:: GROEB_1 semantic presentation

REAL is set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal Element of K10(REAL)
K10(REAL) is non empty set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal set
K10(omega) is non empty non trivial non finite set
K10(NAT) is non empty non trivial non finite set
K227() is set
{} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() cardinal {} -element 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() V50() Function-yielding V141() irreflexive complex ext-real non negative V211() V212() V213() V214() FinSequence-yielding finite-support set
RAT is set
{{}} is non empty trivial functional finite V28() 1 -element set
1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
K205({{}}) is non empty functional FinSequence-membered M10({{}})
K11(K205({{}}),{{}}) is non empty Relation-like set
K10(K11(K205({{}}),{{}})) is non empty set
PFuncs (K205({{}}),{{}}) is set
K11(NAT,NAT) is non empty non trivial Relation-like non finite set
K10(K11(NAT,NAT)) is non empty non trivial non finite set
COMPLEX is set
INT is set
2 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
K11(NAT,REAL) is Relation-like set
K10(K11(NAT,REAL)) is non empty set
3 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
Seg 1 is non empty trivial finite 1 -element Element of K10(NAT)
{1} is non empty trivial finite V28() 1 -element set
Seg 2 is non empty finite 2 -element Element of K10(NAT)
{1,2} is non empty finite V28() set
0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() cardinal {} -element 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() V50() Function-yielding V141() irreflexive complex ext-real non negative V211() V212() V213() V214() FinSequence-yielding finite-support Element of NAT
NATOrd is Relation-like Element of K10(K11(NAT,NAT))
{ K545(NAT,NAT,b₁,b₂) where b₁, b₂ is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT : b₁ <= b₂ } is set
OrderedNAT is non empty transitive antisymmetric quasi_ordered Dickson V251() RelStr
RelStr(# NAT,NATOrd #) is non empty strict RelStr
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty 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
K11((Bags n), the carrier of T) is non empty Relation-like set
K10(K11((Bags n), the carrier of T)) is non empty set
L is non empty Relation-like Function-like total V46( Bags n, the carrier of T) V271( Bags n,T) Element of K10(K11((Bags n), the carrier of T))
{L} is non empty trivial functional finite 1 -element 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
K10( the carrier of (Polynom-Ring (n,T))) is non empty set
I is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HT (G,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
I . GH 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
(I . GH) / (HC (G,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH + (HT (G,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH *' G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((I . GH) / (HC (G,T))) * (GH *' G) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I - (((I . GH) / (HC (G,T))) * (GH *' G)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Monom (((I . GH) / (HC (G,T))),GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(Monom (((I . GH) / (HC (G,T))),GH)) *' G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support H is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
HT (I,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
Support I is functional finite Element of K10((Bags n))
I . GH 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
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HC (GH,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(I . GH) / (HC (GH,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g + (HT (GH,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g *' GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((I . GH) / (HC (GH,T))) * (g *' GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I - (((I . GH) / (HC (GH,T))) * (g *' GH)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Monom (((I . GH) / (HC (GH,T))),g) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(HC (GH,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(I . GH) * ((HC (GH,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient (Monom (((I . GH) / (HC (GH,T))),g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC ((Monom (((I . GH) / (HC (GH,T))),g)),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 *' GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT ((b9 *' GH),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (b9,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(HT (b9,T)) + (HT (GH,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
term b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
(term b9) + (HT (GH,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
(Monom (((I . GH) / (HC (GH,T))),g)) *' GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((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
K10( the carrier of n) is non empty set
T is Element of K10( the carrier of n)
T -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of n)
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
<*L*> is non empty trivial Relation-like NAT -defined the carrier of n -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support M11( the carrier of n,K205( the carrier of n))
K205( the carrier of n) is non empty functional FinSequence-membered M10( the carrier of n)
H is set
dom <*L*> is non empty trivial finite 1 -element Element of K10(NAT)
<*L*> /. H 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
G is non empty Element of K10( the carrier of n)
H is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of G
Sum H 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 non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty 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
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I - G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
H - GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- G is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH 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))
g + GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- G) + G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((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))
- GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
I + (- G) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H + (- GH) 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 non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is Element of K10( the carrier of (Polynom-Ring (n,L)))
GH is Element of K10( the carrier of (Polynom-Ring (n,L)))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
G is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
PolyRedRel (G,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
H is set
GH is set
GH is set
[GH,GH] is V21() set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty 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
K11((Bags n), the carrier of T) is non empty Relation-like set
K10(K11((Bags n), the carrier of T)) is non empty set
L is non empty Relation-like Function-like total V46( Bags n, the carrier of T) V271( Bags n,T) Element of K10(K11((Bags n), the carrier of T))
- L is non empty Relation-like Function-like total total V46( Bags n, the carrier of T) V46( Bags n, the carrier of T) V271( Bags n,T) Element of K10(K11((Bags n), the carrier of T))
Support (- L) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
Support L is functional Element of K10((Bags n))
I is set
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
L . G 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
(- L) . G 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
- (- (0. T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (L . G) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
I is set
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(- L) . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (L . G) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- I is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT ((- I),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (I,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
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
G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (0_ (n,L)) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- (0_ (n,L))) + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((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))
H is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
H + (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))
(- I) + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((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))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support I is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
Support (- I) is functional finite Element of K10((Bags n))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K10(K11((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
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I - G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT ((I - G),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (I,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (G,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
max ((HT (I,T)),(HT (G,T)),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
- G is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I + (- G) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT ((I + (- G)),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT ((- G),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
max ((HT (I,T)),(HT ((- G),T)),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support G is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support I is functional finite Element of K10((Bags n))
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric V251() RelStr
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support GH is functional finite Element of K10((Bags n))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support g is functional finite Element of K10((Bags n))
card (Support GH) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of omega
H + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
Red (GH,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Red (g,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Support (Red (GH,T)) is functional finite Element of K10((Bags n))
{(HT (GH,T))} is non empty trivial functional finite 1 -element set
(Support GH) \ {(HT (GH,T))} is functional finite Element of K10((Bags n))
Support (Red (g,T)) is functional finite Element of K10((Bags n))
{(HT (g,T))} is non empty trivial functional finite 1 -element set
(Support g) \ {(HT (g,T))} is functional finite Element of K10((Bags n))
h is set
h is set
Support (GH,T) is Element of K458( the carrier of RelStr(# (Bags n),T #))
the carrier of RelStr(# (Bags n),T #) is non empty set
K458( the carrier of RelStr(# (Bags n),T #)) is V235() set
Support (g,T) is Element of K458( the carrier of RelStr(# (Bags n),T #))
Support ((Red (GH,T)),T) is Element of K458( the carrier of RelStr(# (Bags n),T #))
PosetMax (Support (GH,T)) is Element of the carrier of RelStr(# (Bags n),T #)
PosetMax (Support (g,T)) is Element of the carrier of RelStr(# (Bags n),T #)
Support ((Red (g,T)),T) is Element of K458( the carrier of RelStr(# (Bags n),T #))
{(PosetMax (Support (g,T)))} is non empty trivial finite 1 -element set
(Support (g,T)) \ {(PosetMax (Support (g,T)))} is Element of K10((Support (g,T)))
K10((Support (g,T))) is non empty set
(Support (Red (GH,T))) \/ {(HT (GH,T))} is non empty finite set
(Support GH) \/ {(HT (GH,T))} is non empty finite set
card (Support (Red (GH,T))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of omega
(card (Support (Red (GH,T)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
[(Support (Red (GH,T))),(Support (Red (g,T)))] is V21() set
FinOrd RelStr(# (Bags n),T #) is Relation-like total V46(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #))) reflexive antisymmetric transitive Element of K10(K11(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #))))
K11(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #))) is Relation-like set
K10(K11(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #)))) is non empty set
[(Support ((Red (GH,T)),T)),(Support ((Red (g,T)),T))] is V21() set
FinOrd-Approx RelStr(# (Bags n),T #) is non empty Relation-like Function-like total V46( NAT ,K10(K11(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #))))) Element of K10(K11(NAT,K10(K11(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #))))))
K11(NAT,K10(K11(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #))))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,K10(K11(K458( the carrier of RelStr(# (Bags n),T #)),K458( the carrier of RelStr(# (Bags n),T #)))))) is non empty non trivial non finite set
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is non empty set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
{(PosetMax (Support (GH,T)))} is non empty trivial finite 1 -element set
(Support (GH,T)) \ {(PosetMax (Support (GH,T)))} is Element of K10((Support (GH,T)))
