:: GROEB_2 semantic presentation

REAL is set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite V29() V30() Element of K19(REAL)
K19(REAL) is set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite V29() V30() set
K19(omega) is non trivial non finite set
K19(NAT) is non trivial non finite set
COMPLEX is set
RAT is set
INT is set
{} is Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite V28() V29() V31( {} ) FinSequence-membered V52() V53() complex ext-real non positive non negative set
1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
{{},1} is non empty finite V28() set
2 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
K20(COMPLEX,COMPLEX) is set
K19(K20(COMPLEX,COMPLEX)) is set
K20(K20(COMPLEX,COMPLEX),COMPLEX) is set
K19(K20(K20(COMPLEX,COMPLEX),COMPLEX)) is set
K20(REAL,REAL) is set
K19(K20(REAL,REAL)) is set
K20(K20(REAL,REAL),REAL) is set
K19(K20(K20(REAL,REAL),REAL)) is set
K20(RAT,RAT) is set
K19(K20(RAT,RAT)) is set
K20(K20(RAT,RAT),RAT) is set
K19(K20(K20(RAT,RAT),RAT)) is set
K20(INT,INT) is set
K19(K20(INT,INT)) is set
K20(K20(INT,INT),INT) is set
K19(K20(K20(INT,INT),INT)) is set
K20(NAT,NAT) is non trivial non finite set
K20(K20(NAT,NAT),NAT) is non trivial non finite set
K19(K20(K20(NAT,NAT),NAT)) is non trivial non finite set
K20(NAT,REAL) is set
K19(K20(NAT,REAL)) is set
3 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
Seg 1 is non empty trivial finite V31(1) Element of K19(NAT)
{1} is non empty trivial finite V28() V31(1) set
Seg 2 is non empty finite V31(2) Element of K19(NAT)
{1,2} is non empty finite V28() set
0 is Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite V28() V29() V31( {} ) FinSequence-membered V52() V53() complex ext-real non positive non negative Element of NAT
n is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of n is non empty set
0. n is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
the ZeroF of n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
T is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
dom T is finite Element of K19(NAT)
Sum T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
T | L is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (T | L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
len P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
dom P is finite Element of K19(NAT)
A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Seg (P + 1) is non empty finite V31(P + 1) V31(P + 1) Element of K19(NAT)
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
Seg P is finite V31(P) Element of K19(NAT)
P | (Seg P) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSubsequence-like finite-support Element of K19(K20(NAT, the carrier of n))
K20(NAT, the carrier of n) is non trivial non finite set
K19(K20(NAT, the carrier of n)) is non trivial non finite set
m is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
len m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom m is finite Element of K19(NAT)
P | P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
P /. (P + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
<*(P /. (P + 1))*> is Relation-like NAT -defined the carrier of n -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of n,K500( the carrier of n))
K500( the carrier of n) is functional non empty FinSequence-membered M28( the carrier of n)
m ^ <*(P /. (P + 1))*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
P . (P + 1) is set
<*(P . (P + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support set
m ^ <*(P . (P + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
P | A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
dom (P | A) is finite Element of K19(NAT)
Seg A is finite V31(A) Element of K19(NAT)
P | (Seg A) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSubsequence-like finite-support Element of K19(K20(NAT, the carrier of n))
dom (P | (Seg A)) is finite Element of K19(NAT)
p is set
s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(dom P) /\ (Seg A) is finite Element of K19(NAT)
p is set
(P | (Seg A)) . p is set
P . p is set
p is set
Sum (P | A) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P . p is set
m . p is set
m /. p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P /. p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum <*(P /. (P + 1))*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(Sum m) + (Sum <*(P /. (P + 1))*>) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(Sum m) + (P /. (P + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
m | A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (m | A) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P | A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (P | A) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P | A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (P | A) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P | A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (P | A) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
len P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom P is finite Element of K19(NAT)
A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Sum P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P | A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (P | A) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
len P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom P is finite Element of K19(NAT)
P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Sum P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P | P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (P | P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
len T is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is non empty Abelian add-associative right_zeroed addLoopStr
the carrier of n is non empty set
T is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum T is Element of the carrier of n
L is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Swap (T,L,P) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (Swap (T,L,P)) is Element of the carrier of n
len T is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
len T is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Seg (len T) is finite V31( len T) Element of K19(NAT)
dom T is finite Element of K19(NAT)
L -' 1 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
T | (L -' 1) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
T /. P is Element of the carrier of n
<*(T /. P)*> is Relation-like NAT -defined the carrier of n -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of n,K500( the carrier of n))
K500( the carrier of n) is functional non empty FinSequence-membered M28( the carrier of n)
(T | (L -' 1)) ^ <*(T /. P)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
P -' L is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(P -' L) -' 1 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
T /^ L is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
(T /^ L) | ((P -' L) -' 1) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1)) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
T /. L is Element of the carrier of n
<*(T /. L)*> is Relation-like NAT -defined the carrier of n -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of n,K500( the carrier of n))
(((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. L)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
T /^ P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
((((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. L)*>) ^ (T /^ P) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum ((((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. L)*>) is Element of the carrier of n
Sum (T /^ P) is Element of the carrier of n
(Sum ((((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. L)*>)) + (Sum (T /^ P)) is Element of the carrier of n
Sum (((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
Sum <*(T /. L)*> is Element of the carrier of n
(Sum (((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. L)*>) is Element of the carrier of n
((Sum (((T | (L -' 1)) ^ <*(T /. P)*>) ^ ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. L)*>)) + (Sum (T /^ P)) is Element of the carrier of n
Sum ((T | (L -' 1)) ^ <*(T /. P)*>) is Element of the carrier of n
Sum ((T /^ L) | ((P -' L) -' 1)) is Element of the carrier of n
(Sum ((T | (L -' 1)) ^ <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
((Sum ((T | (L -' 1)) ^ <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. L)*>) is Element of the carrier of n
(((Sum ((T | (L -' 1)) ^ <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. L)*>)) + (Sum (T /^ P)) is Element of the carrier of n
Sum (T | (L -' 1)) is Element of the carrier of n
Sum <*(T /. P)*> is Element of the carrier of n
(Sum (T | (L -' 1))) + (Sum <*(T /. P)*>) is Element of the carrier of n
((Sum (T | (L -' 1))) + (Sum <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
(((Sum (T | (L -' 1))) + (Sum <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. L)*>) is Element of the carrier of n
((((Sum (T | (L -' 1))) + (Sum <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. L)*>)) + (Sum (T /^ P)) is Element of the carrier of n
((Sum (T | (L -' 1))) + (Sum <*(T /. P)*>)) + (Sum <*(T /. L)*>) is Element of the carrier of n
(((Sum (T | (L -' 1))) + (Sum <*(T /. P)*>)) + (Sum <*(T /. L)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
((((Sum (T | (L -' 1))) + (Sum <*(T /. P)*>)) + (Sum <*(T /. L)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum (T /^ P)) is Element of the carrier of n
(Sum (T | (L -' 1))) + (Sum <*(T /. L)*>) is Element of the carrier of n
((Sum (T | (L -' 1))) + (Sum <*(T /. L)*>)) + (Sum <*(T /. P)*>) is Element of the carrier of n
(((Sum (T | (L -' 1))) + (Sum <*(T /. L)*>)) + (Sum <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
((((Sum (T | (L -' 1))) + (Sum <*(T /. L)*>)) + (Sum <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum (T /^ P)) is Element of the carrier of n
(T | (L -' 1)) ^ <*(T /. L)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum ((T | (L -' 1)) ^ <*(T /. L)*>) is Element of the carrier of n
(Sum ((T | (L -' 1)) ^ <*(T /. L)*>)) + (Sum <*(T /. P)*>) is Element of the carrier of n
((Sum ((T | (L -' 1)) ^ <*(T /. L)*>)) + (Sum <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
(((Sum ((T | (L -' 1)) ^ <*(T /. L)*>)) + (Sum <*(T /. P)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum (T /^ P)) is Element of the carrier of n
(Sum ((T | (L -' 1)) ^ <*(T /. L)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
((Sum ((T | (L -' 1)) ^ <*(T /. L)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. P)*>) is Element of the carrier of n
(((Sum ((T | (L -' 1)) ^ <*(T /. L)*>)) + (Sum ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. P)*>)) + (Sum (T /^ P)) is Element of the carrier of n
((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1)) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) is Element of the carrier of n
(Sum (((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. P)*>) is Element of the carrier of n
((Sum (((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1)))) + (Sum <*(T /. P)*>)) + (Sum (T /^ P)) is Element of the carrier of n
(((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. P)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum ((((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. P)*>) is Element of the carrier of n
(Sum ((((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. P)*>)) + (Sum (T /^ P)) is Element of the carrier of n
((((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. P)*>) ^ (T /^ P) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (((((T | (L -' 1)) ^ <*(T /. L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. P)*>) ^ (T /^ P)) is Element of the carrier of n
T . L is set
<*(T . L)*> is Relation-like NAT -defined Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support set
(T | (L -' 1)) ^ <*(T . L)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((T | (L -' 1)) ^ <*(T . L)*>) ^ ((T /^ L) | ((P -' L) -' 1)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
(((T | (L -' 1)) ^ <*(T . L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. P)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((((T | (L -' 1)) ^ <*(T . L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T /. P)*>) ^ (T /^ P) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
T . P is set
<*(T . P)*> is Relation-like NAT -defined Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support set
(((T | (L -' 1)) ^ <*(T . L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T . P)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((((T | (L -' 1)) ^ <*(T . L)*>) ^ ((T /^ L) | ((P -' L) -' 1))) ^ <*(T . P)*>) ^ (T /^ P) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
Swap (T,P,L) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
P -' 1 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
T | (P -' 1) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
T /. L is Element of the carrier of n
<*(T /. L)*> is Relation-like NAT -defined the carrier of n -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of n,K500( the carrier of n))
K500( the carrier of n) is functional non empty FinSequence-membered M28( the carrier of n)
(T | (P -' 1)) ^ <*(T /. L)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
L -' P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(L -' P) -' 1 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
T /^ P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
(T /^ P) | ((L -' P) -' 1) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1)) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
T /. P is Element of the carrier of n
<*(T /. P)*> is Relation-like NAT -defined the carrier of n -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of n,K500( the carrier of n))
(((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. P)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
T /^ L is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
((((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. P)*>) ^ (T /^ L) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (Swap (T,P,L)) is Element of the carrier of n
Sum ((((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. P)*>) is Element of the carrier of n
Sum (T /^ L) is Element of the carrier of n
(Sum ((((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. P)*>)) + (Sum (T /^ L)) is Element of the carrier of n
Sum (((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
Sum <*(T /. P)*> is Element of the carrier of n
(Sum (((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. P)*>) is Element of the carrier of n
((Sum (((T | (P -' 1)) ^ <*(T /. L)*>) ^ ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. P)*>)) + (Sum (T /^ L)) is Element of the carrier of n
Sum ((T | (P -' 1)) ^ <*(T /. L)*>) is Element of the carrier of n
Sum ((T /^ P) | ((L -' P) -' 1)) is Element of the carrier of n
(Sum ((T | (P -' 1)) ^ <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
((Sum ((T | (P -' 1)) ^ <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. P)*>) is Element of the carrier of n
(((Sum ((T | (P -' 1)) ^ <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. P)*>)) + (Sum (T /^ L)) is Element of the carrier of n
Sum (T | (P -' 1)) is Element of the carrier of n
Sum <*(T /. L)*> is Element of the carrier of n
(Sum (T | (P -' 1))) + (Sum <*(T /. L)*>) is Element of the carrier of n
((Sum (T | (P -' 1))) + (Sum <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
(((Sum (T | (P -' 1))) + (Sum <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. P)*>) is Element of the carrier of n
((((Sum (T | (P -' 1))) + (Sum <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. P)*>)) + (Sum (T /^ L)) is Element of the carrier of n
((Sum (T | (P -' 1))) + (Sum <*(T /. L)*>)) + (Sum <*(T /. P)*>) is Element of the carrier of n
(((Sum (T | (P -' 1))) + (Sum <*(T /. L)*>)) + (Sum <*(T /. P)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
((((Sum (T | (P -' 1))) + (Sum <*(T /. L)*>)) + (Sum <*(T /. P)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum (T /^ L)) is Element of the carrier of n
(Sum (T | (P -' 1))) + (Sum <*(T /. P)*>) is Element of the carrier of n
((Sum (T | (P -' 1))) + (Sum <*(T /. P)*>)) + (Sum <*(T /. L)*>) is Element of the carrier of n
(((Sum (T | (P -' 1))) + (Sum <*(T /. P)*>)) + (Sum <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
