:: POLYRED semantic presentation

REAL is set
NAT is non zero non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal Element of bool REAL
bool REAL is cup-closed diff-closed preBoolean set
NAT is non zero non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal set
bool NAT is non trivial non finite cup-closed diff-closed preBoolean set
bool NAT is non trivial non finite cup-closed diff-closed preBoolean set
COMPLEX is set
RAT is set
INT is set
0 is zero 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 0 -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() V135() ext-real non positive non negative complex irreflexive V242() V243() V244() V245() FinSequence-yielding finite-support set
1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
{0,1} is non zero finite V28() set
2 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
[:COMPLEX,COMPLEX:] is Relation-like set
bool [:COMPLEX,COMPLEX:] is cup-closed diff-closed preBoolean set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is cup-closed diff-closed preBoolean set
[:REAL,REAL:] is Relation-like set
bool [:REAL,REAL:] is cup-closed diff-closed preBoolean set
[:[:REAL,REAL:],REAL:] is Relation-like set
bool [:[:REAL,REAL:],REAL:] is cup-closed diff-closed preBoolean set
[:RAT,RAT:] is Relation-like set
bool [:RAT,RAT:] is cup-closed diff-closed preBoolean set
[:[:RAT,RAT:],RAT:] is Relation-like set
bool [:[:RAT,RAT:],RAT:] is cup-closed diff-closed preBoolean set
[:INT,INT:] is Relation-like set
bool [:INT,INT:] is cup-closed diff-closed preBoolean set
[:[:INT,INT:],INT:] is Relation-like set
bool [:[:INT,INT:],INT:] is cup-closed diff-closed preBoolean set
[:NAT,NAT:] is non trivial Relation-like non finite set
[:[:NAT,NAT:],NAT:] is non trivial Relation-like non finite set
bool [:[:NAT,NAT:],NAT:] is non trivial non finite cup-closed diff-closed preBoolean set
[:NAT,REAL:] is Relation-like set
bool [:NAT,REAL:] is cup-closed diff-closed preBoolean set
K234() is Relation-like NAT -defined Function-like total set
3 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
Seg 1 is non zero trivial finite 1 -element Element of bool NAT
{1} is non zero trivial finite V28() 1 -element set
Seg 2 is non zero finite 2 -element Element of bool NAT
{1,2} is non zero finite V28() set
0 is zero 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 0 -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() V135() ext-real non positive non negative complex irreflexive V242() V243() V244() V245() FinSequence-yielding finite-support Element of NAT
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non trivial ZeroStr
the carrier of T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
NonZero T is non zero Element of bool the carrier of T
bool the carrier of T is cup-closed diff-closed preBoolean set
[#] T is non zero non proper Element of bool the carrier of T
0. T is zero Element of the carrier of T
the ZeroF of T is Element of the carrier of T
{(0. T)} is non zero trivial finite 1 -element set
([#] T) \ {(0. T)} is Element of bool the carrier of T
the Element of NonZero T is Element of NonZero T
P is Element of the carrier of T
P | (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
f is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
(0. T) | (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
the non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
n is set
bool n is cup-closed diff-closed preBoolean set
[:n,n:] is Relation-like set
bool [:n,n:] is cup-closed diff-closed preBoolean set
T is Element of bool n
L is Relation-like n -defined n -valued total V46(n,n) reflexive antisymmetric transitive Element of bool [:n,n:]
field L is set
n is epsilon-transitive epsilon-connected ordinal set
T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
T + P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L + P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f is epsilon-transitive epsilon-connected ordinal set
L . f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
T . f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
g is epsilon-transitive epsilon-connected ordinal set
(T + P) . g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
T . g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
P . g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
(T . g) + (P . g) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
L . g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
(L . g) + (P . g) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
(L + P) . g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
(T + P) . f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
P . f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
(T . f) + (P . f) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
(L + P) . f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
(L . f) + (P . f) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
n is epsilon-transitive epsilon-connected ordinal set
T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P is epsilon-transitive epsilon-connected ordinal set
L . P is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
T . P is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex V241() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non trivial ZeroStr
the carrier of T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
0. T is zero Element of the carrier of T
the ZeroF of T is Element of the carrier of T
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) non-zero finite-Support Element of bool [:(Bags n), the carrier of T:]
bool (Bags n) is cup-closed diff-closed preBoolean set
P is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
P + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
f is functional finite Element of bool (Bags n)
card f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g is non zero functional finite Element of bool (Bags n)
the Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of g
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
{f9} is non zero trivial functional finite 1 -element set
g \ {f9} is functional finite Element of bool (Bags n)
R is set
{f9} \/ g is non zero finite set
{f9} \/ (g \ {f9}) is non zero finite set
card (g \ {f9}) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(card (g \ {f9})) + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
R is non zero set
x is non zero functional finite Element of bool (Bags n)
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Support L is functional Element of bool (Bags n)
P is finite set
card P is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
card (Support L) is epsilon-transitive epsilon-connected ordinal cardinal set
f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
card f is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
g is functional finite Element of bool (Bags n)
card g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
{0} is non zero trivial functional finite V28() 1 -element set
card {0} is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
f9 is set
{f9} is non zero trivial finite 1 -element set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L . f9 is Element of the carrier of T
L . g is Element of the carrier of T
n is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of n is non zero set
T is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
len T is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
L is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
Sum T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
Sum L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
T /. (len T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(Sum L) + (T /. (len T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
P + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
Seg P is finite P -element Element of bool NAT
T | (Seg P) is Relation-like NAT -defined Seg P -defined NAT -defined the carrier of n -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT, the carrier of n:]
[:NAT, the carrier of n:] is non trivial Relation-like non finite set
bool [:NAT, the carrier of n:] is non trivial non finite cup-closed diff-closed preBoolean set
<*(T /. (len T))*> is non zero trivial Relation-like NAT -defined the carrier of n -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support M30( the carrier of n,K500( the carrier of n))
K500( the carrier of n) is non zero functional FinSequence-membered M29( the carrier of n)
L ^ <*(T /. (len T))*> is non zero Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of n
len <*(T /. (len T))*> is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
dom T is finite Element of bool NAT
Seg (P + 1) is non zero finite P + 1 -element K216(P,1) -element Element of bool NAT
K216(P,1) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
f9 is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT : ( 1 <= b₁ & b₁ <= P + 1 ) } is set
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
len L is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(len L) + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
(len L) + (len <*(T /. (len T))*>) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
(L ^ <*(T /. (len T))*>) . g9 is set
g9 - (len L) is V49() ext-real complex set
<*(T /. (len T))*> . (g9 - (len L)) is set
(P + 1) - P is V49() ext-real complex set
<*(T /. (len T))*> . ((P + 1) - P) is set
<*(T /. (len T))*> . 1 is set
T /. (P + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
T . g9 is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT : ( 1 <= b₁ & b₁ <= P ) } is set
dom L is finite Element of bool NAT
(L ^ <*(T /. (len T))*>) . g9 is set
L . g9 is set
T . g9 is set
(L ^ <*(T /. (len T))*>) . g9 is set
T . g9 is set
(L ^ <*(T /. (len T))*>) . g9 is set
T . g9 is set
T . f9 is set
(L ^ <*(T /. (len T))*>) . f9 is set
len (L ^ <*(T /. (len T))*>) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
len L is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(len L) + (len <*(T /. (len T))*>) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
(len L) + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
Seg (len (L ^ <*(T /. (len T))*>)) is non zero finite len (L ^ <*(T /. (len T))*>) -element Element of bool NAT
dom (L ^ <*(T /. (len T))*>) is non zero finite Element of bool NAT
Sum <*(T /. (len T))*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(Sum L) + (Sum <*(T /. (len T))*>) 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 zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) non-zero finite-Support Element of bool [:(Bags n), the carrier of T:]
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) non-zero finite-Support Element of bool [:(Bags n), the carrier of T:]
L *' P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), 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
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
g + f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(L *' P) . (g + f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
decomp (g + f) is non zero Relation-like NAT -defined K501(2,(Bags n)) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V135() FinSequence-yielding finite-support FinSequence of K501(2,(Bags n))
K501(2,(Bags n)) is M29( Bags n)
len (decomp (g + f)) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
g9 is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
Sum g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
len g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
dom g9 is finite Element of bool NAT
(L . g) * (P . f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
bool (Bags n) is cup-closed diff-closed preBoolean set
divisors (g + f) is non zero Relation-like NAT -defined Bags n -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like finite-support FinSequence of Bags n
LexOrder n is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) being_linear-order reflexive antisymmetric transitive admissible Element of bool [:(Bags n),(Bags n):]
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
f9 is non zero functional finite Element of bool (Bags n)
SgmX ((LexOrder n),f9) is non zero Relation-like NAT -defined Bags n -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like finite-support FinSequence of Bags n
rng (SgmX ((LexOrder n),f9)) is non zero finite set
dom (SgmX ((LexOrder n),f9)) is non zero finite Element of bool NAT
R is set
(SgmX ((LexOrder n),f9)) . R is Relation-like Function-like set
dom (decomp (g + f)) is non zero finite Element of bool NAT
(divisors (g + f)) /. R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(decomp (g + f)) /. R is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
(g + f) -' g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*g,((g + f) -' g)*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
<*g,f*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
Seg (len (decomp (g + f))) is non zero finite len (decomp (g + f)) -element Element of bool NAT
x is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(decomp (g + f)) /. x is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
g9 /. x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*x,q*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
L . x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P . q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . x) * (P . q) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
<*g,f*> . 2 is set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(decomp (g + f)) /. u is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
g9 /. u is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
a is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*a,u9*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
L . a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P . u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . a) * (P . u9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
a9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*a9,u9*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
a9 + u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*a9,u9*> . 2 is set
<*a9,u9*> . 1 is set
(decomp (g + f)) . u is FinSequence-like set
(decomp (g + f)) . x is FinSequence-like set
a + u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g + u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(g + u9) -' u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
u9 + a is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f + a is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(f + a) -' a is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*g,f*> . 1 is set
Support (L *' P) is functional finite Element of bool (Bags n)
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
L + P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
- (L + P) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
- L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
- P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
(- L) + (- P) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is set
dom (- (L + P)) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
((- L) + (- P)) . 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
(- P) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- L) . g) + ((- P) . 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
(- (L . g)) + ((- P) . g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (P . g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (L . g)) + (- (P . g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P . g) + (L . g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((P . g) + (L . g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L + P) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((L + P) . g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (L + P)) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (L + P)) . f is set
((- L) + (- P)) . f is set
dom ((- L) + (- P)) is non zero functional Element of bool (Bags n)
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_zeroed addLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
(0_ (n,T)) + L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
P . g is Element of the carrier of T
(0_ (n,T)) . g is Element of the carrier of T
L . g is Element of the carrier of T
((0_ (n,T)) . g) + (L . g) is Element of the carrier of T
0. T is zero Element of the carrier of T
the ZeroF of T is Element of the carrier of T
f is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f . g is Element of the carrier of T
(0. T) + (f . g) is Element of the carrier of T
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
- L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
(- L) + L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
L + (- L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
((- L) + L) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- L) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- L) . f) + (L . f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (L . f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (L . f)) + (L . f) 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
(0_ (n,T)) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(L + (- 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
(L . g) + ((- 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) + (- (L . g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(0_ (n,T)) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
L - (0_ (n,T)) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
P . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (0_ (n,T)) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
L + (- (0_ (n,T))) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
(L + (- (0_ (n,T)))) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (0_ (n,T))) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . f) + ((- (0_ (n,T))) . f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(0_ (n,T)) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((0_ (n,T)) . f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . f) + (- ((0_ (n,T)) . f)) 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
- (0. T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . f) + (- (0. T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . f) - (0. T) 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 zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable left-distributive add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
(0_ (n,T)) *' L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
((0_ (n,T)) *' L) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
decomp f is non zero Relation-like NAT -defined K501(2,(Bags n)) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V135() FinSequence-yielding finite-support FinSequence of K501(2,(Bags n))
K501(2,(Bags n)) is M29( Bags n)
len (decomp f) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
g is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
Sum g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
len g is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
dom g is finite Element of bool NAT
f9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
(decomp f) /. f9 is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