K10((Support (GH,T))) is non empty set
[(Support (GH,T)),(Support (g,T))] is V21() set
[(Support GH),(Support g)] is V21() set
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support GH is functional finite Element of K10((Bags n))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support GH is functional finite Element of K10((Bags n))
card (Support GH) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of omega
card (Support G) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of omega
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support H is functional finite Element of K10((Bags n))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support GH is functional finite Element of K10((Bags n))
card (Support H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of omega
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (G,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (I,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Support I is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,I) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
PolyRedRel ((n,L,I),T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is set
GH is set
[H,GH] is V21() set
GH is set
[H,GH] is V21() set
g is set
g is set
[g,g] is V21() set
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is set
GH is set
[GH,GH] is V21() set
g is set
[GH,g] is V21() set
g is set
b9 is set
[g,b9] is V21() set
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,H) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is set
f is set
[f,f] is V21() set
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (h9 *' H) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (- (h9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h + (- (h9 *' H))) + (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- (h9 *' H)) + (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + ((- (h9 *' H)) + (h9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 *' H) - (g9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (g9 *' H) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 *' H) + (- (g9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- g9 is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- g9) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 *' H) + ((- g9) *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 + (- g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 + (- g9)) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 - g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 - g9) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is set
b9 is set
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (h9 *' H) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (- (h9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h + (- (h9 *' H))) + (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- (h9 *' H)) + (h9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + ((- (h9 *' H)) + (h9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 *' H) - (g9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (g9 *' H) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 *' H) + (- (g9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- g9 is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- g9) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 *' H) + ((- g9) *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 + (- g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 + (- g9)) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 - g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 - g9) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is set
b9 is set
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 - g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- g9 is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 + (- g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h9 + (- g9)) + g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- g9) + g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 + ((- g9) + g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (b9 *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (q *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- b9 is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- b9) + q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- b9) + b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q + ((- b9) + b9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (q *' H) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (- (q *' H)) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (h - (q *' H)) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h - (b9 *' H)) + (- (h - (q *' H))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (- (q *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (h + (- (q *' H))) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h - (b9 *' H)) + (- (h + (- (q *' H)))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- h is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- h) + (- (- (q *' H))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h - (b9 *' H)) + ((- h) + (- (- (q *' H)))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (b9 *' H) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (- (b9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h + (- (b9 *' H))) + ((- h) + (- (- (q *' H)))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h + (- (b9 *' H))) + (- h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((h + (- (b9 *' H))) + (- h)) + (q *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (- h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h + (- h)) + (- (b9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((h + (- h)) + (- (b9 *' H))) + (q *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + (- (b9 *' H)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((0_ (n,L)) + (- (b9 *' H))) + (q *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- (b9 *' H)) + (q *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- b9) *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((- b9) *' H) + (q *' H) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q *' H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r - p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- p is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r + (- p) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(r + (- p)) + p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- p) + p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r + ((- p) + p) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is set
b9 is set
h9 is set
g9 is set
h9 is set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,H) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,L,H) -Ideal is non empty add-closed left-ideal right-ideal finitely_generated Element of K10( the carrier of (Polynom-Ring (n,L)))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,H) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,L,H) -Ideal is non empty add-closed left-ideal right-ideal finitely_generated Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel ((n,L,H),T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
g is set
g is set
[g,g] is V21() set
b9 is set
[g,b9] is V21() set
h is set
h is set
[h,h] is V21() set
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is set
g9 is set
[f,g9] is V21() set
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 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))
q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
GH is Relation-like co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property confluent with_Church-Rosser_property locally-confluent complete irreflexive set
q is set
r is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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
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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((Bags n),(Bags n)))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
K10((Bags n)) is non empty set
H is set
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K10((Bags n)) is non empty set
T is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in T & b₂ divides b₁ ) } is set
I is set
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 Abelian add-associative right_zeroed V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((Bags n),(Bags n)))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((Bags n),(Bags n)))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 Abelian add-associative right_zeroed V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((Bags n),(Bags n)))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is set
H is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (H,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
GH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (H,T)
GH . 1 is set
len GH is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
GH . (len GH) is set
(len GH) - 1 is V49() V50() complex ext-real set
g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
GH . g is set
g + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
Seg (len GH) is non empty finite len GH -element Element of K10(NAT)
dom GH is non empty finite Element of K10(NAT)
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
[(GH . g),G] is V21() set
b9 is set
h is set
[b9,h] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (H,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
GH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (H,T)
GH . 1 is set
len GH is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
GH . (len GH) is set
GH . 2 is set
(len GH) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
Seg (len GH) is non empty finite len GH -element Element of K10(NAT)
dom GH is non empty finite Element of K10(NAT)
[I,(GH . 2)] is V21() set
g is set
b9 is set
[g,b9] is V21() set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H 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))
GH - (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g - GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 is set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I -Ideal & not b₁ is_top_reducible_wrt I,T ) } is set
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is set
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f *' h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f 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))
h9 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))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 * g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (b9 * g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 + (- (b9 * g9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 - (b9 * g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Support g is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
Support g is functional finite Element of K10((Bags n))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support q is functional finite Element of K10((Bags n))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q . (HT (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (q,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(q . (HT (q,T))) / (HC (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
p is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
p + (HT (q,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
p *' q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((q . (HT (q,T))) / (HC (q,T))) * (p *' q) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q - (((q . (HT (q,T))) / (HC (q,T))) * (p *' q)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) / (HC (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g . (HT (g,T))) / (HC (q,T))) * (p *' q) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - (((g . (HT (g,T))) / (HC (q,T))) * (p *' q)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
pp is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(g - (f *' h)) + (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (f *' h) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (- (f *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(g + (- (f *' h))) + (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- (f *' h)) + (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + ((- (f *' h)) + (f *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(HT (q,T)) *' h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (h,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) / (HC (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g . (HT (g,T))) / (HC (h,T))) * ((HT (q,T)) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - (((g . (HT (g,T))) / (HC (h,T))) * ((HT (q,T)) *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(HT (q,T)) + (HT (h,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,(I -Ideal)) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I -Ideal & not b₁ = 0_ (n,L) ) } is set