((((Sum (T | (P -' 1))) + (Sum <*(T /. P)*>)) + (Sum <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum (T /^ L)) is Element of the carrier of n
(T | (P -' 1)) ^ <*(T /. P)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum ((T | (P -' 1)) ^ <*(T /. P)*>) is Element of the carrier of n
(Sum ((T | (P -' 1)) ^ <*(T /. P)*>)) + (Sum <*(T /. L)*>) is Element of the carrier of n
((Sum ((T | (P -' 1)) ^ <*(T /. P)*>)) + (Sum <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
(((Sum ((T | (P -' 1)) ^ <*(T /. P)*>)) + (Sum <*(T /. L)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum (T /^ L)) is Element of the carrier of n
(Sum ((T | (P -' 1)) ^ <*(T /. P)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
((Sum ((T | (P -' 1)) ^ <*(T /. P)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. L)*>) is Element of the carrier of n
(((Sum ((T | (P -' 1)) ^ <*(T /. P)*>)) + (Sum ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. L)*>)) + (Sum (T /^ L)) is Element of the carrier of n
((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1)) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) is Element of the carrier of n
(Sum (((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. L)*>) is Element of the carrier of n
((Sum (((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1)))) + (Sum <*(T /. L)*>)) + (Sum (T /^ L)) is Element of the carrier of n
(((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. L)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum ((((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. L)*>) is Element of the carrier of n
(Sum ((((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. L)*>)) + (Sum (T /^ L)) is Element of the carrier of n
((((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. L)*>) ^ (T /^ L) is Relation-like NAT -defined the carrier of n -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum (((((T | (P -' 1)) ^ <*(T /. P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. L)*>) ^ (T /^ L)) is Element of the carrier of n
T . P is set
<*(T . P)*> is Relation-like NAT -defined Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support set
(T | (P -' 1)) ^ <*(T . P)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((T | (P -' 1)) ^ <*(T . P)*>) ^ ((T /^ P) | ((L -' P) -' 1)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
(((T | (P -' 1)) ^ <*(T . P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. L)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((((T | (P -' 1)) ^ <*(T . P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T /. L)*>) ^ (T /^ L) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
T . L is set
<*(T . L)*> is Relation-like NAT -defined Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support set
(((T | (P -' 1)) ^ <*(T . P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T . L)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((((T | (P -' 1)) ^ <*(T . P)*>) ^ ((T /^ P) | ((L -' P) -' 1))) ^ <*(T . L)*>) ^ (T /^ L) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
len T is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L + P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L + P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
A is set
dom P is Element of K19(n)
K19(n) is set
P . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(L . A) + (P . A) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
((L . A) + (P . A)) -' (L . A) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
T . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T . A) -' (L . A) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(L . A) + (P . A) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
((L . A) + (P . A)) -' (L . A) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom P is Element of K19(n)
n is set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is Relation-like Function-like set
dom P is set
A is set
P is Relation-like n -defined Function-like total set
rng P is set
dom P is Element of K19(n)
K19(n) is set
i is set
P . i is set
T . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . i),(L . i)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
support P is set
A is set
P . A is set
support T is finite set
support L is finite set
(support T) \/ (support L) is finite set
L . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . A),(L . A)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
A is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
dom A is Element of K19(n)
dom L is Element of K19(n)
dom T is Element of K19(n)
i is set
A . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . i),(L . i)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i is set
T . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
A . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . i),(L . i)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i is set
A . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . i),(L . i)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i is set
A . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . i),(L . i)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i is set
A . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . i),(L . i)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
A is set
dom P is Element of K19(n)
K19(n) is set
P . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . A),(L . A)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P . A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
dom P is Element of K19(n)
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
A is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
i is set
P . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
A . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
P . i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((A . i),(P . i)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((P . P),(P . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is set
n is set
n is set
n is set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,L) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(n,T,L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
P is set
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(n,T,L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
n is set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,L) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(n,T,L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
n is set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,L) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
T + L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
(n,T,L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T . P) + (L . P) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(T . P) + 0 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T . P) + (L . P) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
0 + (L . P) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
P is set
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
0 + (L . P) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is set
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T . P) + 0 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is set
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is set
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(T + L) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is set
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
Bags n is non empty set
Bags n is functional non empty Element of K19((Bags n))
K19((Bags n)) is set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
T + (EmptyBag n) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
n is set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,L) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(L . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,L,P) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,L,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
(n,L,T) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(n,L,P) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((L . P),(P . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
max ((L . P),(T . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,L,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,L,P) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,P) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
(n,T,P) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(n,L,P) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((L . P),(P . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(n,L,T) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((L . P),(T . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
max ((T . P),(P . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is set
T is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,P) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,L,P) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
T . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(n,L,P) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
(n,T,P) . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
P . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((T . P),(P . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
L . P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative V233() Element of NAT
max ((L . P),(P . P)) is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
K19((Bags n)) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V283() admissible Element of K19(K20((Bags n),(Bags n)))
L is functional non empty Element of K19((Bags n))
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric V181() V255() RelStr
MinElement (L,RelStr(# (Bags n),T #)) is Element of the carrier of RelStr(# (Bags n),T #)
the carrier of RelStr(# (Bags n),T #) is non empty set
field T is set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of K19(K20( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)))
K20( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) is set
K19(K20( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #))) is set
A is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
[A,A] is V21() set
i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
[i,i] is V21() set
[i,A] is V21() set
[A,i] is V21() set
n is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of n is non empty non trivial set
T is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
0. n is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
the ZeroF of n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- (- T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
n is set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right-distributive left-distributive distributive right_zeroed left_zeroed doubleLoopStr
the carrier of T is non empty set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
P is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
Support L is functional Element of K19((Bags n))
K19((Bags n)) is set
Support (P * L) is functional Element of K19((Bags n))
the Relation-like n -defined Function-like Element of Support (P * L) is Relation-like n -defined Function-like Element of Support (P * L)
i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(P * L) . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
L . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . i) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
0. T is zero left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (0. T) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support L is functional Element of K19((Bags n))
K19((Bags n)) is set
A is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
{A} is functional non empty trivial finite V31(1) set
A is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
{A} is functional non empty trivial finite V31(1) set
0. T is zero left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support (P * L) is functional Element of K19((Bags n))
the Relation-like n -defined Function-like Element of Support (P * L) is Relation-like n -defined Function-like Element of Support (P * L)
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(P * L) . p is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
L . p is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . p) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
0. T is zero left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
m is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
L . m is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
(P * L) . m is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . m) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
L . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . i) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support (P * L) is functional Element of K19((Bags n))
the Relation-like n -defined Function-like Element of Support (P * L) is Relation-like n -defined Function-like Element of Support (P * L)
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(P * L) . p is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
L . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . i) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
m is set
Support (P * L) is functional Element of K19((Bags n))
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(P * L) . p is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
{i} is functional non empty trivial finite V31(1) set
m is set
(P * L) . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
L . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . i) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support (P * L) is functional Element of K19((Bags n))
{i} is functional non empty trivial finite V31(1) set
L . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . i) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support (P * L) is functional Element of K19((Bags n))
{i} is functional non empty trivial finite V31(1) set
0. T is zero left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support (P * L) is functional Element of K19((Bags n))
0. T is zero left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support (P * L) is functional Element of K19((Bags n))
Support L is functional Element of K19((Bags n))
K19((Bags n)) is set
Support L is functional Element of K19((Bags n))
K19((Bags n)) is set
A is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
{A} is functional non empty trivial finite V31(1) set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right-distributive left-distributive distributive right_zeroed domRing-like left_zeroed doubleLoopStr
the carrier of T is non empty non trivial set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) non-zero V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
P is non zero left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
Support L is functional Element of K19((Bags n))
K19((Bags n)) is set
the Relation-like n -defined Function-like Element of Support L is Relation-like n -defined Function-like Element of Support L
0_ (n,T) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like Constant V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
L . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
0. T is zero left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
P * (L . i) is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
(P * L) . i is left_add-cancelable right_add-cancelable add-cancelable Element of the carrier of T
Support (P * L) is functional Element of K19((Bags n))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty right-distributive right_zeroed doubleLoopStr
the carrier of T is non empty set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
L + P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P *' (L + P) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P *' L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P *' P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
(P *' L) + (P *' P) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
m is set
dom (P *' (L + P)) is functional Element of K19((Bags n))
K19((Bags n)) is set
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (L + P)) . p is Element of the carrier of T
p -' P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(L + P) . (p -' P) is Element of the carrier of T
L . (p -' P) is Element of the carrier of T
P . (p -' P) is Element of the carrier of T
(L . (p -' P)) + (P . (p -' P)) is Element of the carrier of T
(P *' L) . p is Element of the carrier of T