g /. f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*g9,f9*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
(0_ (n,T)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((0_ (n,T)) . g9) * (L . f9) 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
(0. T) * (L . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(0_ (n,T)) . f 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 zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() 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 T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
Polynom-Ring (n,T) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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,T)) is non zero set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
- L is non zero Relation-like Bags n -defined Bags n -defined the carrier of T -valued Function-like total total V46( Bags n, the carrier of T) V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
- P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
f9 + P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
(- L) + L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
0. (Polynom-Ring (n,T)) is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
the ZeroF of (Polynom-Ring (n,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() 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 T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
L *' P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
- (L *' P) is non zero Relation-like Bags n -defined Bags n -defined the carrier of T -valued Function-like total total V46( Bags n, the carrier of T) V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
- L is non zero Relation-like Bags n -defined Bags n -defined the carrier of T -valued Function-like total total V46( Bags n, the carrier of T) V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
(- L) *' P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
- P is non zero Relation-like Bags n -defined Bags n -defined the carrier of T -valued Function-like total total V46( Bags n, the carrier of T) V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
L *' (- P) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
Polynom-Ring (n,T) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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,T)) is non zero set
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
f9 * g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
- f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
(- f9) * g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
- g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
f9 * (- g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
- (f9 * g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,T))
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
0. T is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like finite-Support Element of bool [:(Bags n), the carrier of T:]
term P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
{(term P)} is non zero trivial functional finite 1 -element set
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
{(term P)} is non zero trivial functional finite 1 -element set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like finite-Support Element of bool [:(Bags n), the carrier of T:]
P *' L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
term P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (term P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(term P) + f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(P *' L) . ((term P) + f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P . (term P)) * (L . f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
decomp ((term P) + f) is non zero Relation-like NAT -defined K501(2,(Bags n)) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V135() FinSequence-yielding finite-support FinSequence of K501(2,(Bags n))
K501(2,(Bags n)) is M29( Bags n)
len (decomp ((term P) + f)) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
g9 is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
Sum g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
len g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
dom g9 is finite Element of bool NAT
dom (decomp ((term P) + f)) is non zero finite Element of bool NAT
<*(term P),f*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
f9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(decomp ((term P) + f)) /. f9 is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
Seg (len g9) is finite len g9 -element Element of bool NAT
g9 /. f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*g9,R*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
P . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P . g9) * (L . R) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
<*(term P),f*> . 2 is set
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
x is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 /. x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(decomp ((term P) + f)) /. x is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*x,q*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
P . x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P . x) * (L . q) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
divisors ((term P) + f) is non zero Relation-like NAT -defined Bags n -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like finite-support FinSequence of Bags n
(divisors ((term P) + f)) /. x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
((term P) + f) -' x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*x,(((term P) + f) -' x)*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
<*x,(((term P) + f) -' x)*> . 2 is set
<*x,q*> . 2 is set
(decomp ((term P) + f)) . x is FinSequence-like set
(decomp ((term P) + f)) . f9 is FinSequence-like set
<*g9,R*> . 1 is set
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable left-distributive right_zeroed doubleLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
0. T is zero left_add-cancelable Element of the carrier of T
the ZeroF of T is left_add-cancelable Element of the carrier of T
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
(0. T) * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is set
dom ((0. T) * L) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
((0. T) * L) . g is left_add-cancelable Element of the carrier of T
L . g is left_add-cancelable Element of the carrier of T
(0. T) * (L . g) is left_add-cancelable Element of the carrier of T
((0. T) * L) . f is set
(0_ (n,T)) . f is set
dom (0_ (n,T)) is non zero functional Element of bool (Bags n)
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
- L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
- (P * L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
- P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- P) * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P * (- L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
g is set
dom (- (P * L)) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(- (P * L)) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P * L) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((P * L) . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P * (L . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (P * (L . f9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- P) * (L . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((- P) * L) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (P * L)) . g is set
((- P) * L) . g is set
dom ((- P) * L) is non zero functional Element of bool (Bags n)
g is set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(- (P * L)) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P * L) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- ((P * L) . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P * (L . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (P * (L . f9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
- (L . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P * (- (L . f9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- L) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P * ((- L) . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P * (- L)) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(- (P * L)) . g is set
(P * (- L)) . g is set
dom (P * (- L)) is non zero functional Element of bool (Bags n)
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left-distributive doubleLoopStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is Element of the carrier of T
P * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is Element of the carrier of T
f * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
(P * L) + (f * L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P + f is Element of the carrier of T
(P + f) * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
g9 is set
dom ((P * L) + (f * L)) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
((P * L) + (f * L)) . f9 is Element of the carrier of T
(P * L) . f9 is Element of the carrier of T
(f * L) . f9 is Element of the carrier of T
((P * L) . f9) + ((f * L) . f9) is Element of the carrier of T
L . f9 is Element of the carrier of T
P * (L . f9) is Element of the carrier of T
(P * (L . f9)) + ((f * L) . f9) is Element of the carrier of T
f * (L . f9) is Element of the carrier of T
(P * (L . f9)) + (f * (L . f9)) is Element of the carrier of T
(P + f) * (L . f9) is Element of the carrier of T
((P + f) * L) . f9 is Element of the carrier of T
((P * L) + (f * L)) . g9 is set
((P + f) * L) . g9 is set
dom ((P + f) * L) is non zero functional Element of bool (Bags n)
n is set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty associative multLoopStr_0
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is Element of the carrier of T
f is Element of the carrier of T
P * f is Element of the carrier of T
(P * f) * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P * (f * L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
g9 is set
dom ((P * f) * L) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
((P * f) * L) . f9 is Element of the carrier of T
L . f9 is Element of the carrier of T
(P * f) * (L . f9) is Element of the carrier of T
f * (L . f9) is Element of the carrier of T
P * (f * (L . f9)) is Element of the carrier of T
(f * L) . f9 is Element of the carrier of T
P * ((f * L) . f9) is Element of the carrier of T
(P * (f * L)) . f9 is Element of the carrier of T
((P * f) * L) . g9 is set
(P * (f * L)) . g9 is set
dom (P * (f * L)) is non zero functional Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() associative commutative 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 zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
L *' P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f * (L *' P) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f * P is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
L *' (f * P) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f9 is set
dom (f * (L *' P)) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(L *' (f * P)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
decomp g9 is non zero Relation-like NAT -defined K501(2,(Bags n)) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V135() FinSequence-yielding finite-support FinSequence of K501(2,(Bags n))
K501(2,(Bags n)) is M29( Bags n)
len (decomp g9) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
R is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
Sum R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
len R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
dom R is finite Element of bool NAT
(L *' P) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
x is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
Sum x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
len x is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
dom x is finite Element of bool NAT
Seg (len R) is finite len R -element Element of bool NAT
x is set
q is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(decomp g9) /. q is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
x /. q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
u is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
a is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*u,a*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
L . u is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P . a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . u) * (P . a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
R /. q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
a9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*u9,a9*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
L . u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(f * P) . a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . u9) * ((f * P) . a9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
<*u9,a9*> . 2 is set
<*u9,a9*> . 1 is set
R /. x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f * (P . a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(L . u) * (f * (P . a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
x /. x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f * (x /. x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f * x is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
f * (Sum x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(f * (L *' P)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(f * (L *' P)) . f9 is set
(L *' (f * P)) . f9 is set
dom (L *' (f * P)) is non zero functional Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
0. L is zero Element of the carrier of L
the ZeroF of L is Element of the carrier of L
{ [b₁,(P . (b₁ -' T))] where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : T divides b₁ } is set
{ [b₁,(0. L)] where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : not T divides b₁ } is set
{ [b₁,(P . (b₁ -' T))] where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : T divides b₁ } \/ { [b₁,(0. L)] where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : not T divides b₁ } is set
g9 is set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f9 -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (f9 -' T) is Element of the carrier of L
[f9,(P . (f9 -' T))] is V21() set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[f9,(0. L)] is V21() set
f9 is set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[g9,(0. L)] is V21() set
g9 is Relation-like Bags n -defined the carrier of L -valued Element of bool [:(Bags n), the carrier of L:]
dom g9 is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (g9 -' T) is Element of the carrier of L
[g9,(P . (g9 -' T))] is V21() set
g9 is Relation-like Bags n -defined the carrier of L -valued Element of bool [:(Bags n), the carrier of L:]
dom g9 is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 is Relation-like Bags n -defined the carrier of L -valued Element of bool [:(Bags n), the carrier of L:]
dom g9 is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 is Relation-like Bags n -defined the carrier of L -valued Element of bool [:(Bags n), the carrier of L:]
dom g9 is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f9 is set
f9 is set
g9 is set
[f9,g9] is V21() set
R is set
[f9,R] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[x,(0. L)] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
x -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (x -' T) is Element of the carrier of L
[x,(P . (x -' T))] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[x,(0. L)] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
x -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (x -' T) is Element of the carrier of L
[x,(P . (x -' T))] is V21() set
f9 is set
g9 is set
[f9,g9] is V21() set
R is set
[f9,R] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
x -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (x -' T) is Element of the carrier of L
[x,(P . (x -' T))] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
x -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (x -' T) is Element of the carrier of L
[x,(P . (x -' T))] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[x,(0. L)] is V21() set
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[x,(0. L)] is V21() set
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[R,(0. L)] is V21() set
g9 . R is Element of the carrier of L
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
R -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (R -' T) is Element of the carrier of L
[R,(P . (R -' T))] is V21() set
g9 . R is Element of the carrier of L
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 . R is Element of the carrier of L
R -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (R -' T) is Element of the carrier of L
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 . x is Element of the carrier of L
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f . f9 is Element of the carrier of L
f9 -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (f9 -' T) is Element of the carrier of L
g . f9 is Element of the carrier of L
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f . f9 is Element of the carrier of L
g . f9 is Element of the carrier of L
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f . f9 is Element of the carrier of L
g . f9 is Element of the carrier of L
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f . f9 is Element of the carrier of L
g . f9 is Element of the carrier of L
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L + T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P is non empty ZeroStr
the carrier of P is non zero set
[:(Bags n), the carrier of P:] is Relation-like set
bool [:(Bags n), the carrier of P:] is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of P -valued Function-like total V46( Bags n, the carrier of P) Element of bool [:(Bags n), the carrier of P:]
(n,T,P,f) is non zero Relation-like Bags n -defined the carrier of P -valued Function-like total V46( Bags n, the carrier of P) Element of bool [:(Bags n), the carrier of P:]
(n,T,P,f) . (L + T) is Element of the carrier of P
f . L is Element of the carrier of P
(L + T) -' T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f . ((L + T) -' T) is Element of the carrier of P
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty ZeroStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
Support L is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,P,T,L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
Support (n,P,T,L) is functional Element of bool (Bags n)
{ (P + b₁) where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : b₁ in Support L } is set
f is set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(n,P,T,L) . g is Element of the carrier of T
0. T is zero Element of the carrier of T
the ZeroF of T is Element of the carrier of T
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L . f9 is Element of the carrier of T
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,T,L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
{ [b₁,(T + b₁)] where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : b₁ in Support P } is set
g is set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
T + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[f9,(T + f9)] is V21() set
g is set
f9 is set
[g,f9] is V21() set
g9 is set
[g,g9] is V21() set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
T + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[f9,(T + f9)] is V21() set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
T + g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[g9,(T + g9)] is V21() set
f9 is set
g is Relation-like Function-like set
dom g is set
g9 is set
[f9,g9] is V21() set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
T + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[f9,(T + f9)] is V21() set
Support (n,T,L,P) is functional Element of bool (Bags n)
{ (T + b₁) where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : b₁ in Support P } is set
f9 is set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
T + g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[g9,f9] is V21() set
rng g is set
f9 is set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
T + g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[g9,(T + g9)] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
P is non empty ZeroStr
the carrier of P is non zero set
[:(Bags n), the carrier of P:] is Relation-like set
bool [:(Bags n), the carrier of P:] is cup-closed diff-closed preBoolean set
T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f is non zero Relation-like Bags n -defined the carrier of P -valued Function-like total V46( Bags n, the carrier of P) Element of bool [:(Bags n), the carrier of P:]
(n,T,P,f) is non zero Relation-like Bags n -defined the carrier of P -valued Function-like total V46( Bags n, the carrier of P) Element of bool [:(Bags n), the carrier of P:]
L is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L + T is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,T,P,f) . (L + T) is Element of the carrier of P
f . L is Element of the carrier of P
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty ZeroStr
the carrier of T is non zero set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
(n,P,T,L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
Support (n,P,T,L) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support L is functional Element of bool (Bags n)
{ (P + b₁) where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : b₁ in Support L } is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial ZeroStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT ((n,f,L,P),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Support (n,f,L,P) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
f9 is non zero set
the Element of f9 is Element of f9
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,P) . (f + f9) is Element of the carrier of L
(f + f9) -' f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . ((f + f9) -' f) is Element of the carrier of L
P . f9 is Element of the carrier of L
0. L is zero Element of the carrier of L
the ZeroF of L is Element of the carrier of L
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (n,f,L,P) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f9 is non zero set
the Element of f9 is Element of f9
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f9 -' f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,P) . f9 is Element of the carrier of L
0. L is zero Element of the carrier of L
the ZeroF of L is Element of the carrier of L
P . (f9 -' f) is Element of the carrier of L
Support P is functional Element of bool (Bags n)
P . (HT (P,T)) is Element of the carrier of L
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,P) . f9 is Element of the carrier of L
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f + g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . g9 is Element of the carrier of L
[g9,(HT (P,T))] is V21() set
[f9,(f + (HT (P,T)))] is V21() set
(n,f,L,P) . (f + (HT (P,T))) is Element of the carrier of L
Support (n,f,L,P) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (n,f,L,P) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Support P is functional Element of bool (Bags n)
{ (f + b₁) where b₁ is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n : b₁ in Support P } is set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[f9,(HT (P,T))] is V21() set
[(f + f9),(f + (HT (P,T)))] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
(n,(EmptyBag n),L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
g is set
dom P is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(n,(EmptyBag n),L,P) . f9 is Element of the carrier of L
f9 -' (EmptyBag n) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (f9 -' (EmptyBag n)) is Element of the carrier of L
P . f9 is Element of the carrier of L
(n,(EmptyBag n),L,P) . g is set
P . g is set
dom (n,(EmptyBag n),L,P) is non zero functional Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f + g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,(f + g),L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
(n,g,L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
(n,f,L,(n,g,L,P)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) Element of bool [:(Bags n), the carrier of L:]
f9 is set
dom (n,(f + g),L,P) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(f + g) + R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g + R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f + (g + R) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 -' f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,(n,g,L,P)) . g9 is Element of the carrier of L
(n,g,L,P) . (g9 -' f) is Element of the carrier of L
(g9 -' f) -' g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . ((g9 -' f) -' g) is Element of the carrier of L
g9 -' (f + g) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . (g9 -' (f + g)) is Element of the carrier of L
(n,(f + g),L,P) . g9 is Element of the carrier of L
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,(f + g),L,P) . g9 is Element of the carrier of L
0. L is zero Element of the carrier of L
the ZeroF of L is Element of the carrier of L
g9 -' f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(g9 -' f) -' g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
((g9 -' f) -' g) + g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(((g9 -' f) -' g) + g) + f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g + f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
((g9 -' f) -' g) + (g + f) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,(n,g,L,P)) . g9 is Element of the carrier of L
(n,g,L,P) . (g9 -' f) is Element of the carrier of L
(n,f,L,(n,g,L,P)) . g9 is Element of the carrier of L
(n,f,L,(n,g,L,P)) . g9 is Element of the carrier of L
(n,f,L,(n,g,L,P)) . g9 is Element of the carrier of L
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,(n,g,L,P)) . g9 is Element of the carrier of L
(n,(f + g),L,P) . g9 is Element of the carrier of L
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f,L,(n,g,L,P)) . g9 is Element of the carrier of L
(n,(f + g),L,P) . g9 is Element of the carrier of L
(n,(f + g),L,P) . f9 is set
(n,f,L,(n,g,L,P)) . f9 is set
dom (n,f,L,(n,g,L,P)) is non zero functional Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
Support L is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
P * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
Support (P * L) is functional Element of bool (Bags n)
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
dom (0_ (n,T)) is non zero functional Element of bool (Bags n)
dom (P * L) is non zero functional Element of bool (Bags n)
0. T is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f is set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(P * 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
P * (L . g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(0_ (n,T)) . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(P * L) . f is set
(0_ (n,T)) . f is set
f is set
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
g is set
f is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
Support (f * L) is functional Element of bool (Bags n)
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(f * L) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f * (L . f9) 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
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non trivial domRing-like doubleLoopStr
the carrier of T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) finite-Support Element of bool [:(Bags n), the carrier of T:]
Support L is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
P is non zero Element of the carrier of T
P * L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
Support (P * L) is functional Element of bool (Bags n)
f is set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(P * L) . g is Element of the carrier of T
L . g is Element of the carrier of T
P * (L . g) is Element of the carrier of T
0. T is zero Element of the carrier of T
the ZeroF of T is Element of the carrier of T
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f * P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT ((f * P),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Support (f * P) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
g9 is non zero set
the Element of g9 is Element of g9
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(f * P) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
P . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f * (P . g9) 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
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Support (f * P) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 is non zero set
the Element of g9 is Element of g9
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(f * P) . g9 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
P . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f * (P . g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support P is functional Element of bool (Bags n)
P . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(f * P) . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f * (P . (HT (P,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support (f * P) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
T is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of T is non zero non trivial set
[:(Bags n), the carrier of T:] is Relation-like set
bool [:(Bags n), the carrier of T:] is cup-closed diff-closed preBoolean set
L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,P,T,L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f * (n,P,T,L) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), the carrier of T:]
Monom (f,P) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like finite-Support Element of bool [:(Bags n), the carrier of T:]
(Monom (f,P)) *' L is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) Element of bool [:(Bags n), 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
g9 is set
dom (f * (n,P,T,L)) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
((Monom (f,P)) *' L) . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
decomp R is non zero Relation-like NAT -defined K501(2,(Bags n)) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V135() FinSequence-yielding finite-support FinSequence of K501(2,(Bags n))
K501(2,(Bags n)) is M29( Bags n)
len (decomp R) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
x is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
Sum x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
len x is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
dom x is finite Element of bool NAT
Seg (len (decomp R)) is non zero finite len (decomp R) -element Element of bool NAT
dom (decomp R) is non zero finite Element of bool NAT
f9 is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
Monom (f9,P) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like finite-Support Element of bool [:(Bags n), the carrier of T:]
term (Monom (f9,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(f * (n,P,T,L)) . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(n,P,T,L) . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f9 * ((n,P,T,L) . R) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
R -' P is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
L . (R -' P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f9 * (L . (R -' P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P + x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*P,x*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
q is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(decomp R) /. q is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
x /. q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
u is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
a is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*u,a*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
(Monom (f,P)) . u is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((Monom (f,P)) . u) * (L . a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
<*P,x*> . 2 is set
u9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(decomp R) /. u9 is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
x /. u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
a9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*a9,u9*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
(Monom (f,P)) . a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((Monom (f,P)) . a9) * (L . u9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
a9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*a9,q*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
a9 + q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
R -' a9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*a9,u9*> . 1 is set
(decomp R) . u9 is FinSequence-like set
(decomp R) . q is FinSequence-like set
<*P,x*> . 1 is set
coefficient (Monom (f,P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(Monom (f,P)) . (term (Monom (f,P))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(coefficient (Monom (f,P))) * (L . (R -' P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
x is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of T
Sum x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
len x is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
dom x is finite Element of bool NAT
q is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
(decomp R) /. q is Relation-like NAT -defined Bags n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of K501(2,(Bags n))
x /. q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
u is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
a is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*u,a*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
(Monom (f,P)) . u is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
L . a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
((Monom (f,P)) . u) * (L . a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
a9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*u9,a9*> is non zero Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like finite-support set
u9 + a9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
<*u,a*> . 1 is set
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(f * (n,P,T,L)) . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(n,P,T,L) . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f9 * ((n,P,T,L) . R) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f9 * (0. T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(f * (n,P,T,L)) . g9 is set
((Monom (f,P)) *' L) . g9 is set
(f * (n,P,T,L)) . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(f * (n,P,T,L)) . g9 is set
((Monom (f,P)) *' L) . g9 is set
(f * (n,P,T,L)) . R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(f * (n,P,T,L)) . g9 is set
((Monom (f,P)) *' L) . g9 is set
dom ((Monom (f,P)) *' L) is non zero functional Element of bool (Bags n)
0. T is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
the ZeroF of T is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
f9 is set
dom (Monom (f,P)) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
coefficient (Monom (f,P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(Monom (f,P)) . (term (Monom (f,P))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(Monom (f,P)) . f9 is set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
(0_ (n,T)) . f9 is set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(Monom (f,P)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
(0_ (n,T)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(Monom (f,P)) . f9 is set
(0_ (n,T)) . f9 is set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(Monom (f,P)) . f9 is set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
(0_ (n,T)) . f9 is set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
term (Monom (f,P)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(Monom (f,P)) . f9 is set
0_ (n,T) is non zero Relation-like Bags n -defined the carrier of T -valued Function-like total V46( Bags n, the carrier of T) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of T:]
(0_ (n,T)) . f9 is set
dom (0_ (n,T)) is non zero functional Element of bool (Bags n)
f9 is set
dom (f * (n,P,T,L)) is non zero functional Element of bool (Bags n)
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(f * (n,P,T,L)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(n,P,T,L) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(0. T) * ((n,P,T,L) . g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(0_ (n,T)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of T
(f * (n,P,T,L)) . f9 is set
(0_ (n,T)) . f9 is set
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
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support f is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
g *' P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
HT ((g *' P),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
g *' f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (g *' f) is functional finite Element of bool (Bags n)
coefficient g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
term g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g . (term g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (g,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f9 is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom (f9,(term g)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,(term g),L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 * (n,(term g),L,P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT ((n,(term g),L,P),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(term g) + (HT (P,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(g *' f) . (HT ((g *' P),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(g . (term g)) * (f . (HT (P,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HT (g,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
g . (HT (g,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 set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
P is Element of the carrier of RelStr(# (Bags n),T #)
f is Element of the carrier of RelStr(# (Bags n),T #)
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[f9,f9] is V21() set