(n,T,L,I) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (H,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH . (HT (GH,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (GH,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(GH . (HT (GH,T))) / (HC (GH,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g + (HT (GH,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g *' GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((GH . (HT (GH,T))) / (HC (GH,T))) * (g *' GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH - (((GH . (HT (GH,T))) / (HC (GH,T))) * (g *' GH)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,(I -Ideal)) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I -Ideal & not b₁ = 0_ (n,L) ) } is set
(n,T,L,I) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
(n,(n,T,L,I)) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,T,L,I) & b₂ divides b₁ ) } is set
G is set
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,(I -Ideal)) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I -Ideal & not b₁ = 0_ (n,L) ) } is set
(n,T,L,I) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
(n,(n,T,L,I)) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,T,L,I) & b₂ divides b₁ ) } is set
PolyRedRel (I,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (H,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH + g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g *' GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (GH,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) / (HC (GH,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((H . (HT (H,T))) / (HC (GH,T))) * (g *' GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H - (((H . (HT (H,T))) / (HC (GH,T))) * (g *' GH)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support H is functional finite Element of K10((Bags n))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
[H,GH] is V21() set
field (PolyRedRel (I,T)) is set
dom (PolyRedRel (I,T)) is set
rng (PolyRedRel (I,T)) is set
(dom (PolyRedRel (I,T))) \/ (rng (PolyRedRel (I,T))) is set
GH is set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
H - g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h - h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(h - h) - h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h + (- h) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(h + (- h)) - h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(h + (- h)) + (- h) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h + (- h) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(h + (- h)) + (- h) 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))) + (- h) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (- h) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
[g,f] is V21() set
H is set
GH is set
[H,GH] is V21() set
GH is set
[H,GH] is V21() set
g is set
g is set
[g,g] is V21() set
b9 is set
h is set
[b9,h] is V21() set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f 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))
h9 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))
h9 - g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h - f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
G is set
H is set
GH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of PolyRedRel (I,T)
GH . 1 is set
len GH is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
GH . (len GH) is set
(len GH) - 1 is V49() V50() complex ext-real set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
GH . (1 + 1) is set
g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
GH . g is set
Seg (len GH) is non empty finite len GH -element Element of K10(NAT)
dom GH is non empty finite Element of K10(NAT)
[G,(GH . (1 + 1))] is V21() set
h is set
h is set
[h,h] is V21() set
g + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
Seg (len GH) is non empty finite len GH -element Element of K10(NAT)
dom GH is non empty finite Element of K10(NAT)
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
[(GH . g),H] is V21() set
h is set
h is set
[h,h] is V21() set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
G is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
PolyRedRel (G,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
GH is Relation-like co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property confluent with_Church-Rosser_property locally-confluent complete irreflexive set
GH is set
g is set
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
(PolyRedRel (G,T)) ~ is Relation-like Element of K10(K11( the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L)))))
K11( the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L)))) is Relation-like set
K10(K11( the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))))) is non empty set
(PolyRedRel (G,T)) \/ ((PolyRedRel (G,T)) ~) is Relation-like set
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (PolyRedRel (G,T)) \/ ((PolyRedRel (G,T)) ~)
g . 1 is set
len g is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
g . (len g) is set
(len g) - 1 is V49() V50() complex ext-real set
b9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
g . b9 is set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
g . (1 + 1) is set
b9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
Seg (len g) is non empty finite len g -element Element of K10(NAT)
dom g is non empty finite Element of K10(NAT)
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
[(g . b9),g] is V21() set
f is set
f is set
[f,f] is V21() set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
[g,(g . b9)] is V21() set
f is set
f is set
[f,f] is V21() set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
[GH,(g . (1 + 1))] is V21() set
f is set
f is set
[f,f] is V21() set
[(g . (1 + 1)),GH] is V21() set
f is set
f is set
[f,f] is V21() set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
G -Ideal is non empty add-closed left-ideal right-ideal Element of K10( 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))
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g is set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
G -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f 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 natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I 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))
H is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
H -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (H,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
nf (I,(PolyRedRel (H,T))) is set
nf (G,(PolyRedRel (H,T))) is set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
G -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (G,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
G is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (G,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
G -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
H is set
H is set
GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
G is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (G,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
G -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is Element of K10( the carrier of (Polynom-Ring (n,L)))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (I,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is add-closed left-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
G is Element of K10( the carrier of (Polynom-Ring (n,L)))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ is_top_reducible_wrt G,T ) } is set
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f *' h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((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))
h9 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))
q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
q * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (q * h9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 + (- (q * h9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 - (q * h9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Support g is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
Support b9 is functional finite Element of K10((Bags n))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support q is functional finite Element of K10((Bags n))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (r,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q . (HT (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (r,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(q . (HT (q,T))) / (HC (r,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
htq is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
htq + (HT (r,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
htq *' r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((q . (HT (q,T))) / (HC (r,T))) * (htq *' r) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q - (((q . (HT (q,T))) / (HC (r,T))) * (htq *' r)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) / (HC (r,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g . (HT (g,T))) / (HC (r,T))) * (htq *' r) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - (((g . (HT (g,T))) / (HC (r,T))) * (htq *' r)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(g - (f *' h)) + (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- (f *' h) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (- (f *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(g + (- (f *' h))) + (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- (f *' h)) + (f *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + ((- (f *' h)) + (f *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(HT (q,T)) *' h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (h,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) / (HC (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((g . (HT (g,T))) / (HC (h,T))) * ((HT (q,T)) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - (((g . (HT (g,T))) / (HC (h,T))) * ((HT (q,T)) *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(HT (q,T)) + (HT (h,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
G is Element of K10( the carrier of (Polynom-Ring (n,L)))
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,G) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G & not b₁ = 0_ (n,L) ) } is set
(n,T,L,I) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH . (HT (GH,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
(GH . (HT (GH,T))) / (HC (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
b9 + (HT (g,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
b9 *' g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((GH . (HT (GH,T))) / (HC (g,T))) * (b9 *' g) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH - (((GH . (HT (GH,T))) / (HC (g,T))) * (b9 *' g)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
G is Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,G) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G & not b₁ = 0_ (n,L) ) } is set
I is Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,I) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
(n,(n,T,L,I)) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,T,L,I) & b₂ divides b₁ ) } is set
H is set
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,I) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
G is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,G) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G & not b₁ = 0_ (n,L) ) } is set
(n,(n,T,L,G)) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,T,L,G) & b₂ divides b₁ ) } is set
PolyRedRel (G,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH + g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g *' g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH . (HT (GH,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
(GH . (HT (GH,T))) / (HC (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((GH . (HT (GH,T))) / (HC (g,T))) * (g *' g) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH - (((GH . (HT (GH,T))) / (HC (g,T))) * (g *' g)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support GH is functional finite Element of K10((Bags n))
PolyRedRel (I,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
[GH,GH] is V21() set
field (PolyRedRel (G,T)) is set
dom (PolyRedRel (G,T)) is set
rng (PolyRedRel (G,T)) is set
(dom (PolyRedRel (G,T))) \/ (rng (PolyRedRel (G,T))) is set
g is set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
GH - g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h - f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
I -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
(h - f) - h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h + (- f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(h + (- f)) - h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(h + (- f)) + (- h) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h + (- h) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(h + (- h)) + (- f) 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))) + (- f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (- f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
[g,f] is V21() set
G -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
GH is set
GH is set
[GH,GH] is V21() set
g is set
[GH,g] is V21() set
g is set
b9 is set
[g,b9] is V21() set
h is set
h is set
[h,h] is V21() set
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((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))