((P *' L) . p) + (P . (p -' P)) is Element of the carrier of T
(P *' P) . p is Element of the carrier of T
((P *' L) . p) + ((P *' P) . p) is Element of the carrier of T
((P *' L) + (P *' P)) . p is Element of the carrier of T
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (L + P)) . p is Element of the carrier of T
0. T is zero Element of the carrier of T
the ZeroF of T is Element of the carrier of T
(0. T) + (0. T) is Element of the carrier of T
(P *' L) . p is Element of the carrier of T
((P *' L) . p) + (0. T) is Element of the carrier of T
(P *' P) . p is Element of the carrier of T
((P *' L) . p) + ((P *' P) . p) is Element of the carrier of T
((P *' L) + (P *' P)) . p is Element of the carrier of T
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (L + P)) . p is Element of the carrier of T
((P *' L) + (P *' P)) . p is Element of the carrier of T
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (L + P)) . p is Element of the carrier of T
((P *' L) + (P *' P)) . p is Element of the carrier of T
(P *' (L + P)) . m is set
((P *' L) + (P *' P)) . m is set
dom ((P *' L) + (P *' P)) is functional Element of K19((Bags n))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of T is non empty set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
- L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P *' (- L) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P *' L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
- (P *' L) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
i is set
dom (P *' (- L)) is functional Element of K19((Bags n))
K19((Bags n)) is set
m is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' L) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
m -' P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
L . (m -' P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P *' (- L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- L) . (m -' P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (L . (m -' P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (P *' L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
m is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' L) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
0. T is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P *' (- L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (0. T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (P *' L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
m is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (- L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (P *' L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
m is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (- L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (P *' L)) . m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P *' (- L)) . i is set
(- (P *' L)) . i is set
dom (- (P *' L)) is functional Element of K19((Bags n))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty right_add-cancelable right-distributive left_zeroed doubleLoopStr
the carrier of T is non empty set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P *' L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P is right_add-cancelable Element of the carrier of T
P * L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P *' (P * L) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P * (P *' L) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
m is set
dom (P *' (P * L)) is functional Element of K19((Bags n))
K19((Bags n)) is set
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (P * L)) . p is right_add-cancelable Element of the carrier of T
p -' P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P * L) . (p -' P) is right_add-cancelable Element of the carrier of T
L . (p -' P) is right_add-cancelable Element of the carrier of T
P * (L . (p -' P)) is right_add-cancelable Element of the carrier of T
(P *' L) . p is right_add-cancelable Element of the carrier of T
P * ((P *' L) . p) is right_add-cancelable Element of the carrier of T
(P * (P *' L)) . p is right_add-cancelable Element of the carrier of T
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (P * L)) . p is right_add-cancelable Element of the carrier of T
0. T is zero right_add-cancelable Element of the carrier of T
the ZeroF of T is right_add-cancelable Element of the carrier of T
P * (0. T) is right_add-cancelable Element of the carrier of T
(P *' L) . p is right_add-cancelable Element of the carrier of T
P * ((P *' L) . p) is right_add-cancelable Element of the carrier of T
(P * (P *' L)) . p is right_add-cancelable Element of the carrier of T
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (P * L)) . p is right_add-cancelable Element of the carrier of T
(P * (P *' L)) . p is right_add-cancelable Element of the carrier of T
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P *' (P * L)) . p is right_add-cancelable Element of the carrier of T
(P * (P *' L)) . p is right_add-cancelable Element of the carrier of T
(P *' (P * L)) . m is set
(P * (P *' L)) . m is set
dom (P * (P *' L)) is functional Element of K19((Bags n))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty right-distributive doubleLoopStr
the carrier of T is non empty set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
L + P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P is Element of the carrier of T
P * (L + P) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P * L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
P * P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
(P * L) + (P * P) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
m is set
dom (P * (L + P)) is functional Element of K19((Bags n))
K19((Bags n)) is set
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(P * (L + P)) . p is Element of the carrier of T
(L + P) . p is Element of the carrier of T
P * ((L + P) . p) is Element of the carrier of T
L . p is Element of the carrier of T
P . p is Element of the carrier of T
(L . p) + (P . p) is Element of the carrier of T
P * ((L . p) + (P . p)) is Element of the carrier of T
P * (L . p) is Element of the carrier of T
P * (P . p) is Element of the carrier of T
(P * (L . p)) + (P * (P . p)) is Element of the carrier of T
(P * L) . p is Element of the carrier of T
((P * L) . p) + (P * (P . p)) is Element of the carrier of T
(P * P) . p is Element of the carrier of T
((P * L) . p) + ((P * P) . p) is Element of the carrier of T
((P * L) + (P * P)) . p is Element of the carrier of T
(P * (L + P)) . m is set
((P * L) + (P * P)) . m is set
dom ((P * L) + (P * P)) is functional Element of K19((Bags n))
n is set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non empty set
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L | (n,T) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like Constant V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
- (L | (n,T)) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) Element of K19(K20((Bags n), the carrier of T))
- L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- L) | (n,T) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like Constant V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
P is set
dom ((- L) | (n,T)) is functional Element of K19((Bags n))
K19((Bags n)) is set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(L | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((L | (n,T)) . P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- L) | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
0. T is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (0. T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((L | (n,T)) . P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- L) | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(L | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((L | (n,T)) . P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- L) | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(L | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((L | (n,T)) . P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- L) | (n,T)) . P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- L) | (n,T)) . P is set
(- (L | (n,T))) . P is set
dom (- (L | (n,T))) is functional Element of K19((Bags n))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is set
A is Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (A,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
m is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (A,T)
m . 1 is set
len m is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
m . (len m) is set
(len m) - 1 is V52() V53() complex ext-real set
p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
m . p is set
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
Seg (len m) is non empty finite V31( len m) Element of K19(NAT)
dom m is finite Element of K19(NAT)
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
[(m . p),P] is V21() set
g is set
c₁₂ is set
[g,c₁₂] is V21() set
n is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V283() admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
A is set
i is set
[A,i] is V21() set
m is set
[A,m] is V21() set
p is set
s is set
[p,s] is V21() set
{(0_ (n,L))} is functional non empty trivial finite V31(1) Element of K19( the carrier of (Polynom-Ring (n,L)))
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P is set
R is set
[P,R] is V21() set
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Support f9 is functional finite Element of K19((Bags n))
K19((Bags n)) is set
HT (c₁₂,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
Q is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Q *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ - (Q *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((Q *' c₁₈),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
h9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Support A is functional finite Element of K19((Bags n))
g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 *' g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ - (g2 *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((g2 *' g2),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
c₁₂ - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (u,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (c₁₈,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(HT (u,T)) + (HT (c₁₈,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Support (Q *' c₁₈) is functional finite Element of K19((Bags n))
A9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (A9,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (g2,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(HT (A9,T)) + (HT (g2,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Support (g2 *' g2) is functional finite Element of K19((Bags n))
HC (g2,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
u *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (u *' c₁₈) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (- (u *' c₁₈)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A - f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (A9 *' g2) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ + (- (A9 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ - (u *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ + (- (A9 *' g2))) - (c₁₂ - (u *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ + (- (u *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ + (- (A9 *' g2))) - (c₁₂ + (- (u *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (c₁₂ + (- (u *' c₁₈))) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ + (- (A9 *' g2))) + (- (c₁₂ + (- (u *' c₁₈)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- c₁₂ is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- c₁₂) + (- (- (u *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ + (- (A9 *' g2))) + ((- c₁₂) + (- (- (u *' c₁₈)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- c₁₂) + (u *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (A9 *' g2)) + ((- c₁₂) + (u *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ + ((- (A9 *' g2)) + ((- c₁₂) + (u *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (A9 *' g2)) + (u *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- c₁₂) + ((- (A9 *' g2)) + (u *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ + ((- c₁₂) + ((- (A9 *' g2)) + (u *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ + (- c₁₂) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ + (- c₁₂)) + ((- (A9 *' g2)) + (u *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) + ((- (A9 *' g2)) + (u *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(u *' c₁₈) + (- (A9 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Q *' c₁₈) - (g2 *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (c₁₈,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (Q *' c₁₈) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (- (Q *' c₁₈)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (A9 *' c₁₈) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(u *' c₁₈) + (- (A9 *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₈ *' u is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- A9 is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- A9) *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₈ *' u) + ((- A9) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u + (- A9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(u + (- A9)) *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 *' g2) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((Q *' c₁₈) - (g2 *' g2)) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (g2 *' g2) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Q *' c₁₈) + (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) + (- (g2 *' g2))) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(Q *' c₁₈) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (g2 *' g2)) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((Q *' c₁₈) . (HT ((Q *' c₁₈),T))) + ((- (g2 *' g2)) . (HT ((Q *' c₁₈),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((g2 *' g2) . (HT ((Q *' c₁₈),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((Q *' c₁₈) . (HT ((Q *' c₁₈),T))) + (- ((g2 *' g2) . (HT ((Q *' c₁₈),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((Q *' c₁₈) . (HT ((Q *' c₁₈),T))) + (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC ((Q *' c₁₈),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support ((Q *' c₁₈) - (g2 *' g2)) is functional finite Element of K19((Bags n))
(HT (u,T)) *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(((Q *' c₁₈) - (g2 *' g2)) . (HT ((Q *' c₁₈),T))) / (HC (c₁₈,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((((Q *' c₁₈) - (g2 *' g2)) . (HT ((Q *' c₁₈),T))) / (HC (c₁₈,T))) * ((HT (u,T)) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - (((((Q *' c₁₈) - (g2 *' g2)) . (HT ((Q *' c₁₈),T))) / (HC (c₁₈,T))) * ((HT (u,T)) *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (u,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (u,T)) * (HC (c₁₈,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (u,T)) * (HC (c₁₈,T))) / (HC (c₁₈,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (u,T)) * (HC (c₁₈,T))) / (HC (c₁₈,T))) * ((HT (u,T)) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - ((((HC (u,T)) * (HC (c₁₈,T))) / (HC (c₁₈,T))) * ((HT (u,T)) *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (c₁₈,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (u,T)) * (HC (c₁₈,T))) * ((HC (c₁₈,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (u,T)) * (HC (c₁₈,T))) * ((HC (c₁₈,T)) ")) * ((HT (u,T)) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - ((((HC (u,T)) * (HC (c₁₈,T))) * ((HC (c₁₈,T)) ")) * ((HT (u,T)) *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (c₁₈,T)) * ((HC (c₁₈,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (u,T)) * ((HC (c₁₈,T)) * ((HC (c₁₈,T)) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (u,T)) * ((HC (c₁₈,T)) * ((HC (c₁₈,T)) "))) * ((HT (u,T)) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - (((HC (u,T)) * ((HC (c₁₈,T)) * ((HC (c₁₈,T)) "))) * ((HT (u,T)) *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
