pp)),b},{((pp |^ 3) + (a * pp))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((pp |^ 3) + (a * pp)),b] is set
(p,(((pp |^ 3) + (a * pp)) + b)) is V11() V12() integer ext-real set
FF is V11() V12() integer ext-real V113() Element of INT
F1 is V11() V12() integer ext-real V113() Element of INT
F is Relation-like NAT -defined INT -valued Function-like V35() V36() V37() FinSequence-like FinSequence of INT
dom F is V117() V118() V119() V120() V121() V122() Element of bool NAT
len F is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
Sum F is V11() V12() integer ext-real V113() Element of INT
(1 + p) + (Sum F) is V11() V12() integer ext-real set
p -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
REAL * is functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like Element of REAL * : len b1 = p } is set
p |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() p -element FinSequence-like Element of p -tuples_on REAL
K401((Seg p),1) is Relation-like Seg p -defined RAT -valued INT -valued {1} -valued Function-like quasi_total V35() V36() V37() V38() FinSequence-like Element of bool [:(Seg p),{1}:]
{1} is non empty trivial finite V49() 1 -element V117() V118() V119() V120() V121() V122() set
[:(Seg p),{1}:] is RAT -valued INT -valued V35() V36() V37() V38() set
bool [:(Seg p),{1}:] is non empty set
F1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
F1 - 1 is V11() V12() integer ext-real set
L . F1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
F . F1 is V11() V12() integer ext-real set
(p |-> 1) . F1 is V11() V12() ext-real set
((p |-> 1) . F1) + (F . F1) is V11() V12() ext-real set
F2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
F2 |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (F2,3) is set
[F2,3] is V26() set
{F2,3} is non empty finite set
{F2} is non empty trivial finite 1 -element set
{{F2,3},{F2}} is non empty finite V49() set
(power (INT.Ring p)) . [F2,3] is set
a * F2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,F2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,F2] is V26() set
{a,F2} is non empty finite set
{{a,F2},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,F2] is set
(F2 |^ 3) + (a * F2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((F2 |^ 3),(a * F2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(F2 |^ 3),(a * F2)] is V26() set
{(F2 |^ 3),(a * F2)} is non empty finite set
{(F2 |^ 3)} is non empty trivial finite 1 -element set
{{(F2 |^ 3),(a * F2)},{(F2 |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(F2 |^ 3),(a * F2)] is set
((F2 |^ 3) + (a * F2)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((F2 |^ 3) + (a * F2)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((F2 |^ 3) + (a * F2)),b] is V26() set
{((F2 |^ 3) + (a * F2)),b} is non empty finite set
{((F2 |^ 3) + (a * F2))} is non empty trivial finite 1 -element set
{{((F2 |^ 3) + (a * F2)),b},{((F2 |^ 3) + (a * F2))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((F2 |^ 3) + (a * F2)),b] is set
(p,(((F2 |^ 3) + (a * F2)) + b)) is V11() V12() integer ext-real set
X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
X |^ 3 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (X,3) is set
[X,3] is V26() set
{X,3} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,3},{X}} is non empty finite V49() set
(power (INT.Ring p)) . [X,3] is set
a * X is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (a,X) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[a,X] is V26() set
{a,X} is non empty finite set
{{a,X},{a}} is non empty finite V49() set
the multF of (INT.Ring p) . [a,X] is set
(X |^ 3) + (a * X) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . ((X |^ 3),(a * X)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(X |^ 3),(a * X)] is V26() set
{(X |^ 3),(a * X)} is non empty finite set
{(X |^ 3)} is non empty trivial finite 1 -element set
{{(X |^ 3),(a * X)},{(X |^ 3)}} is non empty finite V49() set
the addF of (INT.Ring p) . [(X |^ 3),(a * X)] is set
((X |^ 3) + (a * X)) + b is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) . (((X |^ 3) + (a * X)),b) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((X |^ 3) + (a * X)),b] is V26() set
{((X |^ 3) + (a * X)),b} is non empty finite set
{((X |^ 3) + (a * X))} is non empty trivial finite 1 -element set
{{((X |^ 3) + (a * X)),b},{((X |^ 3) + (a * X))}} is non empty finite V49() set
the addF of (INT.Ring p) . [((X |^ 3) + (a * X)),b] is set
(p,(((X |^ 3) + (a * X)) + b)) is V11() V12() integer ext-real set
1 + (p,(((X |^ 3) + (a * X)) + b)) is V11() V12() integer ext-real set
pp is Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() p -element FinSequence-like Element of p -tuples_on REAL
FF is Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() p -element FinSequence-like Element of p -tuples_on REAL
pp + FF is Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() p -element FinSequence-like Element of p -tuples_on REAL
(pp + FF) . F1 is V11() V12() ext-real set
len (pp + FF) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
Sum (p |-> 1) is V11() V12() ext-real Element of REAL
(Sum (p |-> 1)) + (Sum F) is V11() V12() ext-real set
p * 1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
(p * 1) + (Sum F) is V11() V12() integer ext-real set
bool (p,a,b) is non empty finite V49() set
Class ((p,a,b),[0,1,0]) is finite Element of bool (p,a,b)
{(Class ((p,a,b),[0,1,0]))} is non empty trivial finite V49() 1 -element Element of bool (bool (p,a,b))
bool (bool (p,a,b)) is non empty finite V49() set
F1 is finite set
card F1 is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
F2 is finite set
F1 \/ F2 is finite set
card (F1 \/ F2) is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal V113() V117() V118() V119() V120() V121() V122() Element of NAT
p + (Sum F) is V11() V12() integer ext-real set
1 + (p + (Sum F)) is V11() V12() integer ext-real set
X is V4() V5() V6() V10() V11() V12() integer ext-real non negative finite cardinal set
X - 1 is V11() V12() integer ext-real set
F . X is V11() V12() integer ext-real set