field T is set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[g,g] is V21() set
[P,f] is V21() set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
[f,P] is V21() set
[g,f9] is V21() set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric transitive well_founded admissible Element of bool [:(Bags n),(Bags n):]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
f is set
g is set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[f9,f9] is V21() set
field T is set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
L is non empty non trivial ZeroStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,T,L,P) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
g9 is set
[(HT (P,T)),g9] is V21() set
g9 is set
[(HT (P,T)),g9] is V21() set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty addLoopStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
[(Support P),(Support P)] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (0_ (n,L)) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
[(Support (0_ (n,L))),(Support P)] is V21() set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
{ [b₁,b₂] where b₁, b₂ is finite Element of Fin the carrier of RelStr(# (Bags n),T #) : ( b₁ = 0 or ( not b₁ = 0 & not b₂ = 0 & not PosetMax b₁ = PosetMax b₂ & [(PosetMax b₁),(PosetMax b₂)] in the InternalRel of RelStr(# (Bags n),T #) ) ) } is set
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
FinOrd-Approx RelStr(# (Bags n),T #) is Relation-like NAT -defined bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] -valued Function-like V46( NAT , bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]) Element of bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):]
[:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is Relation-like set
bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is cup-closed diff-closed preBoolean set
(FinOrd-Approx RelStr(# (Bags n),T #)) . 0 is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
dom (FinOrd-Approx RelStr(# (Bags n),T #)) is Element of bool NAT
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty addLoopStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support f is functional Element of bool (Bags n)
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
[(Support P),(Support f)] is V21() set
[(Support f),(Support P)] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty addLoopStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
Support g is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
Support f is functional Element of bool (Bags n)
[(Support P),(Support f)] is V21() set
[(Support f),(Support g)] is V21() set
[(Support P),(Support g)] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty addLoopStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
RelStr(# (Fin the carrier of RelStr(# (Bags n),T #)),(FinOrd RelStr(# (Bags n),T #)) #) is non empty strict total reflexive transitive antisymmetric RelStr
the carrier of RelStr(# (Fin the carrier of RelStr(# (Bags n),T #)),(FinOrd RelStr(# (Bags n),T #)) #) is non zero set
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support f is functional Element of bool (Bags n)
FinPoset RelStr(# (Bags n),T #) is non empty total reflexive transitive antisymmetric connected RelStr
g9 is Element of the carrier of RelStr(# (Fin the carrier of RelStr(# (Bags n),T #)),(FinOrd RelStr(# (Bags n),T #)) #)
f9 is Element of the carrier of RelStr(# (Fin the carrier of RelStr(# (Bags n),T #)),(FinOrd RelStr(# (Bags n),T #)) #)
[(Support P),(Support f)] is V21() set
[(Support f),(Support P)] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty addLoopStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support f is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
Support f is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
Support f is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
Support f is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[(HT (P,T)),f] is V21() set
P . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
[f,(HT (P,T))] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Red (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[(EmptyBag n),f9] is V21() set
P . f9 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
f9 is set
dom (Red (P,T)) is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(Red (P,T)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HM (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (HM (P,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(P - (HM (P,T))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (HM (P,T)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- (HM (P,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(P + (- (HM (P,T)))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
P . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (HM (P,T))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . g9) + ((- (HM (P,T))) . g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HM (P,T)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((HM (P,T)) . g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . g9) + (- ((HM (P,T)) . g9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
P . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (P . (HT (P,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . (HT (P,T))) + (- (P . (HT (P,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0_ (n,L)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0. L) + (- ((HM (P,T)) . g9)) 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
(0. L) + (- (0. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0_ (n,L)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0_ (n,L)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0_ (n,L)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(Red (P,T)) . f9 is set
(0_ (n,L)) . f9 is set
dom (0_ (n,L)) is non zero functional Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Red (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Red (f,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support f is functional Element of bool (Bags n)
(n,T,L,P) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
(n,T,L,f) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
[(HT (P,T)),(HT (f,T))] is V21() set
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[(HT (f,T)),(HT (P,T))] is V21() set
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
[(n,T,L,P),(n,T,L,f)] is V21() set
FinOrd-Approx RelStr(# (Bags n),T #) is Relation-like NAT -defined bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] -valued Function-like V46( NAT , bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]) Element of bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is Relation-like set
bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is cup-closed diff-closed preBoolean set
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
[(Support P),(Support f)] is V21() set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
Support (Red (P,T)) is functional Element of bool (Bags n)
Support (Red (f,T)) is functional Element of bool (Bags n)
[(Support (Red (P,T))),(Support (Red (f,T)))] is V21() set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
{(HT (f,T))} is non zero trivial functional finite 1 -element set
(Support f) \ {(HT (f,T))} is functional Element of bool (Bags n)
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
{(PosetMax (n,T,L,f))} is non zero trivial finite 1 -element set
(n,T,L,f) \ {(PosetMax (n,T,L,f))} is finite Element of bool (n,T,L,f)
bool (n,T,L,f) is finite V28() cup-closed diff-closed preBoolean set
{(HT (P,T))} is non zero trivial functional finite 1 -element set
(Support P) \ {(HT (P,T))} is functional Element of bool (Bags n)
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
{(PosetMax (n,T,L,P))} is non zero trivial finite 1 -element set
(n,T,L,P) \ {(PosetMax (n,T,L,P))} is finite Element of bool (n,T,L,P)
bool (n,T,L,P) is finite V28() cup-closed diff-closed preBoolean set
[((n,T,L,P) \ {(PosetMax (n,T,L,P))}),((n,T,L,f) \ {(PosetMax (n,T,L,f))})] is V21() set
FinOrd-Approx RelStr(# (Bags n),T #) is Relation-like NAT -defined bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] -valued Function-like V46( NAT , bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]) Element of bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):]
[:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is Relation-like set
bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is cup-closed diff-closed preBoolean set
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
[(n,T,L,P),(n,T,L,f)] is V21() set
[(Support P),(Support f)] is V21() set
[(Support P),(Support f)] is V21() set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
FinOrd-Approx RelStr(# (Bags n),T #) is Relation-like NAT -defined bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] -valued Function-like V46( NAT , bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]) Element of bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):]
[:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is Relation-like set
bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is cup-closed diff-closed preBoolean set
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
[(PosetMax (n,T,L,P)),(PosetMax (n,T,L,f))] is V21() set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
{(PosetMax (n,T,L,P))} is non zero trivial finite 1 -element set
(n,T,L,P) \ {(PosetMax (n,T,L,P))} is finite Element of bool (n,T,L,P)
bool (n,T,L,P) is finite V28() cup-closed diff-closed preBoolean set
{(PosetMax (n,T,L,f))} is non zero trivial finite 1 -element set
(n,T,L,f) \ {(PosetMax (n,T,L,f))} is finite Element of bool (n,T,L,f)
bool (n,T,L,f) is finite V28() cup-closed diff-closed preBoolean set
[((n,T,L,P) \ {(PosetMax (n,T,L,P))}),((n,T,L,f) \ {(PosetMax (n,T,L,f))})] is V21() set
{(HT (f,T))} is non zero trivial functional finite 1 -element set
x is set
Support (Red (f,T)) is functional Element of bool (Bags n)
(Support f) \ {(HT (f,T))} is functional Element of bool (Bags n)
(Support (Red (f,T))) \/ {(HT (f,T))} is non zero set
(Support f) \/ {(HT (f,T))} is non zero set
{(HT (P,T))} is non zero trivial functional finite 1 -element set
x is set
Support (Red (P,T)) is functional Element of bool (Bags n)
(Support P) \ {(HT (P,T))} is functional Element of bool (Bags n)
(Support (Red (P,T))) \/ {(HT (P,T))} is non zero set
(Support P) \/ {(HT (P,T))} is non zero set
(n,T,L,(Red (P,T))) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
(n,T,L,(Red (f,T))) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
[(n,T,L,(Red (P,T))),(n,T,L,(Red (f,T)))] is V21() set
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
[(PosetMax (n,T,L,P)),(PosetMax (n,T,L,f))] is V21() set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
{(PosetMax (n,T,L,P))} is non zero trivial finite 1 -element set
(n,T,L,P) \ {(PosetMax (n,T,L,P))} is finite Element of bool (n,T,L,P)
bool (n,T,L,P) is finite V28() cup-closed diff-closed preBoolean set
{(PosetMax (n,T,L,f))} is non zero trivial finite 1 -element set
(n,T,L,f) \ {(PosetMax (n,T,L,f))} is finite Element of bool (n,T,L,f)
bool (n,T,L,f) is finite V28() cup-closed diff-closed preBoolean set
[((n,T,L,P) \ {(PosetMax (n,T,L,P))}),((n,T,L,f) \ {(PosetMax (n,T,L,f))})] is V21() set
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
[(PosetMax (n,T,L,P)),(PosetMax (n,T,L,f))] is V21() set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
{(PosetMax (n,T,L,P))} is non zero trivial finite 1 -element set
(n,T,L,P) \ {(PosetMax (n,T,L,P))} is finite Element of bool (n,T,L,P)
bool (n,T,L,P) is finite V28() cup-closed diff-closed preBoolean set
{(PosetMax (n,T,L,f))} is non zero trivial finite 1 -element set
(n,T,L,f) \ {(PosetMax (n,T,L,f))} is finite Element of bool (n,T,L,f)
bool (n,T,L,f) is finite V28() cup-closed diff-closed preBoolean set
[((n,T,L,P) \ {(PosetMax (n,T,L,P))}),((n,T,L,f) \ {(PosetMax (n,T,L,f))})] is V21() set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty ZeroStr
the carrier of L is non zero set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Red (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Red (f,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,T,L,P) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
Support P is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
(n,T,L,f) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
Support f is functional Element of bool (Bags n)
Support (Red (P,T)) is functional Element of bool (Bags n)
Support (Red (f,T)) is functional Element of bool (Bags n)
[(Support (Red (P,T))),(Support (Red (f,T)))] is V21() set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
FinOrd-Approx RelStr(# (Bags n),T #) is Relation-like NAT -defined bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] -valued Function-like V46( NAT , bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]) Element of bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):]
[:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is Relation-like set
bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is cup-closed diff-closed preBoolean set
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
{(HT (P,T))} is non zero trivial functional finite 1 -element set
(Support P) \ {(HT (P,T))} is functional Element of bool (Bags n)
PosetMax (n,T,L,P) is Element of the carrier of RelStr(# (Bags n),T #)
{(PosetMax (n,T,L,P))} is non zero trivial finite 1 -element set
(n,T,L,P) \ {(PosetMax (n,T,L,P))} is finite Element of bool (n,T,L,P)
bool (n,T,L,P) is finite V28() cup-closed diff-closed preBoolean set
{(HT (f,T))} is non zero trivial functional finite 1 -element set
(Support f) \ {(HT (f,T))} is functional Element of bool (Bags n)
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
{(PosetMax (n,T,L,f))} is non zero trivial finite 1 -element set
(n,T,L,f) \ {(PosetMax (n,T,L,f))} is finite Element of bool (n,T,L,f)
bool (n,T,L,f) is finite V28() cup-closed diff-closed preBoolean set
[(n,T,L,P),(n,T,L,f)] is V21() set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive well_founded admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Element of bool the carrier of (Polynom-Ring (n,L))
{ (n,T,L,b₁) where b₁ is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:] : b₁ in P } is set
the Element of P is Element of P
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,T,L,f9) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected well_founded RelStr
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
Support f9 is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
FinPoset RelStr(# (Bags n),T #) is non empty total reflexive transitive antisymmetric connected RelStr
g9 is non zero set
MinElement (g9,(FinPoset RelStr(# (Bags n),T #))) is Element of the carrier of (FinPoset RelStr(# (Bags n),T #))
the carrier of (FinPoset RelStr(# (Bags n),T #)) is non zero set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
RelStr(# (Fin the carrier of RelStr(# (Bags n),T #)),(FinOrd RelStr(# (Bags n),T #)) #) is non empty strict total reflexive transitive antisymmetric RelStr
x is set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,T,L,x) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
Support x is functional finite Element of bool (Bags n)
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,T,L,x) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
Support x is functional finite Element of bool (Bags n)
the InternalRel of (FinPoset RelStr(# (Bags n),T #)) is Relation-like the carrier of (FinPoset RelStr(# (Bags n),T #)) -defined the carrier of (FinPoset RelStr(# (Bags n),T #)) -valued total V46( the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #))) reflexive antisymmetric transitive Element of bool [: the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #)):]
[: the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #)):] is Relation-like set
bool [: the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,T,L,x) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
Support x is functional finite Element of bool (Bags n)
[(n,T,L,x),(MinElement (g9,(FinPoset RelStr(# (Bags n),T #))))] is V21() set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
g is epsilon-transitive epsilon-connected ordinal set
Bags g is non zero functional Element of bool (Bags g)
Bags g is non zero set
bool (Bags g) is cup-closed diff-closed preBoolean set
[:(Bags g),(Bags g):] is Relation-like set
bool [:(Bags g),(Bags g):] is cup-closed diff-closed preBoolean set
g9 is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of g9 is non zero non trivial set
[:(Bags g), the carrier of g9:] is Relation-like set
bool [:(Bags g), the carrier of g9:] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Red (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Red (f,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags g -defined the carrier of g9 -valued Function-like total V46( Bags g, the carrier of g9) finite-Support Element of bool [:(Bags g), the carrier of g9:]
0_ (g,g9) is non zero Relation-like Bags g -defined the carrier of g9 -valued Function-like total V46( Bags g, the carrier of g9) monomial-like Constant finite-Support Element of bool [:(Bags g), the carrier of g9:]
g9 is non zero Relation-like Bags g -defined the carrier of g9 -valued Function-like total V46( Bags g, the carrier of g9) finite-Support Element of bool [:(Bags g), the carrier of g9:]
f9 is Relation-like Bags g -defined Bags g -valued total V46( Bags g, Bags g) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags g),(Bags g):]
HT (f9,f9) is Relation-like g -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags g
HT (g9,f9) is Relation-like g -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags g
Red (f9,f9) is non zero Relation-like Bags g -defined the carrier of g9 -valued Function-like total V46( Bags g, the carrier of g9) finite-Support Element of bool [:(Bags g), the carrier of g9:]
Red (g9,f9) is non zero Relation-like Bags g -defined the carrier of g9 -valued Function-like total V46( Bags g, the carrier of g9) finite-Support Element of bool [:(Bags g), the carrier of g9:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
Red (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HM (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Support (Red (P,T)) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support (HM (P,T)) is functional Element of bool (Bags n)
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
Support P is functional Element of bool (Bags n)
P . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HM (P,T)) . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
FinOrd-Approx RelStr(# (Bags n),T #) is Relation-like NAT -defined bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] -valued Function-like V46( NAT , bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]) Element of bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):]
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is Relation-like set
bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is cup-closed diff-closed preBoolean set
dom (FinOrd-Approx RelStr(# (Bags n),T #)) is Element of bool NAT