1. L is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the OneF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (u,T)) * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (u,T)) * (1. L)) * ((HT (u,T)) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - (((HC (u,T)) * (1. L)) * ((HT (u,T)) *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (u,T)) * ((HT (u,T)) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - ((HC (u,T)) * ((HT (u,T)) *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (u,T)),(HT (u,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (u,T)),(HT (u,T)))) *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - ((Monom ((HC (u,T)),(HT (u,T)))) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
coefficient u is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((coefficient u),(HT (u,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((coefficient u),(HT (u,T)))) *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - ((Monom ((coefficient u),(HT (u,T)))) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
term u is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom ((coefficient u),(term u)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((coefficient u),(term u))) *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - ((Monom ((coefficient u),(term u))) *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) - (g2 *' g2)) - (Q *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) + (- (g2 *' g2))) - (Q *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) + (- (g2 *' g2))) + (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Q *' c₁₈) + (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Q *' c₁₈) + (- (Q *' c₁₈))) + (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) + (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
[((Q *' c₁₈) - (g2 *' g2)),(- (g2 *' g2))] is V21() set
- A9 is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- A9) *' g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Q *' c₁₈) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 *' g2) - (Q *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 *' g2) + (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) + (- (Q *' c₁₈))) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 *' g2) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (Q *' c₁₈)) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g2 *' g2) . (HT ((g2 *' g2),T))) + ((- (Q *' c₁₈)) . (HT ((g2 *' g2),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((Q *' c₁₈) . (HT ((g2 *' g2),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g2 *' g2) . (HT ((g2 *' g2),T))) + (- ((Q *' c₁₈) . (HT ((g2 *' g2),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g2 *' g2) . (HT ((g2 *' g2),T))) + (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC ((g2 *' g2),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support ((g2 *' g2) - (Q *' c₁₈)) is functional finite Element of K19((Bags n))
- (0_ (n,L)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
hh is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
gg + (0. (Polynom-Ring (n,L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- (0_ (n,L))) + (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- ((g2 *' g2) + (- (Q *' c₁₈))) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (g2 *' g2) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (g2 *' g2)) + (- (- (Q *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Q *' c₁₈) + (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (0. (Polynom-Ring (n,L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(HT (A9,T)) *' g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(((g2 *' g2) - (Q *' c₁₈)) . (HT ((g2 *' g2),T))) / (HC (g2,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((((g2 *' g2) - (Q *' c₁₈)) . (HT ((g2 *' g2),T))) / (HC (g2,T))) * ((HT (A9,T)) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - (((((g2 *' g2) - (Q *' c₁₈)) . (HT ((g2 *' g2),T))) / (HC (g2,T))) * ((HT (A9,T)) *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A9,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A9,T)) * (HC (g2,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (A9,T)) * (HC (g2,T))) / (HC (g2,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (A9,T)) * (HC (g2,T))) / (HC (g2,T))) * ((HT (A9,T)) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - ((((HC (A9,T)) * (HC (g2,T))) / (HC (g2,T))) * ((HT (A9,T)) *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (g2,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (A9,T)) * (HC (g2,T))) * ((HC (g2,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (A9,T)) * (HC (g2,T))) * ((HC (g2,T)) ")) * ((HT (A9,T)) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - ((((HC (A9,T)) * (HC (g2,T))) * ((HC (g2,T)) ")) * ((HT (A9,T)) *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (g2,T)) * ((HC (g2,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A9,T)) * ((HC (g2,T)) * ((HC (g2,T)) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (A9,T)) * ((HC (g2,T)) * ((HC (g2,T)) "))) * ((HT (A9,T)) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - (((HC (A9,T)) * ((HC (g2,T)) * ((HC (g2,T)) "))) * ((HT (A9,T)) *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
1. L is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the OneF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A9,T)) * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (A9,T)) * (1. L)) * ((HT (A9,T)) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - (((HC (A9,T)) * (1. L)) * ((HT (A9,T)) *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (A9,T)) * ((HT (A9,T)) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - ((HC (A9,T)) * ((HT (A9,T)) *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (A9,T)),(HT (A9,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (A9,T)),(HT (A9,T)))) *' g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - ((Monom ((HC (A9,T)),(HT (A9,T)))) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
coefficient A9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((coefficient A9),(HT (A9,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((coefficient A9),(HT (A9,T)))) *' g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - ((Monom ((coefficient A9),(HT (A9,T)))) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
term A9 is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom ((coefficient A9),(term A9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((coefficient A9),(term A9))) *' g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - ((Monom ((coefficient A9),(term A9))) *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) - (Q *' c₁₈)) - (g2 *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) + (- (Q *' c₁₈))) - (g2 *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) + (- (Q *' c₁₈))) + (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 *' g2) + (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 *' g2) + (- (g2 *' g2))) + (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) + (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
[((g2 *' g2) - (Q *' c₁₈)),(- (Q *' c₁₈))] is V21() set
1_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (1_ (n,L)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(1. L) | (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- ((1. L) | (n,L)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (1. L) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (1. L)) | (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- u is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- u) *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (1_ (n,L))) *' ((g2 *' g2) - (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (1_ (n,L))) *' (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (1_ (n,L))) *' ((g2 *' g2) + (- (Q *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (1_ (n,L))) *' (g2 *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (1_ (n,L))) *' (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((- (1_ (n,L))) *' (g2 *' g2)) + ((- (1_ (n,L))) *' (- (Q *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(1_ (n,L)) *' (g2 *' g2) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- ((1_ (n,L)) *' (g2 *' g2)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- ((1_ (n,L)) *' (g2 *' g2))) + ((- (1_ (n,L))) *' (- (Q *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(1_ (n,L)) *' (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((1_ (n,L)) *' (- (g2 *' g2))) + ((- (1_ (n,L))) *' (- (Q *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(1_ (n,L)) *' (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- ((1_ (n,L)) *' (- (Q *' c₁₈))) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((1_ (n,L)) *' (- (g2 *' g2))) + (- ((1_ (n,L)) *' (- (Q *' c₁₈)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(1_ (n,L)) *' (- (- (Q *' c₁₈))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((1_ (n,L)) *' (- (g2 *' g2))) + ((1_ (n,L)) *' (- (- (Q *' c₁₈)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(1_ (n,L)) *' (Q *' c₁₈) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(- (g2 *' g2)) + ((1_ (n,L)) *' (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ - (g2 *' g2)) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (g2 *' g2) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ + (- (g2 *' g2)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ + (- (g2 *' g2))) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
c₁₂ . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (g2 *' g2)) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(c₁₂ . (HT ((g2 *' g2),T))) + ((- (g2 *' g2)) . (HT ((g2 *' g2),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 *' g2) . (HT ((g2 *' g2),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((g2 *' g2) . (HT ((g2 *' g2),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(c₁₂ . (HT ((g2 *' g2),T))) + (- ((g2 *' g2) . (HT ((g2 *' g2),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (- ((g2 *' g2) . (HT ((g2 *' g2),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(c₁₂ - (Q *' c₁₈)) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
c₁₂ + (- (Q *' c₁₈)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(c₁₂ + (- (Q *' c₁₈))) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
c₁₂ . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (Q *' c₁₈)) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(c₁₂ . (HT ((Q *' c₁₈),T))) + ((- (Q *' c₁₈)) . (HT ((Q *' c₁₈),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(Q *' c₁₈) . (HT ((Q *' c₁₈),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((Q *' c₁₈) . (HT ((Q *' c₁₈),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(c₁₂ . (HT ((Q *' c₁₈),T))) + (- ((Q *' c₁₈) . (HT ((Q *' c₁₈),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (- ((Q *' c₁₈) . (HT ((Q *' c₁₈),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC ((Q *' c₁₈),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC ((g2 *' g2),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HM ((Q *' c₁₈),T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC ((g2 *' g2),T)),(HT ((g2 *' g2),T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM ((g2 *' g2),T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (P,T)),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of n is non empty set
K19( the carrier of n) is set
T is Element of K19( the carrier of n)
T -Ideal is non empty add-closed left-ideal right-ideal Element of K19( the carrier of n)
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
<*L*> is Relation-like NAT -defined the carrier of n -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of n,K500( the carrier of n))
K500( the carrier of n) is functional non empty FinSequence-membered M28( the carrier of n)
A is set
dom <*L*> is non empty trivial finite V31(1) Element of K19(NAT)
<*L*> /. A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
<*L*> . 1 is set
1. n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
the OneF of n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(1. n) * L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
((1. n) * L) * (1. n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is non empty Element of K19( the carrier of n)
A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of P
Sum A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P - P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
A - i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- P is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
p + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- P) + P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
P + (- P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A + (- i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
P is Element of K19( the carrier of (Polynom-Ring (n,L)))
P -Ideal is non empty add-closed left-ideal right-ideal Element of K19( the carrier of (Polynom-Ring (n,L)))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,P,A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (P,T)),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (A,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) *' P)) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) *' A)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (A,T)),(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
c₁₂ is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R * c₁₂ is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
P * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(P * g) - (R * c₁₂) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Monom ((HC (A,T)),(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Monom ((HC (A,T)),(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))))) *' P) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) *' A)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Monom ((HC (A,T)),(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))))) *' P) - ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,P,P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (P,T)),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC ((0_ (n,L)),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC ((Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient (Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' (0_ (n,L))) - ((HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - ((HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - ((Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - ((0_ (n,L)) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC ((0_ (n,L)),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC ((Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient (Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) - ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' (0_ (n,L))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Monom ((HC ((0_ (n,L)),T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((0_ (n,L)) *' P) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
term P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom ((coefficient P),(term P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(term P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(HT (P,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
coefficient P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