h9 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))
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 - h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f - f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
PolyRedRel ((n,L,(0_ (n,L))),T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
GH is set
GH is set
[GH,GH] is V21() set
g is set
[GH,g] is V21() set
g is set
b9 is set
[g,b9] is V21() set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,(0_ (n,L))) -Ideal is non empty add-closed left-ideal right-ideal finitely_generated Element of K10( the carrier of (Polynom-Ring (n,L)))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty 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
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,I) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
the carrier of (Polynom-Ring (n,L)) is non empty set
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
(n,L,I) -Ideal is non empty add-closed left-ideal right-ideal finitely_generated Element of K10( the carrier of (Polynom-Ring (n,L)))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((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))
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,G) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel ((n,L,G),T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Bags {} is non empty functional Element of K10((Bags {}))
Bags {} is non empty set
K10((Bags {})) is non empty set
K11((Bags {}),(Bags {})) is non empty Relation-like set
K10(K11((Bags {}),(Bags {}))) is non empty set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT : not 0 <= b₁ } is set
the Element of { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT : not 0 <= b₁ } is Element of { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT : not 0 <= b₁ }
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
T is Relation-like total V46( Bags {}, Bags {}) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((Bags {}),(Bags {})))
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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring ({},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 ({},L)) is non empty set
K10( the carrier of (Polynom-Ring ({},L))) is non empty set
0_ ({},L) is non empty Relation-like Function-like total V46( Bags {}, the carrier of L) monomial-like Constant V271( Bags {},L) Element of K10(K11((Bags {}), the carrier of L))
the carrier of L is non empty non trivial set
K11((Bags {}), the carrier of L) is non empty Relation-like set
K10(K11((Bags {}), the carrier of L)) is non empty set
({},L,(0_ ({},L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring ({},L)))
I is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring ({},L)))
G is non empty Element of K10( the carrier of (Polynom-Ring ({},L)))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
GH is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
g is set
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
g is set
g is set
g is Element of GH
g is Element of GH
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
Support h is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
H is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((Bags n),(Bags n)))
HT (h,H) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (b9,H) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,H,L,GH) is functional Element of K10((Bags n))
{ (HT (b₁,H)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in GH & not b₁ = 0_ (n,L) ) } is set
(n,H,L,GH) is functional Element of K10((Bags n))
{ (HT (b₁,H)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in GH & not b₁ = 0_ (n,L) ) } is set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
(n,(n,H,L,GH)) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,H,L,GH) & b₂ divides b₁ ) } is set
n is non empty epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(EmptyBag n) +* ({},1) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
the carrier of L is non empty non trivial set
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
(1. L) | (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
((1. L) | (n,L)) +* (G,(1. L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) Element of K10(K11((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,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((0. L) | (n,L)) +* (G,(1. L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) Element of K10(K11((Bags n), the carrier of L))
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) Element of K10(K11((Bags n), the carrier of L))
GH . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((1. L) | (n,L)) . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
1_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1_ (n,L)) . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h is set
Support GH is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
{(EmptyBag n),G} is non empty functional finite set
dom (EmptyBag n) is Element of K10(n)
K10(n) is non empty set
G . {} is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) Element of K10(K11((Bags n), the carrier of L))
b9 . (EmptyBag n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((0. L) | (n,L)) . (EmptyBag n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) . (EmptyBag n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
b9 . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((0. L) | (n,L)) . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0_ (n,L)) . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h is set
Support b9 is functional Element of K10((Bags n))
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
b9 . h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
{G} is non empty trivial functional finite 1 -element set
dom ((0. L) | (n,L)) is non empty set
b9 . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h is set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(EmptyBag n) *' h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
h . (HT (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (h,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h . (HT (h,T))) / (HC (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((h . (HT (h,T))) / (HC (h,T))) * ((EmptyBag n) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((h . (HT (h,T))) / (HC (h,T))) * ((EmptyBag n) *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support h is functional finite Element of K10((Bags n))
(EmptyBag n) + (HT (h,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
(HC (h,T)) / (HC (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (h,T)) / (HC (h,T))) * ((EmptyBag n) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((HC (h,T)) / (HC (h,T))) * ((EmptyBag n) *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(HC (h,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (h,T)) * ((HC (h,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (h,T)) * ((HC (h,T)) ")) * ((EmptyBag n) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((HC (h,T)) * ((HC (h,T)) ")) * ((EmptyBag n) *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1. L) * ((EmptyBag n) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - ((1. L) * ((EmptyBag n) *' h)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1. L) * h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - ((1. L) * h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((1. L) | (n,L)) *' h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((1. L) | (n,L)) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1_ (n,L)) *' h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - ((1_ (n,L)) *' h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
dom ((1. L) | (n,L)) is non empty set
GH . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
GH . (EmptyBag n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((1. L) | (n,L)) . (EmptyBag n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1_ (n,L)) . (EmptyBag n) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f is set
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(EmptyBag n) + (HT (g9,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
Support g9 is functional finite Element of K10((Bags n))
(EmptyBag n) *' g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h . (HT (g9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of 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
(h . (HT (g9,T))) / (HC (g9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((h . (HT (g9,T))) / (HC (g9,T))) * ((EmptyBag n) *' g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((h . (HT (g9,T))) / (HC (g9,T))) * ((EmptyBag n) *' g9)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h - g9) + g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- g9 is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (- g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(h + (- g9)) + g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- g9) + g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + ((- g9) + g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{g9,h} is non empty functional finite set
h9 is set
h9 is Element of K10( the carrier of (Polynom-Ring (n,L)))
b9 is Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (b9,T) is Relation-like Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
[h,(0_ (n,L))] is V21() set
g9 . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1. L) / (g9 . G) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((1. L) / (g9 . G)) * ((EmptyBag n) *' g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((1. L) / (g9 . G)) * ((EmptyBag n) *' g9)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1. L) / (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((1. L) / (1. L)) * ((EmptyBag n) *' g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((1. L) / (1. L)) * ((EmptyBag n) *' g9)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1. L) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1. L) * ((1. L) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((1. L) * ((1. L) ")) * ((EmptyBag n) *' g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((1. L) * ((1. L) ")) * ((EmptyBag n) *' g9)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1. L) * ((EmptyBag n) *' g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - ((1. L) * ((EmptyBag n) *' g9)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1. L) * g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - ((1. L) * g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((1. L) | (n,L)) *' g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - (((1. L) | (n,L)) *' g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(1_ (n,L)) *' g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h - ((1_ (n,L)) *' g9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
[h,(h - g9)] is V21() set
r is set
{G} \/ {(EmptyBag n),G} is non empty finite set
(h - g9) . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h + (- g9)) . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- g9) . G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h . G) + ((- g9) . G) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (g9 . G) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h . G) + (- (g9 . G)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1. L) + (- (1. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support (h - g9) is functional finite Element of K10((Bags n))
Support (h + (- g9)) is functional finite Element of K10((Bags n))
Support (- g9) is functional finite Element of K10((Bags n))
(Support h) \/ (Support (- g9)) is functional finite Element of K10((Bags n))
q is set
(h - g9) . q is set
{(EmptyBag n)} is non empty trivial functional finite 1 -element set
q is set
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len p is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
p . 1 is set
p . (len p) is set
dom p is finite Element of K10(NAT)
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
Seg (len p) is finite len p -element Element of K10(NAT)
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
p . 2 is set
[(0_ (n,L)),(p . 2)] is V21() set
htq is set
pp is set
[htq,pp] is V21() set
[(p . 1),(p . 2)] is V21() set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
htg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
htq is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len htq is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
htq . 1 is set
htq . (len htq) is set
dom htq is finite Element of K10(NAT)
- (- (1. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
pp is set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(h - g9) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h + (- g9)) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- g9) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h . g) + ((- g9) . g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g9 . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (g9 . g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(h . g) + (- (g9 . g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0. L) + (- (g9 . g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0. L) + (- (1. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
pp is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