(FinOrd-Approx RelStr(# (Bags n),T #)) . 0 is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is set
[(Support (Red (P,T))),(Support (HM (P,T)))] is V21() set
the InternalRel of RelStr(# (Bags n),T #) is Relation-like the carrier of RelStr(# (Bags n),T #) -defined the carrier of RelStr(# (Bags n),T #) -valued total V46( the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):]
[: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is Relation-like set
bool [: the carrier of RelStr(# (Bags n),T #), the carrier of RelStr(# (Bags n),T #):] is cup-closed diff-closed preBoolean set
{ [b₁,b₂] where b₁, b₂ is finite Element of Fin the carrier of RelStr(# (Bags n),T #) : ( b₁ = 0 or ( not b₁ = 0 & not b₂ = 0 & not PosetMax b₁ = PosetMax b₂ & [(PosetMax b₁),(PosetMax b₂)] in the InternalRel of RelStr(# (Bags n),T #) ) ) } is set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
HT ((Red (P,T)),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(Red (P,T)) . (HT ((Red (P,T)),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
HT ((HM (P,T)),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HM (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (HM (P,T)) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
{f} is non zero trivial functional finite 1 -element set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
HT ((HM (P,T)),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
P . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (P,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC ((HM (P,T)),T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HM (P,T)) . f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
HM (f,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
(n,T,L,(HM (f,T))) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
Support (HM (f,T)) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
(n,T,L,f) is finite Element of Fin the carrier of RelStr(# (Bags n),T #)
Support f is functional Element of bool (Bags n)
PosetMax (n,T,L,(HM (f,T))) is Element of the carrier of RelStr(# (Bags n),T #)
{(PosetMax (n,T,L,(HM (f,T))))} is non zero trivial finite 1 -element set
(n,T,L,(HM (f,T))) \ {(PosetMax (n,T,L,(HM (f,T))))} is finite Element of bool (n,T,L,(HM (f,T)))
bool (n,T,L,(HM (f,T))) is finite V28() cup-closed diff-closed preBoolean set
PosetMax (n,T,L,f) is Element of the carrier of RelStr(# (Bags n),T #)
{(PosetMax (n,T,L,f))} is non zero trivial finite 1 -element set
(n,T,L,f) \ {(PosetMax (n,T,L,f))} is finite Element of bool (n,T,L,f)
bool (n,T,L,f) is finite V28() cup-closed diff-closed preBoolean set
HT ((HM (f,T)),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(HM (f,T)) . (HT (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f . (HT (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (f,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
{(HT (f,T))} is non zero trivial functional finite 1 -element set
[((n,T,L,(HM (f,T))) \ {(PosetMax (n,T,L,(HM (f,T))))}),((n,T,L,f) \ {(PosetMax (n,T,L,f))})] is V21() set
FinOrd-Approx RelStr(# (Bags n),T #) is Relation-like NAT -defined bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] -valued Function-like V46( NAT , bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]) Element of bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is Relation-like set
bool [:NAT,(bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]):] is cup-closed diff-closed preBoolean set
rng (FinOrd-Approx RelStr(# (Bags n),T #)) is set
union (rng (FinOrd-Approx RelStr(# (Bags n),T #))) is set
[(n,T,L,(HM (f,T))),(n,T,L,f)] is V21() set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(Bags n),(Bags n):]
L is non empty non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
Red (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(Red (P,T)) . (HT (P,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support (Red (P,T)) is functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
Support P is functional Element of bool (Bags n)
HM (P,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support P is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(HT (f,T)) + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P . g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (f,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . g) / (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . g) / (HC (f,T))) * (n,f9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (((P . g) / (HC (f,T))) * (n,f9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) / (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 + (HT (f,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((P . f9) / (HC (f,T))) * (n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support g is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Support P is functional finite Element of bool (Bags n)
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
P . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (f,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) / (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 + (HT (f,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((P . f9) / (HC (f,T))) * (n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 + (HT (f,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((P . f9) / (HC (f,T))) * (n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(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
(((P . f9) / (HC (f,T))) * (n,g9,L,f)) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,g9,L,f) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . f9) / (HC (f,T))) * ((n,g9,L,f) . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f . (HT (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . f9) / (HC (f,T))) * (f . (HT (f,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . f9) / (HC (f,T))) * (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (f,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) * ((HC (f,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . f9) * ((HC (f,T)) ")) * (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (f,T)) ") * (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) * (((HC (f,T)) ") * (HC (f,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
(P . f9) * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (((P . f9) / (HC (f,T))) * (n,g9,L,f))) . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) + ((- (((P . f9) / (HC (f,T))) * (n,g9,L,f))) . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((((P . f9) / (HC (f,T))) * (n,g9,L,f)) . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) + (- ((((P . f9) / (HC (f,T))) * (n,g9,L,f)) . f9)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support P is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
g *' f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (g *' f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT ((g *' f),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
HC (f,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 (f,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (f,T)) * ((HC (f,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
P . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) * ((HC (f,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) / (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 + (HT (f,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((P . f9) / (HC (f,T))) * (n,g9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (- (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(g *' f) - (g *' f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + ((g *' f) - (g *' f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (g *' f) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(g *' f) + (- (g *' f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + ((g *' f) + (- (g *' f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- (g *' f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(P + (- (g *' f))) + (g *' f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(g *' f) + (P - (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - ((g *' f) + (P - (((P . f9) / (HC (f,T))) * (n,g9,L,f)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- ((g *' f) + (P - (((P . f9) / (HC (f,T))) * (n,g9,L,f)))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- ((g *' f) + (P - (((P . f9) / (HC (f,T))) * (n,g9,L,f))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (P - (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- (g *' f)) + (- (P - (((P . f9) / (HC (f,T))) * (n,g9,L,f)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + ((- (g *' f)) + (- (P - (((P . f9) / (HC (f,T))) * (n,g9,L,f))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (P + (- (((P . f9) / (HC (f,T))) * (n,g9,L,f)))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- (g *' f)) + (- (P + (- (((P . f9) / (HC (f,T))) * (n,g9,L,f))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + ((- (g *' f)) + (- (P + (- (((P . f9) / (HC (f,T))) * (n,g9,L,f)))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- P is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- P) + (- (- (((P . f9) / (HC (f,T))) * (n,g9,L,f)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- (g *' f)) + ((- P) + (- (- (((P . f9) / (HC (f,T))) * (n,g9,L,f))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + ((- (g *' f)) + ((- P) + (- (- (((P . f9) / (HC (f,T))) * (n,g9,L,f)))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- P) + ((- (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + ((- P) + ((- (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- P) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(P + (- P)) + ((- (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(P - P) + ((- (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(0_ (n,L)) + ((- (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(g *' f) + ((- (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((g *' f) + (- (g *' f))) + (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((g *' f) - (g *' f)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(0_ (n,L)) + (((P . f9) / (HC (f,T))) * (n,g9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT ((n,g9,L,f),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Support g is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support g is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support P is functional finite Element of bool (Bags n)
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
P . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (f,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) / (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 + (HT (f,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((P . f9) / (HC (f,T))) * (n,f9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (((P . f9) / (HC (f,T))) * (n,f9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (n,f9,L,f) is functional finite Element of bool (Bags n)
(((P . f9) / (HC (f,T))) * (n,f9,L,f)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,f9,L,f) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . f9) / (HC (f,T))) * ((n,f9,L,f) . g9) 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
((P . f9) / (HC (f,T))) * (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P - (((P . f9) / (HC (f,T))) * (n,f9,L,f))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (((P . f9) / (HC (f,T))) * (n,f9,L,f)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- (((P . f9) / (HC (f,T))) * (n,f9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(P + (- (((P . f9) / (HC (f,T))) * (n,f9,L,f)))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
P . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (((P . f9) / (HC (f,T))) * (n,f9,L,f))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . g9) + ((- (((P . f9) / (HC (f,T))) * (n,f9,L,f))) . g9) 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
(P . g9) + (- (0. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . g9) + (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
P . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
g . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
P . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (f,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . f9) / (HC (f,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 + (HT (f,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,f9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((P . f9) / (HC (f,T))) * (n,f9,L,f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P - (((P . f9) / (HC (f,T))) * (n,f9,L,f)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (n,f9,L,f) is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
(((P . f9) / (HC (f,T))) * (n,f9,L,f)) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,f9,L,f) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((P . f9) / (HC (f,T))) * ((n,f9,L,f) . g9) 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
((P . f9) / (HC (f,T))) * (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P - (((P . f9) / (HC (f,T))) * (n,f9,L,f))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (((P . f9) / (HC (f,T))) * (n,f9,L,f)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
P + (- (((P . f9) / (HC (f,T))) * (n,f9,L,f))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(P + (- (((P . f9) / (HC (f,T))) * (n,f9,L,f)))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (((P . f9) / (HC (f,T))) * (n,f9,L,f))) . g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . g9) + ((- (((P . f9) / (HC (f,T))) * (n,f9,L,f))) . g9) 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
(P . g9) + (- (0. L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(P . g9) + (0. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support g is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
field T is set
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Support P is functional finite Element of bool (Bags n)
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[f9,f9] is V21() set
[g9,g9] is V21() set
[g9,f9] is V21() set
[f9,g9] is V21() set
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected RelStr
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
Support P is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
card (Support P) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
f9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
field T is set
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support g9 is functional finite Element of bool (Bags n)
card (Support g9) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
HT (R,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
g9 . x 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
(g9 . x) / (HC (R,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q + (HT (R,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,q,L,R) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((g9 . x) / (HC (R,T))) * (n,q,L,R) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 - (((g9 . x) / (HC (R,T))) * (n,q,L,R)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (x,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[(HT (x,T)),(HT (x,T))] is V21() set
[(HT (g9,T)),(HT (g9,T))] is V21() set
[(HT (g9,T)),(HT (x,T))] is V21() set
[(HT (x,T)),(HT (g9,T))] is V21() set
Support x is functional finite Element of bool (Bags n)
EmptyBag n is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
[(Support x),(Support g9)] is V21() set
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
HT (x,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
{(HT (g9,T))} is non zero trivial functional finite 1 -element set
u is set
Red (g9,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support (Red (g9,T)) is functional finite Element of bool (Bags n)
(Support g9) \ {(HT (g9,T))} is functional finite Element of bool (Bags n)
u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 . (HT (g9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
x . (HT (x,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (g9,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (x,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HM (g9,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
Monom ((HC (x,T)),(HT (x,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
HM (x,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
Red (x,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(g9 - (((g9 . x) / (HC (R,T))) * (n,q,L,R))) - (HM (g9,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(HM (g9,T)) + u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((HM (g9,T)) + u) - (((g9 . x) / (HC (R,T))) * (n,q,L,R)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(((HM (g9,T)) + u) - (((g9 . x) / (HC (R,T))) * (n,q,L,R))) - (HM (g9,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u . x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(u . x) / (HC (R,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((u . x) / (HC (R,T))) * (n,q,L,R) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((HM (g9,T)) + u) - (((u . x) / (HC (R,T))) * (n,q,L,R)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(((HM (g9,T)) + u) - (((u . x) / (HC (R,T))) * (n,q,L,R))) - (HM (g9,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (((u . x) / (HC (R,T))) * (n,q,L,R)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((HM (g9,T)) + u) + (- (((u . x) / (HC (R,T))) * (n,q,L,R))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(((HM (g9,T)) + u) + (- (((u . x) / (HC (R,T))) * (n,q,L,R)))) - (HM (g9,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u + (- (((u . x) / (HC (R,T))) * (n,q,L,R))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(HM (g9,T)) + (u + (- (((u . x) / (HC (R,T))) * (n,q,L,R)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((HM (g9,T)) + (u + (- (((u . x) / (HC (R,T))) * (n,q,L,R))))) - (HM (g9,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (HM (g9,T)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((HM (g9,T)) + (u + (- (((u . x) / (HC (R,T))) * (n,q,L,R))))) + (- (HM (g9,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(HM (g9,T)) + (- (HM (g9,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(u + (- (((u . x) / (HC (R,T))) * (n,q,L,R)))) + ((HM (g9,T)) + (- (HM (g9,T)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u - (((u . x) / (HC (R,T))) * (n,q,L,R)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(u - (((u . x) / (HC (R,T))) * (n,q,L,R))) + ((HM (g9,T)) + (- (HM (g9,T)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(HM (g9,T)) - (HM (g9,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(u - (((u . x) / (HC (R,T))) * (n,q,L,R))) + ((HM (g9,T)) - (HM (g9,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(u - (((u . x) / (HC (R,T))) * (n,q,L,R))) + (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(Support (Red (g9,T))) \/ {(HT (g9,T))} is non zero finite set
(Support g9) \/ {(HT (g9,T))} is non zero finite set
card (Support (Red (g9,T))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
(card (Support (Red (g9,T)))) + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
Support (Red (x,T)) is functional finite Element of bool (Bags n)
Support u is functional finite Element of bool (Bags n)
[(Support (Red (x,T))),(Support u)] is V21() set