term P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom ((coefficient P),(term P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(term P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(HT (P,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom (((HC (P,T)) * (HC (P,T))),((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) + (HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom (((HC (P,T)) * (HC (P,T))),(n,(HT (P,T)),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom (((HC (P,T)) * (HC (P,T))),((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) + (HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,P,(0_ (n,L))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT ((0_ (n,L)),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (P,T)),(HT ((0_ (n,L)),T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC ((0_ (n,L)),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT ((0_ (n,L)),T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT ((0_ (n,L)),T))) *' (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT ((0_ (n,L)),T))) *' (0_ (n,L))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P)) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT ((0_ (n,L)),T))) *' (0_ (n,L)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,(0_ (n,L)),P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(HT ((0_ (n,L)),T)),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT ((0_ (n,L)),T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT ((0_ (n,L)),T))) *' (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT ((0_ (n,L)),T))) *' (0_ (n,L))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC ((0_ (n,L)),T)) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT ((0_ (n,L)),T))) *' (0_ (n,L)))) - ((HC ((0_ (n,L)),T)) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT ((0_ (n,L)),T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT ((0_ (n,L)),T))))) *' (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P)) - ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT ((0_ (n,L)),T))))) *' (0_ (n,L))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC ((0_ (n,L)),T)) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0. L) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((0. L) * ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0. L) | (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((0. L) | (n,L)) *' ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(((0. L) | (n,L)) *' ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) *' ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((0_ (n,L)) *' ((n,(n,(HT (P,T)),(HT ((0_ (n,L)),T))),(HT (P,T))) *' P)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((HC (P,T)),(n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT ((0_ (n,L)),T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((HC (P,T)),(n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT ((0_ (n,L)),T))))) *' (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Monom ((HC (P,T)),(n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT ((0_ (n,L)),T))))) *' (0_ (n,L))) - ((HC ((0_ (n,L)),T)) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - ((HC ((0_ (n,L)),T)) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0. L) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - ((0. L) * ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((0. L) | (n,L)) *' ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - (((0. L) | (n,L)) *' ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) *' ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(0_ (n,L)) - ((0_ (n,L)) *' ((n,(n,(HT ((0_ (n,L)),T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,P,P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (P,T)),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((n,T,L,P,P),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
term (Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
HC ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient (Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T)) * (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(coefficient (Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))))) * (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(HT ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T)) + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
term (Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
HC ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient (Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support (n,T,L,P,P) is functional finite Element of K19((Bags n))
K19((Bags n)) is set
HC (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T)) * (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(coefficient (Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T)))))) * (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))) *' P),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(HT ((Monom ((HC (P,T)),(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))))),T)) + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,T,L,P,P) . (n,(HT (P,T)),(HT (P,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) + (- ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) + (- ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)))) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P))) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T))) + ((- ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P))) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T))) + (- (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)) + (- (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) . (HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (HC (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)) + (- (HC (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
max ((HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)),(HT (((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)),T)),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HC (P,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,P,P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(HT (P,T)),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (P,T))),(HT (P,T))) *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(HT (P,T)) + i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
i *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (P,T)) * P) . (HT (P,T))) / (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((((HC (P,T)) * P) . (HT (P,T))) / (HC (P,T))) * (i *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) - (((((HC (P,T)) * P) . (HT (P,T))) / (HC (P,T))) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support P is functional finite Element of K19((Bags n))
K19((Bags n)) is set
Support ((HC (P,T)) * P) is functional finite Element of K19((Bags n))
HT (((HC (P,T)) * P),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
P . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * (P . (HT (P,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (P,T)) * (P . (HT (P,T)))) / (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (P,T)) * (P . (HT (P,T)))) / (HC (P,T))) * (i *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) - ((((HC (P,T)) * (P . (HT (P,T)))) / (HC (P,T))) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (P,T)) * (HC (P,T))) / (HC (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (P,T)) * (HC (P,T))) / (HC (P,T))) * (i *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) - ((((HC (P,T)) * (HC (P,T))) / (HC (P,T))) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (P,T)) * (HC (P,T))) * ((HC (P,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (P,T)) * (HC (P,T))) * ((HC (P,T)) ")) * (i *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) - ((((HC (P,T)) * (HC (P,T))) * ((HC (P,T)) ")) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * ((HC (P,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((HC (P,T)) * ((HC (P,T)) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (P,T)) * ((HC (P,T)) * ((HC (P,T)) "))) * (i *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) - (((HC (P,T)) * ((HC (P,T)) * ((HC (P,T)) "))) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
1. L is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the OneF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (P,T)) * (1. L)) * (i *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) - (((HC (P,T)) * (1. L)) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * (i *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * P) - ((HC (P,T)) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(EmptyBag n) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * ((EmptyBag n) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((EmptyBag n) *' P)) - ((HC (P,T)) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(HT (P,T)),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(HT (P,T)),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HC (P,T)) * ((n,(HT (P,T)),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (P,T)) * ((n,(HT (P,T)),(HT (P,T))) *' P)) - ((HC (P,T)) * (i *' P)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V283() admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,A,i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (A,T)),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A)) - ((HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is set
[(0_ (n,L)),i] is V21() set
m is set
p is set
[m,p] is V21() set
{(0_ (n,L))} is functional non empty trivial finite V31(1) Element of K19( the carrier of (Polynom-Ring (n,L)))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,i,m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (m,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (i,T)),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (m,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i)) - ((HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A -Ideal is non empty add-closed left-ideal right-ideal Element of K19( the carrier of (Polynom-Ring (n,L)))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,i,m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (m,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (i,T)),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (m,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i)) - ((HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V283() admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,A,i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (A,T)),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A)) - ((HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
field (PolyRedRel (P,T)) is set
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,A,i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (A,T)),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A)) - ((HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
field (PolyRedRel (P,T)) is set
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,A,i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (A,T)),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A)) - ((HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
field (PolyRedRel (P,T)) is set
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,A,i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (A,T)),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A)) - ((HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
field (PolyRedRel (P,T)) is set
m is set
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,A,i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (A,T)),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (i,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (A,T))) *' A)) - ((HC (A,T)) * ((n,(n,(HT (A,T)),(HT (i,T))),(HT (i,T))) *' i)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V283() admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
P is Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM ((g *' P),T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM ((c₁₂ *' A),T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g *' P) - (c₁₂ *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient c₁₂ is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
term g is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
term c₁₂ is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g *' f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC ((g *' f9),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HM ((g *' f9),T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
coefficient (HM ((g *' f9),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ *' g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC ((c₁₂ *' g9),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (g,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g *' f9) - (c₁₂ *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (c₁₂,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g *' f9) - (c₁₂ *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h9 is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,(HT (P,T)),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
h9 is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(HT (P,T)) + h9 is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
HC (c₁₂,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (g,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Q is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(term g) + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom ((g2 * Q),((term g) + (HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom (g2,(term g)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom (Q,(HT (P,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom (g2,(term g))) *' (Monom (Q,(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u9 *' (Monom (Q,(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM (u9,T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HM (u9,T)) *' (Monom (Q,(HT (P,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM (f9,T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HM (u9,T)) *' (HM (f9,T)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u *' g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM ((u *' g9),T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM (u,T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HM (g9,T) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HM (u,T)) *' (HM (g9,T)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom (h9,(HT (A,T))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(HM (u,T)) *' (Monom (h9,(HT (A,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u *' (Monom (h9,(HT (A,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom (g2,(term c₁₂)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom (g2,(term c₁₂))) *' (Monom (h9,(HT (A,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(term c₁₂) + (HT (A,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
Monom ((g2 * h9),((term c₁₂) + (HT (A,T)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
coefficient (Monom ((g2 * h9),((term c₁₂) + (HT (A,T))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * Q) / h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h9 " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * h9) * (h9 ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h9 * (h9 ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * (h9 * (h9 ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
1. L is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the OneF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 / Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g2 * Q) / h9) / Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * Q) * (h9 ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g2 * Q) * (h9 ")) / Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Q " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g2 * Q) * (h9 ")) * (Q ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * (h9 ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * (h9 ")) * Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g2 * (h9 ")) * Q) * (Q ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Q * (Q ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * (h9 ")) * (Q * (Q ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * (h9 ")) * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 / h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
term (Monom ((g2 * h9),((term c₁₂) + (HT (A,T))))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
A9 is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(HT (P,T)),(HT (A,T))) + A9 is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
A9 + h9 is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(A9 + h9) + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
((A9 + h9) + (HT (P,T))) -' (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
hh is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(HT (A,T)) + hh is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
A9 + hh is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(A9 + hh) + (HT (A,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
((A9 + hh) + (HT (A,T))) -' (HT (A,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (f9,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (f9,T)),(HT (g9,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (f9,T)),(HT (g9,T))),(HT (g9,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(g2 / Q) * Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * (Q ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * (Q ")) * Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(Q ") * Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * ((Q ") * Q) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,(n,(HT (f9,T)),(HT (g9,T))),(HT (f9,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(g2 / h9) * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g2 * (h9 ")) * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h9 ") * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * ((h9 ") * h9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g2 * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