htg is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
htg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (htg,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
b is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
Seg (len htq) is finite len htq -element Element of K10(NAT)
htq . 2 is set
[(h - g9),(htq . 2)] is V21() set
pp is set
g is set
[pp,g] is V21() set
htg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal set
T is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
I is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
G is set
T . G is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
L . G is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
I . G is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like Element of K10(K11((Bags n),(Bags n)))
L is set
I is set
G is set
[L,I] is V21() set
[I,G] is V21() set
[L,G] is V21() set
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
L is set
[L,L] is V21() set
dom T is set
field T is set
rng T is set
(dom T) \/ (rng T) is set
L is set
I is set
[L,I] is V21() set
[I,L] is V21() set
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
b9 is set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
dom g is Element of K10(n)
K10(n) is non empty set
g . b9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g . b9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
G . b9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
H . b9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
dom g is Element of K10(n)
L is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric transitive Element of K10(K11((Bags n),(Bags n)))
I is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
G is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
[I,G] is V21() set
H is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric transitive Element of K10(K11((Bags n),(Bags n)))
L is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric transitive Element of K10(K11((Bags n),(Bags n)))
I is set
G is set
[I,G] is V21() set
H is set
GH is set
[H,GH] is V21() set
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
H is set
GH is set
[H,GH] is V21() set
GH is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
(n) is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric transitive Element of K10(K11((Bags n),(Bags n)))
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
RelStr(# (Bags n),(n) #) is non empty strict total reflexive transitive antisymmetric RelStr
n --> OrderedNAT is Relation-like n -defined Function-like constant T-Sequence-like finite total V46(n,{OrderedNAT}) V153() V181() finite-support Element of K10(K11(n,{OrderedNAT}))
{OrderedNAT} is non empty trivial finite 1 -element set
K11(n,{OrderedNAT}) is Relation-like finite set
K10(K11(n,{OrderedNAT})) is non empty finite V28() set
Carrier (n --> OrderedNAT) is Relation-like n -defined Function-like total finite-support set
product (Carrier (n --> OrderedNAT)) is set
product (n --> OrderedNAT) is non empty strict antisymmetric quasi_ordered Dickson RelStr
GH is set
dom (Carrier (n --> OrderedNAT)) is finite Element of K10(n)
K10(n) is non empty finite V28() set
GH is Relation-like Function-like set
dom GH is set
g is Relation-like Function-like set
dom g is set
g is set
g . g is set
(n --> OrderedNAT) . g is set
(Carrier (n --> OrderedNAT)) . g is set
b9 is 1-sorted
the carrier of b9 is set
GH . g is set
GH is set
dom (Carrier (n --> OrderedNAT)) is finite Element of K10(n)
K10(n) is non empty finite V28() set
GH is Relation-like Function-like set
dom GH is set
g is set
GH . g is set
g is Relation-like Function-like set
dom g is set
b9 is set
g is Relation-like n -defined Function-like total finite-support set
rng g is set
dom g is finite Element of K10(n)
h is set
g . h is set
GH . h is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH is Relation-like Function-like set
dom GH is set
the carrier of RelStr(# (Bags n),(n) #) is non empty set
the carrier of (product (n --> OrderedNAT)) is non empty set
GH is Element of the carrier of RelStr(# (Bags n),(n) #)
g is set
dom (Carrier (n --> OrderedNAT)) is finite Element of K10(n)
K10(n) is non empty finite V28() set
(n --> OrderedNAT) . g is set
(Carrier (n --> OrderedNAT)) . g is set
b9 is 1-sorted
the carrier of b9 is set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g . g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
dom g is finite Element of K10(n)
g is Element of the carrier of (product (n --> OrderedNAT))
GH . g is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
GH is set
rng GH is set
g is set
GH . g is set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
K10( the carrier of RelStr(# (Bags n),(n) #)) is non empty set
GH is Element of K10( the carrier of RelStr(# (Bags n),(n) #))
GH " GH is set
K10( the carrier of (product (n --> OrderedNAT))) is non empty set
g is Element of K10( the carrier of (product (n --> OrderedNAT)))
b9 is set
GH .: b9 is set
h is Element of the carrier of (product (n --> OrderedNAT))
f is Element of the carrier of (product (n --> OrderedNAT))
f is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
h9 is Relation-like Function-like set
g9 is Relation-like Function-like set
h9 is set
(n --> OrderedNAT) . h9 is set
h9 . h9 is set
g9 . h9 is set
b9 is RelStr
the carrier of b9 is set
q is Element of the carrier of b9
q is Element of the carrier of b9
[q,q] is V21() set
r is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
[r,p] is V21() set
f . h9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
g9 . h9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative V210() Element of NAT
h is Element of the carrier of RelStr(# (Bags n),(n) #)
f is Element of the carrier of (product (n --> OrderedNAT))
GH . f is set
f is Element of the carrier of (product (n --> OrderedNAT))
GH . f is set
h9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g9 is Element of the carrier of RelStr(# (Bags n),(n) #)
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
h9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
[g9,h] is V21() set
h is set
f is set
GH . f is set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
(n) is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric transitive Element of K10(K11((Bags n),(Bags n)))
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
RelStr(# (Bags n),(n) #) is non empty strict total reflexive transitive antisymmetric Dickson RelStr
the carrier of RelStr(# (Bags n),(n) #) is non empty set
K10( the carrier of RelStr(# (Bags n),(n) #)) is non empty set
K10((Bags n)) is non empty set
T is Element of K10( the carrier of RelStr(# (Bags n),(n) #))
L is set
I is set
K10(T) is non empty set
I is finite Element of K10(T)
G is functional finite Element of K10((Bags n))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
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))
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel ((n,L,(0_ (n,L))),T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( the carrier of (Polynom-Ring (n,L)))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
GH is set
GH is set
[GH,GH] is V21() set
g is set
[GH,g] is V21() set
g is set
b9 is set
[g,b9] is V21() set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,(0_ (n,L))) -Ideal is non empty add-closed left-ideal right-ideal finitely_generated Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
G is set
H is set
G is set
G is Element of I
G is Element of I
(n) is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric transitive Element of K10(K11((Bags n),(Bags n)))
RelStr(# (Bags n),(n) #) is non empty strict total reflexive transitive antisymmetric Dickson RelStr
(n,T,L,I) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
the carrier of RelStr(# (Bags n),(n) #) is non empty set
K10( the carrier of RelStr(# (Bags n),(n) #)) is non empty set
GH is Element of K10( the carrier of RelStr(# (Bags n),(n) #))
g is functional finite Element of K10((Bags n))
{ { b₂ where b₂ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₂ in I & HT (b₂,T) = b₁ & not b₂ = 0_ (n,L) ) } where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : b₁ in g } is set
the Relation-like n -defined Function-like Element of g is Relation-like n -defined Function-like Element of g
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
f is Element of the carrier of RelStr(# (Bags n),(n) #)
f is Element of the carrier of RelStr(# (Bags n),(n) #)
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = the Relation-like n -defined Function-like Element of g & not b₁ = 0_ (n,L) ) } is set
f is non empty set
g9 is set
h9 is set
g9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = g9 & not b₁ = 0_ (n,L) ) } is set
h9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = h9 & not b₁ = 0_ (n,L) ) } is set
g9 /\ h9 is set
the Element of g9 /\ h9 is Element of g9 /\ h9
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g9 is set
h9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = h9 & not b₁ = 0_ (n,L) ) } is set
g9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
g9 is set
the Element of f is Element of f
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = a₁ & not b₁ = 0_ (n,L) ) } is set
g9 is set
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = g9 & not b₁ = 0_ (n,L) ) } is set
g9 is Relation-like Function-like set
dom g9 is set
h9 is set
rng g9 is set
b9 is set
g9 . b9 is set
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = b9 & not b₁ = 0_ (n,L) ) } is set
h9 is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = b9 & not b₁ = 0_ (n,L) ) } is set
g9 . b9 is set
g9 /\ the Element of f is set
b9 is set
{b9} is non empty trivial finite 1 -element set
h9 is non empty set
{ b₁ where b₁ is Element of h9 : ex b₂ being set st
( b₂ in f & h9 /\ b₂ = {b₁} ) } is set
q is set
q is Element of h9
{q} is non empty trivial finite 1 -element set
r is set
h9 /\ r is set
r is set
h9 /\ r is set
p is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = p & not b₁ = 0_ (n,L) ) } is set
htq is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (htq,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is Element of K10( the carrier of (Polynom-Ring (n,L)))
q is set
h9 /\ q is set
r is set
{r} is non empty trivial finite 1 -element set
p is Element of h9
q is Relation-like Function-like set
dom q is set
r is set
p is Element of h9
{p} is non empty trivial finite 1 -element set
htq is set
h9 /\ htq is set
htq is set
h9 /\ htq is set
q . htq is set
{(q . htq)} is non empty trivial finite 1 -element set
rng q is set
r is set
p is set
q . p is set
h9 /\ the Element of f is set
p is set
{p} is non empty trivial finite 1 -element set
r is non empty finite Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,r) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in r & not b₁ = 0_ (n,L) ) } is set
p is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
htq is Element of the carrier of RelStr(# (Bags n),(n) #)
pp is Element of the carrier of RelStr(# (Bags n),(n) #)
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = pp & not b₁ = 0_ (n,L) ) } is set
h9 /\ { b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = pp & not b₁ = 0_ (n,L) ) } is set
htg is set
{htg} is non empty trivial finite 1 -element set
b is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
[pp,htq] is V21() set
m is Element of h9
gg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (gg,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,(n,T,L,r)) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,T,L,r) & b₂ divides b₁ ) } is set
p is set
htq is Element of h9
{htq} is non empty trivial finite 1 -element set
pp is set
h9 /\ pp is set
pp is set
h9 /\ pp is set
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HT (b₁,T) = g & not b₁ = 0_ (n,L) ) } is set
htg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (htg,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,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
K10( 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
{(0. n)} is non empty trivial finite 1 -element set
L is non empty Element of K10( the carrier of n)
T is non empty Element of K10( the carrier of n)
T \ {(0. n)} is Element of K10( the carrier of n)
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
I + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
G is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of T
len G is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Sum G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Seg I is finite I -element Element of K10(NAT)
G | (Seg I) is Relation-like NAT -defined Seg I -defined NAT -defined the carrier of n -valued Function-like finite FinSubsequence-like finite-support Element of K10(K11(NAT, the carrier of n))
K11(NAT, the carrier of n) is non empty non trivial Relation-like non finite set
K10(K11(NAT, the carrier of n)) is non empty non trivial non finite set
rng G is finite set
G /. (len G) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Seg (len G) is finite len G -element Element of K10(NAT)
dom G is finite Element of K10(NAT)
G . (len G) is set
GH is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len GH is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
dom GH is finite Element of K10(NAT)