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (x,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (x,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support g9 is functional finite Element of bool (Bags n)
card (Support g9) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support x is functional finite Element of bool (Bags n)
[(Support x),(Support g9)] is V21() set
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support f9 is functional finite Element of bool (Bags n)
card (Support f9) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support R is functional finite Element of bool (Bags n)
[(Support R),(Support f9)] is V21() set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
Support g is functional finite Element of bool (Bags n)
[(Support g),(Support P)] is V21() set
f9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of (Polynom-Ring (n,L)) is non zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(Bags n),(Bags n):]
P is Element of bool the carrier of (Polynom-Ring (n,L))
f9 is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
[g9,f9] is V21() set
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
[g9,f9] is V21() set
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
[g9,R] is V21() set
f9 is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
g9 is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
f9 is set
g9 is set
[f9,g9] is V21() set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
R is set
x is set
[R,x] is V21() set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is set
x is set
[R,x] is V21() set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (f,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HT (P,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
g is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,g) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
g9 is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,g)
g9 . 1 is set
len g9 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
g9 . (len g9) is set
f9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
f9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,g)
x . 1 is set
len x is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
x . (len x) is set
dom x is non zero finite Element of bool NAT
Seg (f9 + 1) is non zero finite f9 + 1 -element K216(f9,1) -element Element of bool NAT
K216(f9,1) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
Seg f9 is finite f9 -element Element of bool NAT
x | (Seg f9) is Relation-like NAT -defined Seg f9 -defined NAT -defined Function-like finite FinSubsequence-like finite-support set
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom q is finite Element of bool NAT
len q is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
q . (len q) is set
x . f9 is set
x . (f9 + 1) is set
[(x . f9),(x . (f9 + 1))] is V21() set
[(q . (len q)),R] is V21() set
a is set
u9 is set
[a,u9] is V21() set
a9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
a9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
x . a9 is set
x . (a9 + 1) is set
[(x . a9),(x . (a9 + 1))] is V21() set
q . a9 is set
q . (a9 + 1) is set
[(q . a9),(q . (a9 + 1))] is V21() set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
u9 is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,g)
dom u9 is non zero finite Element of bool NAT
u9 . 1 is set
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,g)
x . 1 is set
len x is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
x . (len x) is set
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,g)
R . 1 is set
len R is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
R . (len R) is set
f9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
Support f is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
[(HT (f,T)),(HT (f,T))] is V21() set
field T is set
[(HT (P,T)),(HT (P,T))] is V21() set
[(HT (P,T)),(HT (f,T))] is V21() set
[(HT (f,T)),(HT (P,T))] is V21() set
Support P is functional finite Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
L is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive well_founded admissible Element of bool [:(Bags n),(Bags n):]
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
RelStr(# (Bags n),T #) is non empty strict total reflexive transitive antisymmetric connected well_founded RelStr
FinPoset RelStr(# (Bags n),T #) is non empty total reflexive transitive antisymmetric connected RelStr
the InternalRel of (FinPoset RelStr(# (Bags n),T #)) is Relation-like the carrier of (FinPoset RelStr(# (Bags n),T #)) -defined the carrier of (FinPoset RelStr(# (Bags n),T #)) -valued total V46( the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #))) reflexive antisymmetric transitive Element of bool [: the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #)):]
the carrier of (FinPoset RelStr(# (Bags n),T #)) is non zero set
[: the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #)):] is Relation-like set
bool [: the carrier of (FinPoset RelStr(# (Bags n),T #)), the carrier of (FinPoset RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
g9 is set
(n,T,L,P) ~ is Relation-like the carrier of (Polynom-Ring (n,L)) -defined NonZero (Polynom-Ring (n,L)) -valued Element of bool [: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):]
[: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):] is Relation-like set
bool [: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):] is cup-closed diff-closed preBoolean set
field ((n,T,L,P) ~) is set
the Element of g9 is Element of g9
dom ((n,T,L,P) ~) is Element of bool the carrier of (Polynom-Ring (n,L))
rng ((n,T,L,P) ~) is Element of bool (NonZero (Polynom-Ring (n,L)))
bool (NonZero (Polynom-Ring (n,L))) is cup-closed diff-closed preBoolean set
(dom ((n,T,L,P) ~)) \/ (rng ((n,T,L,P) ~)) is set
{ (Support b₁) where b₁ is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:] : ex b₂ being set st
( b₂ in g9 & b₁ = b₂ ) } is set
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support g9 is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
x is set
x is non zero set
the carrier of RelStr(# (Bags n),T #) is non zero set
Fin the carrier of RelStr(# (Bags n),T #) is non zero cup-closed diff-closed preBoolean set
FinOrd RelStr(# (Bags n),T #) is Relation-like Fin the carrier of RelStr(# (Bags n),T #) -defined Fin the carrier of RelStr(# (Bags n),T #) -valued total V46( Fin the carrier of RelStr(# (Bags n),T #), Fin the carrier of RelStr(# (Bags n),T #)) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):]
[:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is Relation-like set
bool [:(Fin the carrier of RelStr(# (Bags n),T #)),(Fin the carrier of RelStr(# (Bags n),T #)):] is cup-closed diff-closed preBoolean set
RelStr(# (Fin the carrier of RelStr(# (Bags n),T #)),(FinOrd RelStr(# (Bags n),T #)) #) is non empty strict total reflexive transitive antisymmetric RelStr
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support q is functional finite Element of bool (Bags n)
u is set
x is set
the InternalRel of (FinPoset RelStr(# (Bags n),T #)) -Seg x is set
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support q is functional finite Element of bool (Bags n)
((n,T,L,P) ~) -Seg q is set
(((n,T,L,P) ~) -Seg q) /\ g9 is set
the Element of (((n,T,L,P) ~) -Seg q) /\ g9 is Element of (((n,T,L,P) ~) -Seg q) /\ g9
[ the Element of (((n,T,L,P) ~) -Seg q) /\ g9,q] is V21() set
[q, the Element of (((n,T,L,P) ~) -Seg q) /\ g9] is V21() set
a is set
u9 is set
[a,u9] is V21() set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
u9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support a9 is functional finite Element of bool (Bags n)
Support a9 is functional finite Element of bool (Bags n)
[(Support a9),(Support a9)] is V21() set
the InternalRel of (FinPoset RelStr(# (Bags n),T #)) -Seg (Support a9) is set
( the InternalRel of (FinPoset RelStr(# (Bags n),T #)) -Seg x) /\ x is set
u is set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
the carrier of (Polynom-Ring (n,L)) \ {(0_ (n,L))} is Element of bool the carrier of (Polynom-Ring (n,L))
g9 is set
field (n,T,L,P) is set
dom (n,T,L,P) is Element of bool (NonZero (Polynom-Ring (n,L)))
rng (n,T,L,P) is Element of bool the carrier of (Polynom-Ring (n,L))
(dom (n,T,L,P)) \/ (rng (n,T,L,P)) is set
[g9,g9] is V21() set
x is set
x is set
[x,x] is V21() set
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support q is functional finite Element of bool (Bags n)
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive well_founded admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g *' f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
{ b₁ where b₁ is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:] : not (n,T,L,P) reduces b₁ *' f, 0_ (n,L) } is set
g9 is set
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Element of bool the carrier of (Polynom-Ring (n,L))
R is non zero set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
Red (x,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(Red (x,T)) *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (x,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT ((x *' f9),T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(x *' f9) . (HT ((x *' f9),T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (f9,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((x *' f9) . (HT ((x *' f9),T))) / (HC (f9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((x *' f9) . (HT ((x *' f9),T))) / (HC (f9,T))) * (n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(x *' f9) - ((((x *' f9) . (HT ((x *' f9),T))) / (HC (f9,T))) * (n,(HT (x,T)),L,f9)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support (x *' f9) is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
HC ((x *' f9),T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC ((x *' f9),T)) / (HC (f9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC ((x *' f9),T)) / (HC (f9,T))) * (n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HC (x,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (x,T)) * (HC (f9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (x,T)) * (HC (f9,T))) / (HC (f9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (x,T)) * (HC (f9,T))) / (HC (f9,T))) * (n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(HC (f9,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (x,T)) * (HC (f9,T))) * ((HC (f9,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((HC (x,T)) * (HC (f9,T))) * ((HC (f9,T)) ")) * (n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(HC (f9,T)) * ((HC (f9,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (x,T)) * ((HC (f9,T)) * ((HC (f9,T)) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (x,T)) * ((HC (f9,T)) * ((HC (f9,T)) "))) * (n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
1. L is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the OneF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (x,T)) * (1. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((HC (x,T)) * (1. L)) * (n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(HC (x,T)) * (n,(HT (x,T)),L,f9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Monom ((HC (x,T)),(HT (x,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
(Monom ((HC (x,T)),(HT (x,T)))) *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HM (x,T) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
(HM (x,T)) *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
- ((HM (x,T)) *' f9) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(x *' f9) + (- ((HM (x,T)) *' f9)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
- (HM (x,T)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' (- (HM (x,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' x) + (f9 *' (- (HM (x,T)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x + (- (HM (x,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(x + (- (HM (x,T)))) *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x - (HM (x,T)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(x - (HM (x,T))) *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (f9,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(HT (x,T)) + (HT (f9,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
[(x *' f9),((Red (x,T)) *' f9)] is V21() set
u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u *' f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is Element of bool the carrier of (Polynom-Ring (n,L))
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
HT (f9,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f9 + (HT (f9,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Support f is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
Support f9 is functional finite Element of bool (Bags n)
term f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
f9 . (term f9) 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
(f9 *' f) . (f9 + (HT (f9,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(term f9) + f9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(f9 *' f) . ((term f9) + f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
f . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f9 . (term f9)) * (f . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support (f9 *' f) is functional finite Element of bool (Bags n)
HT (g9,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
HC (g9,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f . f9) / (HC (g9,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
R is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
R + (HT (g9,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,R,L,g9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((f . f9) / (HC (g9,T))) * (n,R,L,g9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f - (((f . f9) / (HC (g9,T))) * (n,R,L,g9)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R + (HT (f9,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (x,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
(R + (HT (f9,T))) + (HT (x,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,(R + (HT (f9,T))),L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HC (x,T) is non zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((f9 *' f) . (f9 + (HT (f9,T)))) / (HC (x,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(((f9 *' f) . (f9 + (HT (f9,T)))) / (HC (x,T))) * (n,(R + (HT (f9,T))),L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' f) - ((((f9 *' f) . (f9 + (HT (f9,T)))) / (HC (x,T))) * (n,(R + (HT (f9,T))),L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
u . f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(u . f9) / (HC (x,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f9 . (term f9)) * ((u . f9) / (HC (x,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(HC (x,T)) " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(u . f9) * ((HC (x,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f9 . (term f9)) * ((u . f9) * ((HC (x,T)) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f9 . (term f9)) * (u . f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((f9 . (term f9)) * (u . f9)) * ((HC (x,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((f9 . (term f9)) * (u . f9)) / (HC (x,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f9 *' u) . (f9 + (HT (f9,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f9 *' u) . ((term f9) + f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(n,R,L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(n,(HT (f9,T)),L,(n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((f9 . (term f9)) * ((u . f9) / (HC (x,T)))) * (n,(HT (f9,T)),L,(n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) - (((f9 . (term f9)) * ((u . f9) / (HC (x,T)))) * (n,(HT (f9,T)),L,(n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 . (term f9)) * (n,(HT (f9,T)),L,(n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((u . f9) / (HC (x,T))) * ((f9 . (term f9)) * (n,(HT (f9,T)),L,(n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) - (((u . f9) / (HC (x,T))) * ((f9 . (term f9)) * (n,(HT (f9,T)),L,(n,R,L,x)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Monom ((f9 . (term f9)),(HT (f9,T))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
(Monom ((f9 . (term f9)),(HT (f9,T)))) *' (n,R,L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((u . f9) / (HC (x,T))) * ((Monom ((f9 . (term f9)),(HT (f9,T)))) *' (n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) - (((u . f9) / (HC (x,T))) * ((Monom ((f9 . (term f9)),(HT (f9,T)))) *' (n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
coefficient f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Monom ((coefficient f9),(term f9)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
(Monom ((coefficient f9),(term f9))) *' (n,R,L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((u . f9) / (HC (x,T))) * ((Monom ((coefficient f9),(term f9))) *' (n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) - (((u . f9) / (HC (x,T))) * ((Monom ((coefficient f9),(term f9))) *' (n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' (n,R,L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((u . f9) / (HC (x,T))) * (f9 *' (n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) - (((u . f9) / (HC (x,T))) * (f9 *' (n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((u . f9) / (HC (x,T))) * (n,R,L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' (((u . f9) / (HC (x,T))) * (n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) - (f9 *' (((u . f9) / (HC (x,T))) * (n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (f9 *' (((u . f9) / (HC (x,T))) * (n,R,L,x))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) + (- (f9 *' (((u . f9) / (HC (x,T))) * (n,R,L,x)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (((u . f9) / (HC (x,T))) * (n,R,L,x)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' (- (((u . f9) / (HC (x,T))) * (n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 *' u) + (f9 *' (- (((u . f9) / (HC (x,T))) * (n,R,L,x)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u + (- (((u . f9) / (HC (x,T))) * (n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' (u + (- (((u . f9) / (HC (x,T))) * (n,R,L,x)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u - (((u . f9) / (HC (x,T))) * (n,R,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' (u - (((u . f9) / (HC (x,T))) * (n,R,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
g9 . 1 is set
len g9 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
g9 . (len g9) is set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
x is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
x + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
u . 1 is set
len u is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
u . (len u) is set
dom u is non zero finite Element of bool NAT
Seg (x + 1) is non zero finite x + 1 -element K216(x,1) -element Element of bool NAT
K216(x,1) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
Seg x is finite x -element Element of bool NAT
u | (Seg x) is Relation-like NAT -defined Seg x -defined NAT -defined Function-like finite FinSubsequence-like finite-support set
u9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom u9 is finite Element of bool NAT
len u9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