u9 *' f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(u9 *' f9) - (u *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom (g2,(term g))) *' f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Monom (g2,(term g))) *' f9) - (u *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom (g2,(term c₁₂))) *' g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((Monom (g2,(term g))) *' f9) - ((Monom (g2,(term c₁₂))) *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(A9 + h9) *' f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 * ((A9 + h9) *' f9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom (g2,(A9 + hh)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom (g2,(A9 + hh))) *' g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 * ((A9 + h9) *' f9)) - ((Monom (g2,(A9 + hh))) *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
h9 *' f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' (h9 *' f9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 * (A9 *' (h9 *' f9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 * (A9 *' (h9 *' f9))) - ((Monom (g2,(A9 + hh))) *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(A9 + hh) *' g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 * ((A9 + hh) *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 * (A9 *' (h9 *' f9))) - (g2 * ((A9 + hh) *' g9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
hh *' g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' (hh *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 * (A9 *' (hh *' g9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 * (A9 *' (h9 *' f9))) - (g2 * (A9 *' (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (g2 * (A9 *' (hh *' g9))) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 * (A9 *' (h9 *' f9))) + (- (g2 * (A9 *' (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (A9 *' (hh *' g9)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g2 * (- (A9 *' (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 * (A9 *' (h9 *' f9))) + (g2 * (- (A9 *' (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 / h9) * h9) * (A9 *' (h9 *' f9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 / Q) * Q) * (- (A9 *' (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(((g2 / h9) * h9) * (A9 *' (h9 *' f9))) + (((g2 / Q) * Q) * (- (A9 *' (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (hh *' g9) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' (- (hh *' g9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 / Q) * Q) * (A9 *' (- (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(((g2 / h9) * h9) * (A9 *' (h9 *' f9))) + (((g2 / Q) * Q) * (A9 *' (- (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Q * (A9 *' (- (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * (Q * (A9 *' (- (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(((g2 / h9) * h9) * (A9 *' (h9 *' f9))) + ((g2 / h9) * (Q * (A9 *' (- (hh *' g9))))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
h9 * (A9 *' (h9 *' f9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * (h9 * (A9 *' (h9 *' f9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((g2 / h9) * (h9 * (A9 *' (h9 *' f9)))) + ((g2 / h9) * (Q * (A9 *' (- (hh *' g9))))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(h9 * (A9 *' (h9 *' f9))) + (Q * (A9 *' (- (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * ((h9 * (A9 *' (h9 *' f9))) + (Q * (A9 *' (- (hh *' g9))))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Q * (- (hh *' g9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' (Q * (- (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(h9 * (A9 *' (h9 *' f9))) + (A9 *' (Q * (- (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * ((h9 * (A9 *' (h9 *' f9))) + (A9 *' (Q * (- (hh *' g9))))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Q * (hh *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
- (Q * (hh *' g9)) is Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like non empty total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' (- (Q * (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(h9 * (A9 *' (h9 *' f9))) + (A9 *' (- (Q * (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * ((h9 * (A9 *' (h9 *' f9))) + (A9 *' (- (Q * (hh *' g9))))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
h9 * (h9 *' f9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' (h9 * (h9 *' f9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(A9 *' (h9 * (h9 *' f9))) + (A9 *' (- (Q * (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * ((A9 *' (h9 * (h9 *' f9))) + (A9 *' (- (Q * (hh *' g9))))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(h9 * (h9 *' f9)) + (- (Q * (hh *' g9))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' ((h9 * (h9 *' f9)) + (- (Q * (hh *' g9)))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * (A9 *' ((h9 * (h9 *' f9)) + (- (Q * (hh *' g9))))) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,f9,g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (f9,T)),(HT (g9,T))),(HT (f9,T))) *' f9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (g9,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (g9,T)) * ((n,(n,(HT (f9,T)),(HT (g9,T))),(HT (f9,T))) *' f9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (f9,T)),(HT (g9,T))),(HT (g9,T))) *' g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (f9,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (f9,T)) * ((n,(n,(HT (f9,T)),(HT (g9,T))),(HT (g9,T))) *' g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (g9,T)) * ((n,(n,(HT (f9,T)),(HT (g9,T))),(HT (f9,T))) *' f9)) - ((HC (f9,T)) * ((n,(n,(HT (f9,T)),(HT (g9,T))),(HT (g9,T))) *' g9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 *' (n,T,L,f9,g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(g2 / h9) * (A9 *' (n,T,L,f9,g9)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Monom ((g2 / h9),A9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(Monom ((g2 / h9),A9)) *' (n,T,L,f9,g9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
P is Element of K19( the carrier of (Polynom-Ring (n,L)))
{ (n,T,L,b₁,b₂) where b₁, b₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L)) : ( b₁ in P & b₂ in P ) } is set
A is set
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,i,m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (m,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (i,T)),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (m,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i)) - ((HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
P is finite Element of K19( the carrier of (Polynom-Ring (n,L)))
(n,T,L,P) is Element of K19( the carrier of (Polynom-Ring (n,L)))
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
{ (n,T,L,b₁,b₂) where b₁, b₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L)) : ( b₁ in P & b₂ in P ) } is set
[:P,P:] is Relation-like the carrier of (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued finite Element of K19(K20( the carrier of (Polynom-Ring (n,L)), the carrier of (Polynom-Ring (n,L))))
K20( the carrier of (Polynom-Ring (n,L)), the carrier of (Polynom-Ring (n,L))) is set
K19(K20( the carrier of (Polynom-Ring (n,L)), the carrier of (Polynom-Ring (n,L)))) is set
P is set
P `1 is set
P `2 is set
A is set
i is set
[A,i] is V21() set
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,m,p) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (m,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (p,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (m,T)),(HT (p,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) *' m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (p,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (p,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) *' m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (m,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (m,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) *' p) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (p,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) *' m)) - ((HC (m,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) *' p)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
[m,p] is V21() set
[m,p] `1 is set
[m,p] `2 is set
P is Relation-like Function-like set
dom P is set
A is set
i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,i,m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (i,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (m,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (i,T)),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (m,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (i,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (m,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (i,T))) *' i)) - ((HC (i,T)) * ((n,(n,(HT (i,T)),(HT (m,T))),(HT (m,T))) *' m)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
[i,m] is V21() set
[i,m] `1 is set
[i,m] `2 is set
P . [i,m] is set
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,p,s) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (p,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (s,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (p,T)),(HT (s,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (p,T)),(HT (s,T))),(HT (p,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (p,T)),(HT (s,T))),(HT (p,T))) *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (s,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (s,T)) * ((n,(n,(HT (p,T)),(HT (s,T))),(HT (p,T))) *' p) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (p,T)),(HT (s,T))),(HT (s,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (p,T)),(HT (s,T))),(HT (s,T))) *' s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (p,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (p,T)) * ((n,(n,(HT (p,T)),(HT (s,T))),(HT (s,T))) *' s) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (s,T)) * ((n,(n,(HT (p,T)),(HT (s,T))),(HT (p,T))) *' p)) - ((HC (p,T)) * ((n,(n,(HT (p,T)),(HT (s,T))),(HT (s,T))) *' s)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
rng P is set
A is set
i is set
P . i is set
i `1 is set
i `2 is set
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,m,p) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (m,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (p,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (m,T)),(HT (p,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) *' m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (p,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (p,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) *' m) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (m,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (m,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) *' p) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (p,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (m,T))) *' m)) - ((HC (m,T)) * ((n,(n,(HT (m,T)),(HT (p,T))),(HT (p,T))) *' p)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V283() admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
P is Element of K19( the carrier of (Polynom-Ring (n,L)))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,T,L,P,A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (A,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(n,(HT (P,T)),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (A,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (A,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) *' P) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) *' A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (P,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) *' A) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
((HC (A,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (P,T))) *' P)) - ((HC (P,T)) * ((n,(n,(HT (P,T)),(HT (A,T))),(HT (A,T))) *' A)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
n is non empty multLoopStr
the carrier of n is non empty set
K19( the carrier of n) is set
T is non empty Element of K19( the carrier of n)
L is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of T
P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
L | P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Seg P is finite V31(P) Element of K19(NAT)
L | (Seg P) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSubsequence-like finite-support Element of K19(K20(NAT, the carrier of n))
K20(NAT, the carrier of n) is non trivial non finite set
K19(K20(NAT, the carrier of n)) is non trivial non finite set
A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
dom A is finite Element of K19(NAT)
dom L is finite Element of K19(NAT)
i is set
A . i is set
L . i is set
A /. i is Element of the carrier of n
L /. i is Element of the carrier of n
n is non empty multLoopStr
the carrier of n is non empty set
K19( the carrier of n) is set
T is non empty Element of K19( the carrier of n)
L is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of T
P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
L /^ P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
len L is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(len L) - P is V52() V53() complex ext-real set
m is set
A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
dom A is finite Element of K19(NAT)
len A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Seg (len A) is finite V31( len A) Element of K19(NAT)
i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Seg i is finite V31(i) Element of K19(NAT)
p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
p + P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
- P is V52() V53() complex ext-real non positive set
(len L) + (- P) is V52() V53() complex ext-real set
((len L) + (- P)) + P is V52() V53() complex ext-real set
P + p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Seg (len L) is finite V31( len L) Element of K19(NAT)
dom L is finite Element of K19(NAT)
L /. (P + p) is Element of the carrier of n
A /. m is Element of the carrier of n
s is Element of the carrier of n
g is Element of T
s * g is Element of the carrier of n
len L is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
<*> the carrier of n is Relation-like NAT -defined the carrier of n -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete V49() V52() V53() irreflexive complex ext-real non positive non negative V234() V235() V236() V237() FinSequence-yielding finite-support M29( the carrier of n,K500( the carrier of n))
K500( the carrier of n) is functional non empty FinSequence-membered M28( the carrier of n)
dom A is finite Element of K19(NAT)
i is set
A /. i is Element of the carrier of n
len L is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
len L is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is non empty multLoopStr
the carrier of n is non empty set
K19( the carrier of n) is set
T is non empty Element of K19( the carrier of n)
L is non empty Element of K19( the carrier of n)
P is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of T
P is set
dom P is finite Element of K19(NAT)
P /. P is Element of the carrier of n
A is Element of the carrier of n
i is Element of T
A * i is Element of the carrier of n
n is epsilon-transitive epsilon-connected ordinal set
T is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,T) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,T)) is non empty set
K19( the carrier of (Polynom-Ring (n,T))) is set
L is non empty Element of K19( the carrier of (Polynom-Ring (n,T)))
P is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of L
P is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of L
P ^ P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
P ^ P is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of L \/ L
L \/ L is non empty Element of K19( the carrier of (Polynom-Ring (n,T)))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non empty non trivial set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
Polynom-Ring (n,T) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,T)) is non empty set
K19( the carrier of (Polynom-Ring (n,T))) is set