Seg (I + 1) is non empty finite I + 1 -element I + 1 -element Element of K10(NAT)
I + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
g is set
rng GH is finite set
g is set
GH . g is set
G . g is set
g 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 g is finite Element of K10(NAT)
g is set
g /. g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
b9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
g /. b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g . b9 is set
G . b9 is set
G /. b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of T
Sum g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
b9 is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of L
Sum b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
h is set
len g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
(len g) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
(Sum g) + (G /. (len G)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
<*(G /. (len G))*> is non empty trivial Relation-like NAT -defined the carrier of n -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support M11( the carrier of n,K205( the carrier of n))
K205( the carrier of n) is non empty functional FinSequence-membered M10( the carrier of n)
b9 ^ <*(G /. (len G))*> is non empty 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 (b9 ^ <*(G /. (len G))*>) is non empty finite Element of K10(NAT)
f is set
(b9 ^ <*(G /. (len G))*>) /. f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
len (b9 ^ <*(G /. (len G))*>) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
len b9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
len <*(G /. (len G))*> is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
(len b9) + (len <*(G /. (len G))*>) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
(len b9) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real positive non negative Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g9 is Element of T
g9 * g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(g9 * g9) * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(0. n) * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(b9 ^ <*(G /. (len G))*>) /. f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(b9 ^ <*(G /. (len G))*>) . f is set
f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Seg (len (b9 ^ <*(G /. (len G))*>)) is non empty finite len (b9 ^ <*(G /. (len G))*>) -element Element of K10(NAT)
Seg (len b9) is finite len b9 -element Element of K10(NAT)
dom b9 is finite Element of K10(NAT)
(b9 ^ <*(G /. (len G))*>) /. f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(b9 ^ <*(G /. (len G))*>) . f is set
b9 . f is set
b9 /. f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g9 is Element of L
g9 * g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(g9 * g9) * h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
q is Element of L
h9 * q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(h9 * q) * b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of L
Sum f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum <*(G /. (len G))*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(Sum b9) + (Sum <*(G /. (len G))*>) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
h is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of L
Sum h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
G is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of T
len G is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
H is set
Sum G is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
I is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of T
Sum I is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
G is set
len I is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
<*> the carrier of n is empty Relation-like non-empty empty-yielding NAT -defined the carrier of n -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() cardinal {} -element 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() V50() Function-yielding V141() irreflexive complex ext-real non negative V211() V212() V213() V214() FinSequence-yielding finite-support M11( the carrier of n,K205( the carrier of n))
K205( the carrier of n) is non empty functional FinSequence-membered M10( the carrier of n)
GH 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 GH is finite Element of K10(NAT)
GH is set
GH /. GH is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of T
len g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Sum g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
GH is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of L
g is set
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
I is non empty add-closed left-ideal right-ideal Element of K10( 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))
G is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (G,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( the carrier of (Polynom-Ring (n,L)))
{(0. (Polynom-Ring (n,L)))} is non empty trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
G -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
G \ (n,L,(0_ (n,L))) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel ((G \ (n,L,(0_ (n,L)))),T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
g is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
g is set
b9 is set
g is set
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
g is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
h is set
g is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
b9 is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
h is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of g
Sum h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
h is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of b9
Sum h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
h is set
g is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
g is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
g -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
g is set
b9 is set
h is set
[b9,h] is V21() set
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
L is non empty multLoopStr_0
the carrier of L is non empty set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty 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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is add-closed left-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
G is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (H,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (GH,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (H,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
term (HM (H,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HC (H,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
H . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HM (H,T)) . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
GH . (HT (GH,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (GH,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
H - GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(H - GH) + GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- GH is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H + (- GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(H + (- GH)) + GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- GH) + GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H + ((- GH) + GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H - GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((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 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
HT ((H - GH),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
H . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
GH . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H - (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support (H - GH) is functional finite Element of K10((Bags n))
K10((Bags n)) is non empty set
(H - GH) . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- GH is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H + (- GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(H + (- GH)) . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- GH) . (HT (GH,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) + ((- GH) . (HT (GH,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (GH . (HT (GH,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) + (- (GH . (HT (GH,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (H,T)) + (- (GH . (HT (GH,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (HC (GH,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (H,T)) + (- (HC (GH,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
max ((HT (H,T)),(HT (H,T)),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
(H - GH) . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H - (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)) is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H + (- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(H + (- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)))) . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) + ((- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) . (HT (H,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)) . (HT (H,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)) . (HT (H,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) + (- ((((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)) . (HT (H,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (0. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) + (- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (0. L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) + (- (0. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT (H,T))) + (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support H is functional finite Element of K10((Bags n))
Support (H - (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) is functional finite Element of K10((Bags n))
HT ((H - (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Support (H + (- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)))) is functional finite Element of K10((Bags n))
Support (- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) is functional finite Element of K10((Bags n))
(Support H) \/ (Support (- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)))) is functional finite Element of K10((Bags n))
Support (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)) is functional finite Element of K10((Bags n))
(Support H) \/ (Support (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) is functional finite Element of K10((Bags n))
(Support H) \/ (Support (H - GH)) is functional finite Element of K10((Bags n))
Support GH is functional finite Element of K10((Bags n))
Support (H + (- GH)) is functional finite Element of K10((Bags n))
Support (- GH) is functional finite Element of K10((Bags n))
(Support H) \/ (Support (- GH)) is functional finite Element of K10((Bags n))
(Support H) \/ (Support GH) is functional finite Element of K10((Bags n))
(Support H) \/ (Support H) is functional finite Element of K10((Bags n))
HC ((H - (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HM ((H - (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))),T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Monom ((HC (H,T)),(HT (H,T))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) | (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) | (n,L)) *' (H - GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(H + (- GH)) . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- GH) . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) + ((- GH) . (HT ((H - GH),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (GH . (HT ((H - GH),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) + (- (GH . (HT ((H - GH),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * ((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * ((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ") * ((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) * ((((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ") * ((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((H . (HT ((H - GH),T))) * ((((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ") * ((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))))) 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
(H . (HT ((H - GH),T))) * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((H . (HT ((H - GH),T))) * (1. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (H . (HT ((H - GH),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H - (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H + (- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH)))) . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) + ((- (((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) * (H - GH))) . (HT ((H - GH),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- ((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) "))) * (H - GH) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((- ((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) "))) * (H - GH)) . (HT ((H - GH),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) + (((- ((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) "))) * (H - GH)) . (HT ((H - GH),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- ((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) "))) * ((H - GH) . (HT ((H - GH),T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) + ((- ((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) "))) * ((H - GH) . (HT ((H - GH),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(H . (HT ((H - GH),T))) + (- (H . (HT ((H - GH),T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f 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))