u9 . (len u9) is set
u . x is set
u . (x + 1) is set
[(u . x),(u . (x + 1))] is V21() set
[(u9 . (len u9)),q] is V21() set
u9 is set
a9 is set
[u9,a9] is V21() set
q is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
q + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
u . q is set
u . (q + 1) is set
[(u . q),(u . (q + 1))] is V21() set
u9 . q is set
u9 . (q + 1) is set
[(u9 . q),(u9 . (q + 1))] is V21() set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
[(f9 *' q),(f9 *' q)] is V21() set
sumq is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
dom sumq is non zero finite Element of bool NAT
sumq . 1 is set
f9 *' x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
u . 1 is set
len u is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
u . (len u) is set
f9 *' x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
q . 1 is set
len q is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
q . (len q) is set
f9 *' x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 *' x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
g *' f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g *' (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f - g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
f9 . 1 is set
len f9 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
f9 . (len f9) is set
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
g9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R - x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
u . 1 is set
len u is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
u . (len u) is set
u . g9 is set
dom u is non zero finite Element of bool NAT
Seg (g9 + 1) is non zero finite g9 + 1 -element K216(g9,1) -element Element of bool NAT
K216(g9,1) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
u . (g9 + 1) is set
[(u . g9),(u . (g9 + 1))] is V21() set
u9 is set
a9 is set
[u9,a9] is V21() set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
u9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
sumq is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
Seg g9 is finite g9 -element Element of bool NAT
u | (Seg g9) is Relation-like NAT -defined Seg g9 -defined NAT -defined Function-like finite FinSubsequence-like finite-support set
h9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom h9 is finite Element of bool NAT
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
u . g9 is set
u . (g9 + 1) is set
[(u . g9),(u . (g9 + 1))] is V21() set
h9 . g9 is set
h9 . (g9 + 1) is set
[(h9 . g9),(h9 . (g9 + 1))] is V21() set
len h9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
dom g9 is non zero finite Element of bool NAT
g9 . 1 is set
len g9 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
g9 . (len g9) is set
g9 . g9 is set
gg is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - gg is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
HT (q,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
a9 . sumq 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
(a9 . sumq) / (HC (q,T)) 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 V242() V243() V244() V245() finite-support set
h + (HT (q,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((a9 . sumq) / (HC (q,T))) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 - (((a9 . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg . sumq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(gg . sumq) / (HC (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) / (HC (q,T))) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg . sumq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(gg . sumq) / (HC (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) / (HC (q,T))) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- ((gg . sumq) / (HC (q,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) / (HC (q,T))) + (- ((gg . sumq) / (HC (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
(gg . sumq) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) * ((HC (q,T)) ")) + (- ((gg . sumq) / (HC (q,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(gg . sumq) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- ((gg . sumq) * ((HC (q,T)) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) * ((HC (q,T)) ")) + (- ((gg . sumq) * ((HC (q,T)) "))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (gg . sumq) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (gg . sumq)) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) * ((HC (q,T)) ")) + ((- (gg . sumq)) * ((HC (q,T)) ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(gg . sumq) + (- (gg . sumq)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) + (- (gg . sumq))) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- gg is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- gg) . sumq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(gg . sumq) + ((- gg) . sumq) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg . sumq) + ((- gg) . sumq)) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
gg + (- gg) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg + (- gg)) . sumq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg + (- gg)) . sumq) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(gg - gg) . sumq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg - gg) . sumq) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((gg - gg) . sumq) / (HC (q,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
Support gg is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0. L) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((0. L) * ((HC (q,T)) ")) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - (((0. L) * ((HC (q,T)) ")) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(0. L) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - ((0. L) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support gg is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
f2 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
[f2,(gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))] is V21() set
Support gg is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support gg is functional finite Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
Support gg is functional finite Element of bool (Bags n)
0. L is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
the ZeroF of L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0. L) * ((HC (q,T)) ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((0. L) * ((HC (q,T)) ")) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - (((0. L) * ((HC (q,T)) ")) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(0. L) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - ((0. L) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg - (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Support gg is functional finite Element of bool (Bags n)
f2 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
[f2,(gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))] is V21() set
Support gg is functional finite Element of bool (Bags n)
Support gg is functional finite Element of bool (Bags n)
- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- ((gg . sumq) / (HC (q,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- ((gg . sumq) / (HC (q,T)))) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((- ((gg . sumq) / (HC (q,T)))) * (n,h,L,q)) + (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T)))) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T)))) * (n,h,L,q)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (- (((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T)))) * (n,h,L,q))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) - (gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) + (- (gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) + (- (gg - (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) + (- (gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- gg) + (- (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) + ((- gg) + (- (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) + (- gg) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((gg + (- (((gg . sumq) / (HC (q,T))) * (n,h,L,q)))) + (- gg)) + (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) + (gg + (- gg)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) + (gg + (- gg))) + (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) + (((gg . sumq) / (HC (q,T))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg + (- gg)) + ((- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) + (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg - gg) + ((- (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) + (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg - gg) + (((- ((gg . sumq) / (HC (q,T)))) * (n,h,L,q)) + (((gg . sumq) / (HC (q,T))) * (n,h,L,q))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- ((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- ((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T))))) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- ((- ((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T))))) * (n,h,L,q)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg - gg) + (- ((- ((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T))))) * (n,h,L,q))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg - gg) - ((- ((- ((gg . sumq) / (HC (q,T)))) + ((gg . sumq) / (HC (q,T))))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (- ((gg . sumq) / (HC (q,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- (- ((gg . sumq) / (HC (q,T))))) + (- ((gg . sumq) / (HC (q,T)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
((- (- ((gg . sumq) / (HC (q,T))))) + (- ((gg . sumq) / (HC (q,T))))) * (n,h,L,q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(gg - gg) - (((- (- ((gg . sumq) / (HC (q,T))))) + (- ((gg . sumq) / (HC (q,T))))) * (n,h,L,q)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 - R is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
q is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P)
q . 1 is set
len q is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
q . (len q) is set
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f - g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 - g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 - g9) + g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- g9 is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 + (- g9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f9 + (- g9)) + g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- g9) + g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 + ((- g9) + g9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 + (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f - g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is set
(n,T,L,P) ~ is Relation-like the carrier of (Polynom-Ring (n,L)) -defined NonZero (Polynom-Ring (n,L)) -valued Element of bool [: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):]
[: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):] is Relation-like set
bool [: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):] is cup-closed diff-closed preBoolean set
(n,T,L,P) \/ ((n,T,L,P) ~) is Relation-like set
n is non empty addLoopStr
the carrier of n is non zero set
bool the carrier of n is cup-closed diff-closed preBoolean set
n is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable right-distributive add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of n is non zero set
bool the carrier of n is cup-closed diff-closed preBoolean set
T is non zero right-ideal Element of bool the carrier of n
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L - L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
0. n is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
the ZeroF of n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
n is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() right-distributive right_unital well-unital left_unital add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of n is non zero set
bool the carrier of n is cup-closed diff-closed preBoolean set
T is non zero right-ideal Element of bool the carrier of n
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L - P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- (L - P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P - L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(P - L) - (- (L - P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- (- (L - P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(P - L) + (- (- (L - P))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(P - L) + (L - P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + (- L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(P + (- L)) + (L - P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- L) + (L - P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + ((- L) + (L - P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- L) + (L + (- P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + ((- L) + (L + (- P))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- L) + L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
((- L) + L) + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + (((- L) + L) + (- P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
0. n is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
the ZeroF of n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(0. n) + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + ((0. n) + (- P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
n is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like addLoopStr
the carrier of n is non zero set
bool the carrier of n is cup-closed diff-closed preBoolean set
T is non zero add-closed Element of bool the carrier of n
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L - P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P - f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L - P) + (P - f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L + (- P)) + (P - f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- P) + (P - f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + ((- P) + (P - f)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + (- f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- P) + (P + (- f)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + ((- P) + (P + (- f))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- P) + P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
((- P) + P) + (- f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + (((- P) + P) + (- f)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
0. n is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
the ZeroF of n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(0. n) + (- f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + ((0. n) + (- f)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + (- f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L - f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
n is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable V102() associative 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 n is non zero non trivial set
bool the carrier of n is cup-closed diff-closed preBoolean set
T is non zero add-closed Element of bool the carrier of n
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P + g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L - P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f - g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L - P) + (f - g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L + f) - (P + g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- (P + g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L + f) + (- (P + g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- g) + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L + f) + ((- g) + (- P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f + ((- g) + (- P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + (f + ((- g) + (- P))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f + (- g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(f + (- g)) + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + ((f + (- g)) + (- P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L + (- P)) + (f + (- g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L - P) + (f + (- g)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
n is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable commutative right-distributive left-distributive distributive add-associative right_zeroed left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
the carrier of n is non zero set
bool the carrier of n is cup-closed diff-closed preBoolean set
T is non zero add-closed left-ideal right-ideal Element of bool the carrier of n
L is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L * f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f - g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(f - g) * P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f + (- g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(f + (- g)) * P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
f * P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- g) * P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(f * P) + ((- g) * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L - P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L - P) * f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
L + (- P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L + (- P)) * f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- P) * f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) + ((- P) * f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
((L - P) * f) + ((f - g) * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
((- P) * f) + ((f * P) + ((- g) * P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) + (((- P) * f) + ((f * P) + ((- g) * P))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
((- P) * f) + (f * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(((- P) * f) + (f * P)) + ((- g) * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) + ((((- P) * f) + (f * P)) + ((- g) * P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
P * f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- (P * f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(- (P * f)) + (f * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
((- (P * f)) + (f * P)) + ((- g) * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) + (((- (P * f)) + (f * P)) + ((- g) * P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
0. n is zero left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
the ZeroF of n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(0. n) + ((- g) * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) + ((0. n) + ((- g) * P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) + ((- g) * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
g * P is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
- (g * P) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) + (- (g * P)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of n