P is non empty Element of K19( the carrier of (Polynom-Ring (n,T)))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non empty non trivial set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
Polynom-Ring (n,T) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,T)) is non empty set
K19( the carrier of (Polynom-Ring (n,T))) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
Support L is functional finite Element of K19((Bags n))
K19((Bags n)) is set
P is non empty Element of K19( the carrier of (Polynom-Ring (n,T)))
P is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
dom P is finite Element of K19(NAT)
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom P & P /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom P & P /. b₃ = b₁ *' b₂ ) } is set
len P is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
A + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
i is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
Support i is functional finite Element of K19((Bags n))
m is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
len m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom m is finite Element of K19(NAT)
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom m & m /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom m & m /. b₃ = b₁ *' b₂ ) } is set
<*> the carrier of (Polynom-Ring (n,T)) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete V49() V52() V53() irreflexive complex ext-real non positive non negative V234() V235() V236() V237() FinSequence-yielding finite-support M29( the carrier of (Polynom-Ring (n,T)),K500( the carrier of (Polynom-Ring (n,T))))
K500( the carrier of (Polynom-Ring (n,T))) is functional non empty FinSequence-membered M28( the carrier of (Polynom-Ring (n,T)))
Sum m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
p is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
s is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
<*g*> is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of (Polynom-Ring (n,T)),K500( the carrier of (Polynom-Ring (n,T))))
s ^ <*g*> is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,T))
dom p is finite Element of K19(NAT)
Seg (A + 1) is non empty finite V31(A + 1) V31(A + 1) Element of K19(NAT)
A + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
Sum <*g*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
Sum s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
(Sum s) + (Sum <*g*>) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
f9 is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
c₁₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
f9 + c₁₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
Support f9 is functional finite Element of K19((Bags n))
Support c₁₂ is functional finite Element of K19((Bags n))
(Support f9) \/ (Support c₁₂) is functional finite Element of K19((Bags n))
len p is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
len s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
len <*g*> is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
(len s) + (len <*g*>) is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
(len s) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
dom s is finite Element of K19(NAT)
Seg A is finite V31(A) Element of K19(NAT)
g9 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
p /. g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
p . g9 is set
s . g9 is set
s /. g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom s & s /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom s & s /. b₃ = b₁ *' b₂ ) } is set
g9 is set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
R is set
A is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
c₁₈ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
A *' c₁₈ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
Support (A *' c₁₈) is functional finite Element of K19((Bags n))
Q is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
s /. Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
Q is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
s /. Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
p /. Q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
p . Q is set
s . Q is set
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
Seg (len p) is non empty finite V31( len p) Element of K19(NAT)
p /. (len p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
p . (len p) is set
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
A is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
R is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
R *' A is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom p & p /. b₃ = b₁ *' b₂ ) } is set
i is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
m is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
len m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Support i is functional finite Element of K19((Bags n))
dom m is finite Element of K19(NAT)
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom m & m /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom m & m /. b₃ = b₁ *' b₂ ) } is set
A is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
Support A is functional finite Element of K19((Bags n))
i is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
len i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom i is finite Element of K19(NAT)
{ (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom i & i /. b₃ = b₁ *' b₂ ) } is set
union { (Support (b₁ *' b₂)) where b₁ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)), b₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T)) : ex b₃ being epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT st
( b₃ in dom i & i /. b₃ = b₁ *' b₂ ) } is set
<*> the carrier of (Polynom-Ring (n,T)) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete V49() V52() V53() irreflexive complex ext-real non positive non negative V234() V235() V236() V237() FinSequence-yielding finite-support M29( the carrier of (Polynom-Ring (n,T)),K500( the carrier of (Polynom-Ring (n,T))))
K500( the carrier of (Polynom-Ring (n,T))) is functional non empty FinSequence-membered M28( the carrier of (Polynom-Ring (n,T)))
Sum i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
0. (Polynom-Ring (n,T)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
the ZeroF of (Polynom-Ring (n,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
0_ (n,T) is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like Constant V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
T is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non empty non trivial set
K20((Bags n), the carrier of T) is set
K19(K20((Bags n), the carrier of T)) is set
Polynom-Ring (n,T) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,T)) is non empty set
K19( the carrier of (Polynom-Ring (n,T))) is set
L is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
L + P is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
P is non empty Element of K19( the carrier of (Polynom-Ring (n,T)))
A is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
i is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
(n,T,P,A,i) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,T)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom (n,T,P,A,i) is finite Element of K19(NAT)
dom A is finite Element of K19(NAT)
(n,T,P,A,i) /. m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
(n,T,P,A,i) . m is set
A . m is set
A /. m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
dom i is finite Element of K19(NAT)
len A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative set
(len A) + p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative set
(len A) + p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(n,T,P,A,i) /. m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
(n,T,P,A,i) . m is set
i . p is set
i /. p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
dom A is finite Element of K19(NAT)
dom i is finite Element of K19(NAT)
len A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(n,T,P,A,i) /. m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
dom A is finite Element of K19(NAT)
(n,T,P,A,i) /. m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
dom i is finite Element of K19(NAT)
len A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
s is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
p is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
p *' s is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative set
(len A) + g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
f9 is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
c₁₂ is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) monomial-like V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
c₁₂ *' f9 is Relation-like Bags n -defined the carrier of T -valued Function-like non empty total V46( Bags n, the carrier of T) V293( Bags n,T) Element of K19(K20((Bags n), the carrier of T))
m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
Sum (n,T,P,A,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
Sum A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
Sum i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
(Sum A) + (Sum i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
s + (Sum i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
s + g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
A is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
dom A is finite Element of K19(NAT)
i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
P . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
s is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom s is finite Element of K19(NAT)
Seg m is finite V31(m) Element of K19(NAT)
s | (Seg m) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSubsequence-like finite-support Element of K19(K20(NAT, the carrier of (Polynom-Ring (n,L))))
K20(NAT, the carrier of (Polynom-Ring (n,L))) is non trivial non finite set
K19(K20(NAT, the carrier of (Polynom-Ring (n,L)))) is non trivial non finite set
c₁₂ is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
f9 is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Seg (m + 1) is non empty finite V31(m + 1) V31(m + 1) Element of K19(NAT)
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
s /. (m + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom f9 is finite Element of K19(NAT)
R is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
f9 /. R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 . R is set
s . R is set
s /. R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
R is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
f9 . R is set
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
s . R is set
(A *' c₁₈) . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(A *' c₁₈) . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
<*(s /. (m + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of (Polynom-Ring (n,L)),K500( the carrier of (Polynom-Ring (n,L))))
K500( the carrier of (Polynom-Ring (n,L))) is functional non empty FinSequence-membered M28( the carrier of (Polynom-Ring (n,L)))
f9 ^ <*(s /. (m + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
s . (m + 1) is set
<*(s . (m + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support set
f9 ^ <*(s . (m + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
Sum <*(s /. (m + 1))*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum f9) + (Sum <*(s /. (m + 1))*>) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum f9) + (s /. (m + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P + R is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
R . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . i) + (R . i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A *' c₁₈ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
len f9 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
s is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom s is finite Element of K19(NAT)
p . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m . i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
p is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len p is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom p is finite Element of K19(NAT)
<*> the carrier of (Polynom-Ring (n,L)) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete V49() V52() V53() irreflexive complex ext-real non positive non negative V234() V235() V236() V237() FinSequence-yielding finite-support M29( the carrier of (Polynom-Ring (n,L)),K500( the carrier of (Polynom-Ring (n,L))))
K500( the carrier of (Polynom-Ring (n,L))) is functional non empty FinSequence-membered M28( the carrier of (Polynom-Ring (n,L)))
Sum (<*> the carrier of (Polynom-Ring (n,L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
len A is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Sum A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
A is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
i is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom A is finite Element of K19(NAT)
A /. m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p *' s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((p *' s),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
Sum A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
m is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (m,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
p is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (m,T)
p . 1 is set
len p is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
p . (len p) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative set
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
R is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (P,T)
R . 1 is set
len R is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
R . (len R) is set
Seg s is finite V31(s) Element of K19(NAT)
R | (Seg s) is Relation-like NAT -defined Function-like finite FinSubsequence-like finite-support set
c₁₈ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom c₁₈ is finite Element of K19(NAT)
dom R is finite Element of K19(NAT)
Seg (s + 1) is non empty finite V31(s + 1) V31(s + 1) Element of K19(NAT)
Q is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Q + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
R . Q is set
R . (Q + 1) is set
[(R . Q),(R . (Q + 1))] is V21() set
c₁₈ . Q is set
c₁₈ . (Q + 1) is set
[(c₁₈ . Q),(c₁₈ . (Q + 1))] is V21() set
len c₁₈ is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Q is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (P,T)
dom Q is finite Element of K19(NAT)
Q . 1 is set
R . s is set
R . (s + 1) is set
[(R . s),(R . (s + 1))] is V21() set
h9 is set
g2 is set
[h9,g2] is V21() set
{(0_ (n,L))} is functional non empty trivial finite V31(1) Element of K19( the carrier of (Polynom-Ring (n,L)))
Q . s is set
h9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len Q is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
Q . (len Q) is set
u is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A9 is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum A9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
u9 + (Sum A9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom A9 is finite Element of K19(NAT)
g2 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Support g2 is functional finite Element of K19((Bags n))
K19((Bags n)) is set
HT (h9,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
m9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m9 *' p9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
h9 - (m9 *' p9) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((m9 *' p9),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
h9 - (0_ (n,L)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
mp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
<*mp*> is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support M29( the carrier of (Polynom-Ring (n,L)),K500( the carrier of (Polynom-Ring (n,L))))
K500( the carrier of (Polynom-Ring (n,L))) is functional non empty FinSequence-membered M28( the carrier of (Polynom-Ring (n,L)))
A9 ^ <*mp*> is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh - mp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len (A9 ^ <*mp*>) is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
len A9 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
m9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m9 *' p9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