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 - b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 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))
g9 * (h9 - b9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
GH is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
h9 - h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
H - ((((H . (HT ((H - GH),T))) * (((H . (HT ((H - GH),T))) - (GH . (HT ((H - GH),T)))) ")) | (n,L)) *' (H - GH)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
H - GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((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
I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (I,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),(HT (I,T))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
HC (I,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (I,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 (I,T)) ") * (HC (I,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
GH is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
GH * I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM ((GH * I),T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
GH | (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g 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))
(GH | (n,L)) *' I is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h * b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
HT ((GH * I),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HC ((GH * I),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(GH * I) . (HT (I,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
I . (HT (I,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
GH * (I . (HT (I,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (I,T)) * ((HC (I,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient (HM ((GH * I),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
I is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
G is Element of K10( the carrier of (Polynom-Ring (n,L)))
H is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (H,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,L,H) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
G \ (n,L,H) is Element of K10( the carrier of (Polynom-Ring (n,L)))
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G \ (n,L,H) & not b₁ = 0_ (n,L) ) } is set
GH is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
GH -Ideal is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
PolyRedRel (G,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,T,L,I) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
(n,T,L,(G \ (n,L,H))) is functional Element of K10((Bags n))
g is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
(n,T,L,G) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G & not b₁ = 0_ (n,L) ) } is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
h is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
f is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
(n,(n,T,L,(G \ (n,L,H)))) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,T,L,(G \ (n,L,H))) & b₂ divides b₁ ) } is set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
(n,L,(0_ (n,L))) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
I is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
(n) is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric transitive Element of K10(K11((Bags n),(Bags n)))
RelStr(# (Bags n),(n) #) is non empty strict total reflexive transitive antisymmetric Dickson RelStr
H is set
GH is set
H is set
H is Element of I
H is Element of I
GH is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (GH,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
the carrier of RelStr(# (Bags n),(n) #) is non empty set
K10( the carrier of RelStr(# (Bags n),(n) #)) is non empty set
(n,T,L,I) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
GH is non empty Element of K10( the carrier of RelStr(# (Bags n),(n) #))
g is set
h is set
h is set
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
h is functional finite Element of K10((Bags n))
{ { b₂ where b₂ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₂ in I & HM (b₂,T) = Monom ((1. L),b₁) & not b₂ = 0_ (n,L) & ( for b₃ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₃ in I or not b₃ < b₂,T or b₃ = 0_ (n,L) or not HM (b₃,T) = Monom ((1. L),b₁) ) ) ) } where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : b₁ in h } is set
the Relation-like n -defined Function-like Element of h is Relation-like n -defined Function-like Element of h
b9 is Element of the carrier of RelStr(# (Bags n),(n) #)
f is Element of the carrier of RelStr(# (Bags n),(n) #)
f is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),f) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),f) & not b₁ = 0_ (n,L) & ( for b₂ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₂ in I or not b₂ < b₁,T or b₂ = 0_ (n,L) or not HM (b₂,T) = Monom ((1. L),f) ) ) ) } is set
g9 is Element of the carrier of RelStr(# (Bags n),(n) #)
g9 is non empty set
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ex b₂ being Element of g9 st b₂ = (n,L,b₁) } is set
g9 is set
h9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),h9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),h9) & not b₁ = 0_ (n,L) & ( for b₂ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₂ in I or not b₂ < b₁,T or b₂ = 0_ (n,L) or not HM (b₂,T) = Monom ((1. L),h9) ) ) ) } is set
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (b9,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),(HT (b9,T))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (q,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),h9) & not b₁ = 0_ (n,L) ) } is set
r is set
p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (p,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
p is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
htq is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
pp is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (pp,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (g,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (g,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((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
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (g,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (g,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HC (g,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
coefficient (Monom ((1. L),h9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g is set
htg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (htg,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (b,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (b,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HC (b,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,L,pp) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
g is set
g9 is set
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,h9) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
b9 is Element of g9
b9 is Element of g9
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,q) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ = a₁ & b₁ in I & HM (b₁,T) = Monom ((1. L),b₂) & not b₁ = 0_ (n,L) & ( for b₃ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₃ in I or not b₃ < b₁,T or b₃ = 0_ (n,L) or not HM (b₃,T) = Monom ((1. L),b₂) ) ) ) } is set
g9 is set
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ = g9 & b₁ in I & HM (b₁,T) = Monom ((1. L),b₂) & not b₁ = 0_ (n,L) & ( for b₃ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₃ in I or not b₃ < b₁,T or b₃ = 0_ (n,L) or not HM (b₃,T) = Monom ((1. L),b₂) ) ) ) } is set
g9 is Relation-like Function-like set
dom g9 is set
h9 is set
rng g9 is set
b9 is set
g9 . b9 is set
q is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),q) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),q) & not b₁ = 0_ (n,L) & ( for b₂ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₂ in I or not b₂ < b₁,T or b₂ = 0_ (n,L) or not HM (b₂,T) = Monom ((1. L),q) ) ) ) } is set
g9 . q is set
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ = q & b₁ in I & HM (b₁,T) = Monom ((1. L),b₂) & not b₁ = 0_ (n,L) & ( for b₃ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₃ in I or not b₃ < b₁,T or b₃ = 0_ (n,L) or not HM (b₃,T) = Monom ((1. L),b₂) ) ) ) } is set
r is set
p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (p,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is set
p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
htq is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HM (p,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Monom ((1. L),htq) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
h9 is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),b9) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),b9) & not b₁ = 0_ (n,L) & ( for b₂ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₂ in I or not b₂ < b₁,T or b₂ = 0_ (n,L) or not HM (b₂,T) = Monom ((1. L),b9) ) ) ) } is set
g9 . b9 is set
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ = b9 & b₁ in I & HM (b₁,T) = Monom ((1. L),b₂) & not b₁ = 0_ (n,L) & ( for b₃ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₃ in I or not b₃ < b₁,T or b₃ = 0_ (n,L) or not HM (b₃,T) = Monom ((1. L),b₂) ) ) ) } is set
q is set
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (q,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q is set
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HM (q,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Monom ((1. L),r) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g9 is set
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,b9) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
h9 is Element of g9
g9 is Relation-like Function-like set
dom g9 is set
h9 is set
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,b9) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
q is Element of g9
q is Element of g9
g9 . q is set
r is Element of g9
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,q) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
r is Element of g9
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,q) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
rng g9 is set
h9 is set
b9 is set
g9 . b9 is set
q is Element of g9
g9 . q is set
r is Element of g9
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,q) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
g9 is set
h9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is Element of g9
(n,L,h9) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
g9 is Element of K10( the carrier of (Polynom-Ring (n,L)))
the Element of g9 is Element of g9
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,b9) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
h9 is non empty finite Element of K10( the carrier of (Polynom-Ring (n,L)))
(n,T,L,h9) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in h9 & not b₁ = 0_ (n,L) ) } is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
q is Element of the carrier of RelStr(# (Bags n),(n) #)
q is Element of the carrier of RelStr(# (Bags n),(n) #)
[q,q] is V21() set
r is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
Monom ((1. L),r) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),r) & not b₁ = 0_ (n,L) & ( for b₂ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₂ in I or not b₂ < b₁,T or b₂ = 0_ (n,L) or not HM (b₂,T) = Monom ((1. L),r) ) ) ) } is set
htq is Element of g9
pp is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,pp) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (g,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
term (HM (g,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,(n,T,L,h9)) is functional Element of K10((Bags n))
{ b₁ where b₁ is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n : ex b₂ being Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set st
( b₂ in (n,T,L,h9) & b₂ divides b₁ ) } is set
b9 is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,q) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
q is Element of g9
q is Element of g9
r is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),r) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),r) & not b₁ = 0_ (n,L) & ( for b₂ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₂ in I or not b₂ < b₁,T or b₂ = 0_ (n,L) or not HM (b₂,T) = Monom ((1. L),r) ) ) ) } is set
p is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (p,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (q,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
coefficient (HM (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (q,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