(L * f) - (P * g) 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 zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is Element of bool the carrier of (Polynom-Ring (n,L))
P -Ideal is non zero add-closed left-ideal right-ideal Element of bool the carrier of (Polynom-Ring (n,L))
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- g is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R + g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- g) + g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(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))
- g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
HT (x,T) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support Element of Bags n
f . x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
HC (x,T) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(f . x) / (HC (x,T)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
q is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
q + (HT (x,T)) is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
(n,q,L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
((f . x) / (HC (x,T))) * (n,q,L,x) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f - (((f . x) / (HC (x,T))) * (n,q,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
Monom (((f . x) / (HC (x,T))),q) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like finite-Support Element of bool [:(Bags n), the carrier of L:]
(Monom (((f . x) / (HC (x,T))),q)) *' x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
<*((Monom (((f . x) / (HC (x,T))),q)) *' x)*> is non zero trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
rng <*((Monom (((f . x) / (HC (x,T))),q)) *' x)*> is non zero trivial finite 1 -element set
{((Monom (((f . x) / (HC (x,T))),q)) *' x)} is non zero trivial functional finite 1 -element set
u9 is set
sumq is set
u9 is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of (Polynom-Ring (n,L))
dom u9 is finite Element of bool NAT
a9 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))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 * h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
1. (Polynom-Ring (n,L)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the OneF 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))
(h9 * h) * (1. (Polynom-Ring (n,L))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
u9 . sumq is set
u is non zero Element of bool the carrier of (Polynom-Ring (n,L))
u9 /. sumq is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a9 is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LinearCombination of u
Sum a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
u -Ideal is non zero add-closed left-ideal right-ideal Element of bool the carrier of (Polynom-Ring (n,L))
f - g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f + (- g) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 + (- g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 - g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (((f . x) / (HC (x,T))) * (n,q,L,x)) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (- (((f . x) / (HC (x,T))) * (n,q,L,x))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (f - (((f . x) / (HC (x,T))) * (n,q,L,x))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f + (- (f - (((f . x) / (HC (x,T))) * (n,q,L,x)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f + (- (((f . x) / (HC (x,T))) * (n,q,L,x))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- (f + (- (((f . x) / (HC (x,T))) * (n,q,L,x)))) is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f + (- (f + (- (((f . x) / (HC (x,T))) * (n,q,L,x))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- f is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(- f) + (- (- (((f . x) / (HC (x,T))) * (n,q,L,x)))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f + ((- f) + (- (- (((f . x) / (HC (x,T))) * (n,q,L,x))))) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f + (- f) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(f + (- f)) + (((f . x) / (HC (x,T))) * (n,q,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(0_ (n,L)) + (((f . x) / (HC (x,T))) * (n,q,L,x)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
P -Ideal is non zero add-closed left-ideal right-ideal Element of bool 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 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(n,T,L,P) ~ is Relation-like the carrier of (Polynom-Ring (n,L)) -defined NonZero (Polynom-Ring (n,L)) -valued Element of bool [: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):]
[: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):] is Relation-like set
bool [: the carrier of (Polynom-Ring (n,L)),(NonZero (Polynom-Ring (n,L))):] is cup-closed diff-closed preBoolean set
(n,T,L,P) \/ ((n,T,L,P) ~) is Relation-like set
f9 is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P) \/ ((n,T,L,P) ~)
f9 . 1 is set
len f9 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
f9 . (len f9) is set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
g9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P) \/ ((n,T,L,P) ~)
x . 1 is set
len x is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
x . (len x) is set
dom x is non zero finite Element of bool NAT
Seg (g9 + 1) is non zero finite g9 + 1 -element K216(g9,1) -element Element of bool NAT
K216(g9,1) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
Seg g9 is finite g9 -element Element of bool NAT
x | (Seg g9) is Relation-like NAT -defined Seg g9 -defined NAT -defined Function-like finite FinSubsequence-like finite-support set
u is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom u is finite Element of bool NAT
len u is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
u . (len u) is set
x . g9 is set
x . (g9 + 1) is set
[(x . g9),(x . (g9 + 1))] is V21() set
[(u . (len u)),x] is V21() set
u9 is set
a9 is set
[u9,a9] is V21() set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
the carrier of (Polynom-Ring (n,L)) \ {(0_ (n,L))} is Element of bool the carrier of (Polynom-Ring (n,L))
[x,(u . (len u))] is V21() set
u9 is set
a9 is set
[u9,a9] is V21() set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
the carrier of (Polynom-Ring (n,L)) \ {(0_ (n,L))} is Element of bool the carrier of (Polynom-Ring (n,L))
[x,(u . (len u))] is V21() set
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
the carrier of (Polynom-Ring (n,L)) \ {(0_ (n,L))} is Element of bool the carrier of (Polynom-Ring (n,L))
{(0_ (n,L))} is non zero trivial functional finite 1 -element set
the carrier of (Polynom-Ring (n,L)) \ {(0_ (n,L))} is Element of bool the carrier of (Polynom-Ring (n,L))
[x,(u . (len u))] is V21() set
u9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
u9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
x . u9 is set
x . (u9 + 1) is set
[(x . u9),(x . (u9 + 1))] is V21() set
u . u9 is set
u . (u9 + 1) is set
[(u . u9),(u . (u9 + 1))] is V21() set
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
u9 is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P) \/ ((n,T,L,P) ~)
dom u9 is non zero finite Element of bool NAT
u9 . 1 is set
a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
[a9,x] is V21() set
q is set
sumq is set
[q,sumq] is V21() set
h is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(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 non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(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))
R - x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
[x,a9] is V21() set
q is set
sumq is set
[q,sumq] is V21() set
g9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(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))
h is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
h9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(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))
gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R - x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
[a9,x] is V21() set
[x,a9] is V21() set
R - x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
[a9,x] is V21() set
R - x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
[x,a9] is V21() set
R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P) \/ ((n,T,L,P) ~)
x . 1 is set
len x is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
x . (len x) is set
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x is non zero Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support RedSequence of (n,T,L,P) \/ ((n,T,L,P) ~)
x . 1 is set
len x is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
x . (len x) is set
g9 - R is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive well_founded admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is non zero Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f + (f9 * g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
R 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 non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
a is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
u *' a is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x + (u *' a) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
u9 + (u *' a) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(u9 + (u *' a)) - u9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- u9 is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(u9 + (u *' a)) + (- u9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u9 + (- u9) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(u *' a) + (u9 + (- u9)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
(0_ (n,L)) + (u *' a) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
- u is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 is set
dom u is non zero functional Element of bool (Bags n)
bool (Bags n) is cup-closed diff-closed preBoolean set
u9 is Relation-like n -defined RAT -valued Function-like total V242() V243() V244() V245() finite-support set
u . u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
- (u . u9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(- u) . u9 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. L) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
(0_ (n,L)) . u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of L
u . a9 is set
(0_ (n,L)) . a9 is set
dom (0_ (n,L)) is non zero functional Element of bool (Bags n)
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 + a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a9 + u is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
- f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- f9) * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a9 *' a is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) non-zero finite-Support Element of bool [:(Bags n), the carrier of L:]
- (f9 * g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive well_founded admissible Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
P is non zero Element of bool the carrier of (Polynom-Ring (n,L))
P -Ideal is non zero add-closed left-ideal right-ideal Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued co-well_founded weakly-normalizing strongly-normalizing irreflexive Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
f 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))
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
R is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum R 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))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 - f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
R /. (g9 + 1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 + (R /. (g9 + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
Seg g9 is finite g9 -element Element of bool NAT
R | (Seg g9) is Relation-like NAT -defined Seg g9 -defined NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT, the carrier of (Polynom-Ring (n,L)):]
[:NAT, the carrier of (Polynom-Ring (n,L)):] is non trivial Relation-like non finite set
bool [:NAT, the carrier of (Polynom-Ring (n,L)):] is non trivial non finite cup-closed diff-closed preBoolean set
dom R is finite Element of bool NAT
Seg (g9 + 1) is non zero finite g9 + 1 -element K216(g9,1) -element Element of bool NAT
K216(g9,1) is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex Element of NAT
u is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a is Element of P
u * a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
u9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
a9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
u9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
u9 *' a9 is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len q is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
q is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum q is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum q) + (R /. (g9 + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum R) - (R /. (g9 + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (R /. (g9 + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
((Sum q) + (R /. (g9 + 1))) + (- (R /. (g9 + 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(R /. (g9 + 1)) + (- (R /. (g9 + 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum q) + ((R /. (g9 + 1)) + (- (R /. (g9 + 1)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(Sum q) + (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))
(g9 - f9) + (- (R /. (g9 + 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 + (- f9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(g9 + (- f9)) + (- (R /. (g9 + 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- f9) + (- (R /. (g9 + 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 + ((- f9) + (- (R /. (g9 + 1)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- (f9 + (R /. (g9 + 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 + (- (f9 + (R /. (g9 + 1)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 - (f9 + (R /. (g9 + 1))) 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 zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
sumq is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
sumq + (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
R is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum R 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))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 - f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
R is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum R 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))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 - f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
g9 + 1 is non zero epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real positive non negative complex set
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 - g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
<*> the carrier of (Polynom-Ring (n,L)) is zero Relation-like non-empty empty-yielding NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V28() cardinal 0 -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() V135() ext-real non positive non negative complex irreflexive V242() V243() V244() V245() FinSequence-yielding finite-support M30( the carrier of (Polynom-Ring (n,L)),K500( the carrier of (Polynom-Ring (n,L))))
K500( the carrier of (Polynom-Ring (n,L))) is non zero functional FinSequence-membered M29( the carrier of (Polynom-Ring (n,L)))
g - f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
P -LeftIdeal is non zero add-closed left-ideal right-ideal Element of bool the carrier of (Polynom-Ring (n,L))
g9 is Relation-like NAT -defined the carrier of (Polynom-Ring (n,L)) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support LeftLinearCombination of P
Sum g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
len g9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex Element of NAT
f9 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V49() ext-real non negative complex set
n is epsilon-transitive epsilon-connected ordinal set
Bags n is non zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
P -Ideal is non zero add-closed left-ideal right-ideal Element of bool the carrier of (Polynom-Ring (n,L))
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f - g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
- g is non zero Relation-like Bags n -defined Bags n -defined the carrier of L -valued Function-like total total V46( Bags n, the carrier of L) V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
x 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))
x + g9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
(- g) + g is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(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))
f9 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f + (- g) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f9 + (- g9) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (Polynom-Ring (n,L))
f9 - g9 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 zero functional Element of bool (Bags n)
Bags n is non zero set
bool (Bags n) is cup-closed diff-closed preBoolean set
[:(Bags n),(Bags n):] is Relation-like set
bool [:(Bags n),(Bags n):] is cup-closed diff-closed preBoolean set
T is Relation-like Bags n -defined Bags n -valued total V46( Bags n, Bags n) reflexive antisymmetric connected transitive Element of bool [:(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 V102() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like left_zeroed add-left-invertible add-right-invertible Loop-like doubleLoopStr
Polynom-Ring (n,L) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V102() 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 zero set
bool the carrier of (Polynom-Ring (n,L)) is cup-closed diff-closed preBoolean set
the carrier of L is non zero non trivial set
[:(Bags n), the carrier of L:] is Relation-like set
bool [:(Bags n), the carrier of L:] is cup-closed diff-closed preBoolean set
0_ (n,L) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) monomial-like Constant finite-Support Element of bool [:(Bags n), the carrier of L:]
P is Element of bool the carrier of (Polynom-Ring (n,L))
(n,T,L,P) is Relation-like NonZero (Polynom-Ring (n,L)) -defined the carrier of (Polynom-Ring (n,L)) -valued Element of bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):]
NonZero (Polynom-Ring (n,L)) is Element of bool the carrier of (Polynom-Ring (n,L))
[#] (Polynom-Ring (n,L)) is non zero non proper Element of bool 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 zero trivial finite 1 -element set
([#] (Polynom-Ring (n,L))) \ {(0. (Polynom-Ring (n,L)))} is Element of bool the carrier of (Polynom-Ring (n,L))
[:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is Relation-like set
bool [:(NonZero (Polynom-Ring (n,L))), the carrier of (Polynom-Ring (n,L)):] is cup-closed diff-closed preBoolean set
P -Ideal is non zero add-closed left-ideal right-ideal Element of bool the carrier of (Polynom-Ring (n,L))
f is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]
f - (0_ (n,L)) is non zero Relation-like Bags n -defined the carrier of L -valued Function-like total V46( Bags n, the carrier of L) finite-Support Element of bool [:(Bags n), the carrier of L:]