<*(m9 *' p9)*> is Relation-like NAT -defined Function-like constant non empty trivial finite V31(1) FinSequence-like FinSubsequence-like finite-support set
len <*(m9 *' p9)*> is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
(len A9) + (len <*(m9 *' p9)*>) is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
(len A9) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
dom (A9 ^ <*mp*>) is finite Element of K19(NAT)
Seg ((len A9) + 1) is non empty finite V31((len A9) + 1) V31((len A9) + 1) Element of K19(NAT)
(len A9) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
mm is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
pp is Element of P
mm * pp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
B is set
B is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(A9 ^ <*mp*>) . B is set
(A9 ^ <*mp*>) /. B is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(A9 ^ <*mp*>) /. B is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Seg (len A9) is finite V31( len A9) Element of K19(NAT)
A9 . B is set
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((m *' p),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(A9 ^ <*mp*>) . B is set
(A9 ^ <*mp*>) /. B is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a9 is Element of P
u9 * a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(A9 ^ <*mp*>) /. B is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(A9 ^ <*mp*>) /. B is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(A9 ^ <*mp*>) /. B is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
p is Element of P
m * p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
u9 is Element of P
a9 * u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
HT ((m9 *' p9),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
B is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
dom B is finite Element of K19(NAT)
B . B is set
Seg (len A9) is finite V31( len A9) Element of K19(NAT)
A9 . B is set
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((m *' p),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
B . B is set
B . B is set
B . B is set
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((m *' p),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
u9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
a9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
a9 *' u9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((a9 *' u9),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
B is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum B is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
gg + (Sum B) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Sum <*mp*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum A9) + (Sum <*mp*>) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
gg + ((Sum A9) + (Sum <*mp*>)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum A9) + mp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
gg + ((Sum A9) + mp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- mp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh + (- mp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(hh + (- mp)) + ((Sum A9) + mp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- mp) + ((Sum A9) + mp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh + ((- mp) + ((Sum A9) + mp)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- mp) + mp is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum A9) + ((- mp) + mp) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh + ((Sum A9) + ((- mp) + mp)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum A9) + (0. (Polynom-Ring (n,L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh + ((Sum A9) + (0. (Polynom-Ring (n,L)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh + (Sum A9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
hh is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum hh is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 + (Sum hh) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom hh is finite Element of K19(NAT)
p9 is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum p9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 + (Sum p9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom p9 is finite Element of K19(NAT)
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
c₁₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (P,T)
R . 1 is set
len R is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
R . (len R) is set
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
<*> the carrier of (Polynom-Ring (n,L)) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete V49() V52() V53() irreflexive complex ext-real non positive non negative V234() V235() V236() V237() FinSequence-yielding finite-support M29( the carrier of (Polynom-Ring (n,L)),K500( the carrier of (Polynom-Ring (n,L))))
K500( the carrier of (Polynom-Ring (n,L))) is functional non empty FinSequence-membered M28( the carrier of (Polynom-Ring (n,L)))
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
c₁₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
R is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (P,T)
R . 1 is set
len R is non empty epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real positive non negative Element of NAT
R . (len R) is set
dom (<*> the carrier of (Polynom-Ring (n,L))) is Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite V28() V29() V31( {} ) FinSequence-membered V52() V53() complex ext-real non positive non negative Element of K19(NAT)
A is set
(<*> the carrier of (Polynom-Ring (n,L))) /. A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
A is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 + (Sum A) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom A is finite Element of K19(NAT)
g9 + (0. (Polynom-Ring (n,L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
c₁₈ is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
A . c₁₈ is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P + P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
i is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of A
m is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of A
(n,L,A,i,m) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of A
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom (n,L,A,i,m) is finite Element of K19(NAT)
dom i is finite Element of K19(NAT)
(n,L,A,i,m) /. s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(n,L,A,i,m) . s is set
i . s is set
i /. s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom m is finite Element of K19(NAT)
len i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative set
(len i) + g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative set
(len i) + g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(n,L,A,i,m) /. s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(n,L,A,i,m) . s is set
m . g is set
m /. g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom i is finite Element of K19(NAT)
dom m is finite Element of K19(NAT)
len i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
(n,L,A,i,m) /. s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom i is finite Element of K19(NAT)
(n,L,A,i,m) /. s is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom m is finite Element of K19(NAT)
len i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
c₁₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g *' c₁₂ is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((g *' c₁₂),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
f9 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative set
(len i) + f9 is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g9 is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g9 *' P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((g9 *' P),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
Sum i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Sum m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum i) + (Sum m) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Sum (n,L,A,i,m) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P - P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
i is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of A
m is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of A
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i | s is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
i /^ s is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
Sum (i /^ s) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Sum i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Seg s is finite V31(s) Element of K19(NAT)
i | (Seg s) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSubsequence-like finite-support Element of K19(K20(NAT, the carrier of (Polynom-Ring (n,L))))
K20(NAT, the carrier of (Polynom-Ring (n,L))) is non trivial non finite set
K19(K20(NAT, the carrier of (Polynom-Ring (n,L)))) is non trivial non finite set
dom (i | (Seg s)) is finite Element of K19(NAT)
dom i is finite Element of K19(NAT)
dom m is finite Element of K19(NAT)
g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i /. g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
i . g is set
(i | (Seg s)) . g is set
m . g is set
m /. g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
m ^ (i /^ s) is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
Sum m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum m) + (Sum (i /^ s)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (Sum (i /^ s)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum i) + (- (Sum (i /^ s))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum (i /^ s)) + (- (Sum (i /^ s))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum m) + ((Sum (i /^ s)) + (- (Sum (i /^ s)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum m) + (0. (Polynom-Ring (n,L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum i) - (Sum (i /^ s)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P - P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
i is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of A
m is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of A
len i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
p is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i /^ s is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
i | s is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
Sum (i | s) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Sum i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom m is finite Element of K19(NAT)
g + s is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
dom i is finite Element of K19(NAT)
m /. g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
m . g is set
i . (g + s) is set
i /. (g + s) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(i | s) ^ m is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
Sum m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum (i | s)) + (Sum m) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (Sum (i | s)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum i) + (- (Sum (i | s))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum (i | s)) + (- (Sum (i | s))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
((Sum (i | s)) + (- (Sum (i | s)))) + (Sum m) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(0. (Polynom-Ring (n,L))) + (Sum m) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum i) - (Sum (i | s)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
A is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
dom A is finite Element of K19(NAT)
HC (P,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
P . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
A . i is set
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(m *' p) . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
(m *' p) . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
g *' s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Support (g *' s) is functional finite Element of K19((Bags n))
K19((Bags n)) is set
HT ((g *' s),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
A is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
dom A is finite Element of K19(NAT)
i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A . i is set
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((m *' p),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
A /. i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
s *' g is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((s *' g),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
A is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
i is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(0. (Polynom-Ring (n,L))) + (Sum i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
dom i is finite Element of K19(NAT)
m is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
i . m is set
i /. m is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
p *' s is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((p *' s),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
n is epsilon-transitive epsilon-connected ordinal set
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
A is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
dom A is finite Element of K19(NAT)
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
i is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
A /. i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
m is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero monomial-like V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
m *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((m *' p),T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (m,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
HT (p,T) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support Element of Bags n
(HT (m,T)) + (HT (p,T)) is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
(HT (m,T)) *' p is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (p,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . (HT (P,T))) / (HC (p,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . (HT (P,T))) / (HC (p,T))) * ((HT (m,T)) *' p) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P - (((P . (HT (P,T))) / (HC (p,T))) * ((HT (m,T)) *' p)) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
Support P is functional finite Element of K19((Bags n))
K19((Bags n)) is set
n is epsilon-transitive epsilon-connected ordinal natural finite V29() V52() V53() complex ext-real non negative Element of NAT
Bags n is functional non empty Element of K19((Bags n))
Bags n is non empty set
K19((Bags n)) is set
K20((Bags n),(Bags n)) is set
K19(K20((Bags n),(Bags n))) is set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V283() admissible Element of K19(K20((Bags n),(Bags n)))
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non empty set
K19( the carrier of (Polynom-Ring (n,L))) is set
the carrier of L is non empty non trivial set
K20((Bags n), the carrier of L) is set
K19(K20((Bags n), the carrier of L)) is set
P is non empty Element of K19( the carrier of (Polynom-Ring (n,L)))
P -Ideal is non empty add-closed left-ideal right-ideal Element of K19( the carrier of (Polynom-Ring (n,L)))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
HT ((P -Ideal),T) is functional Element of K19((Bags n))
K19((Bags n)) is set
HT (P,T) is functional Element of K19((Bags n))
P is Relation-like n -defined RAT -valued Function-like total V234() V235() V236() V237() finite-support set
multiples (HT (P,T)) is functional Element of K19((Bags n))
PolyRedRel (P,T) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K19( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K19( the carrier of (Polynom-Ring (n,L)))
0. (Polynom-Ring (n,L)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the ZeroF of (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite V31(1) set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K19( the carrier of (Polynom-Ring (n,L)))
K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is set
K19(K20((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is set
0_ (n,L) is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) monomial-like Constant V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
P is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))
A is Relation-like Bags n -defined the carrier of L -valued Function-like non empty total V46( Bags n, the carrier of L) non-zero V293( Bags n,L) Element of K19(K20((Bags n), the carrier of L))