term (HM (q,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
HT (b9,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,L,b9) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
h9 \ (n,L,b9) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
pp is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
b is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
Support b9 is functional finite Element of K10((Bags n))
b9 . b 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
(b9 . b) / (HC (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
htq is Element of the carrier of RelStr(# (Bags n),(n) #)
{htq} is non empty trivial finite 1 -element set
h \ {htq} is functional finite Element of K10((Bags n))
gg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(n,L,gg) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
qq is Element of g9
qq is Element of g9
mm is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
Monom ((1. L),mm) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
{ b₁ where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & HM (b₁,T) = Monom ((1. L),mm) & not b₁ = 0_ (n,L) & ( for b₂ being non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) holds
( not b₂ in I or not b₂ < b₁,T or b₂ = 0_ (n,L) or not HM (b₂,T) = Monom ((1. L),mm) ) ) ) } is set
gg is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (gg,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
term (HM (gg,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
htg is Element of the carrier of RelStr(# (Bags n),(n) #)
qq is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
qq + (HT (g,T)) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
qq *' g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
((b9 . b) / (HC (g,T))) * (qq *' g) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 - (((b9 . b) / (HC (g,T))) * (qq *' g)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
[htg,htq] is V21() set
qq is Element of the carrier of RelStr(# (Bags n),(n) #)
mm is Element of the carrier of RelStr(# (Bags n),(n) #)
c₃₇ is Element of the carrier of RelStr(# (Bags n),(n) #)
c₃₈ is Element of the carrier of RelStr(# (Bags n),(n) #)
pp . (HT (b9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
b9 . (HT (b9,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
Support pp is functional finite Element of K10((Bags n))
HT (pp,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
HC (pp,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((HC (pp,T)),(HT (pp,T))) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (pp,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HM (b9,T) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
coefficient (HM (pp,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
m is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
m *' g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 - (m *' g) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
qq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
mm is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
mm 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))
mm * gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (mm * gg) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
qq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
qq + (- (mm * gg)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
qq - (mm * gg) 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 natural finite cardinal V49() V50() complex ext-real non negative Element of NAT
Bags n is non empty functional Element of K10((Bags n))
Bags n is non empty set
K10((Bags n)) is non empty set
K11((Bags n),(Bags n)) is non empty Relation-like set
K10(K11((Bags n),(Bags n))) is non empty set
T is Relation-like total V46( Bags n, Bags n) reflexive antisymmetric connected transitive V261() admissible Element of K10(K11((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 V130() 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
K10( the carrier of (Polynom-Ring (n,L))) is non empty set
I is non empty add-closed left-ideal right-ideal Element of K10( the carrier of (Polynom-Ring (n,L)))
G is non empty finite Element of K10( the carrier of (Polynom-Ring (n,L)))
H is non empty finite Element of K10( the carrier of (Polynom-Ring (n,L)))
H -Ideal is non empty add-closed left-ideal right-ideal finitely_generated Element of K10( the carrier of (Polynom-Ring (n,L)))
G \/ H is non empty finite Element of K10( the carrier of (Polynom-Ring (n,L)))
G /\ H is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
(G \/ H) \ (G /\ H) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
GH is set
GH is set
g is set
GH is non empty Element of K10( the carrier of (Polynom-Ring (n,L)))
G \ H is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
H \ G is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
(G \ H) \/ (H \ G) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
the carrier of L is non empty non trivial set
K11((Bags n), the carrier of L) is non empty Relation-like set
K10(K11((Bags n), the carrier of L)) is non empty set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
G -Ideal is non empty add-closed left-ideal right-ideal finitely_generated Element of K10( the carrier of (Polynom-Ring (n,L)))
g is set
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HC (h,T) 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
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_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
b9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HC (h,T) 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
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_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
0_ (n,L) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) monomial-like Constant V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
PolyRedRel (G,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
NonZero (Polynom-Ring (n,L)) is Element of K10( the carrier of (Polynom-Ring (n,L)))
[#] (Polynom-Ring (n,L)) is non empty non proper Element of K10( 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 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of K10( the carrier of (Polynom-Ring (n,L)))
K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))) is Relation-like set
K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)))) is non empty set
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HC (g,T) 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
g is set
g is set
PolyRedRel (H,T) is Relation-like co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of K10(K11((NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L))))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,T,L,(H -Ideal)) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in H -Ideal & not b₁ = 0_ (n,L) ) } is set
(n,T,L,H) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in H & not b₁ = 0_ (n,L) ) } is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- h is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (- h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(g + (- h)) + h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- h) + h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + ((- h) + h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support g is functional finite Element of K10((Bags n))
(n,L,g) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
G \ (n,L,g) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support f is functional finite Element of K10((Bags n))
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
f . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g + (- h)) . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- h) . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) + ((- h) . (HT (g,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h . (HT (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (h . (HT (h,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) + (- (h . (HT (h,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (g,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (g,T)) + (- (h . (HT (h,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (h,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (HC (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (g,T)) + (- (HC (h,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1. L) + (- (HC (h,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1. L) + (- (1. L)) 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
max ((HT (g,T)),(HT (h,T)),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 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))
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 - h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(n,T,L,I) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
Support (g + (- h)) is functional finite Element of K10((Bags n))
Support (- h) is functional finite Element of K10((Bags n))
(Support g) \/ (Support (- h)) is functional finite Element of K10((Bags n))
Support h is functional finite Element of K10((Bags n))
(Support g) \/ (Support h) is functional finite Element of K10((Bags n))
(n,T,L,G) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G & not b₁ = 0_ (n,L) ) } is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,L,h) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
H \ (n,L,h) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
g is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,T,L,(G -Ideal)) is functional Element of K10((Bags n))
K10((Bags n)) is non empty set
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G -Ideal & not b₁ = 0_ (n,L) ) } is set
(n,T,L,G) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in G & not b₁ = 0_ (n,L) ) } is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g - h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(0_ (n,L)) + h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
- h is non empty Relation-like Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (- h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(g + (- h)) + h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
(- h) + h is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + ((- h) + h) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
g + (0_ (n,L)) is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support g is functional finite Element of K10((Bags n))
(n,L,g) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
H \ (n,L,g) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (h,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
f is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
Support f is functional finite Element of K10((Bags n))
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
f . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g + (- h)) . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- h) . (HT (g,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) + ((- h) . (HT (g,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
h . (HT (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (h . (HT (h,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (HT (g,T))) + (- (h . (HT (h,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (g,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (g,T)) + (- (h . (HT (h,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (h,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (HC (h,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (g,T)) + (- (HC (h,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1. L) + (- (HC (h,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(1. L) + (- (1. L)) 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
max ((HT (g,T)),(HT (h,T)),T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 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))
h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 - h9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(n,T,L,I) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in I & not b₁ = 0_ (n,L) ) } is set
Support (g + (- h)) is functional finite Element of K10((Bags n))
Support (- h) is functional finite Element of K10((Bags n))
(Support g) \/ (Support (- h)) is functional finite Element of K10((Bags n))
Support h is functional finite Element of K10((Bags n))
(Support g) \/ (Support h) is functional finite Element of K10((Bags n))
(n,T,L,H) is functional Element of K10((Bags n))
{ (HT (b₁,T)) where b₁ is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L)) : ( b₁ in H & not b₁ = 0_ (n,L) ) } is set
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
b9 is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support set
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
q is non empty Relation-like Function-like total V46( Bags n, the carrier of L) non-zero V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
r is non empty Relation-like Function-like total V46( Bags n, the carrier of L) V271( Bags n,L) Element of K10(K11((Bags n), the carrier of L))
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V211() V212() V213() V214() finite-support Element of Bags n
(n,L,h) is non empty trivial functional finite 1 -element Element of K10( the carrier of (Polynom-Ring (n,L)))
G \ (n,L,h) is finite Element of K10( the carrier of (Polynom-Ring (n,L)))