Nuprl Lemma : mvp-add_wf
∀[r:CRng]. ∀[p,q:mv-polynomial(r)]. (mvp-add(r;p;q) ∈ mv-polynomial(r))
Proof
Definitions occuring in Statement :
mvp-add: mvp-add(r;p;q),
mv-polynomial: mv-polynomial(r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mvp-add: mvp-add(r;p;q),
mv-polynomial: mv-polynomial(r),
prop: ℙ,
fps-support: fps-support(r;f;s),
uimplies: b supposing a,
fps-add: (f+g),
fps-coeff: f[b],
crng: CRng,
rng: Rng,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
false: False,
guard: {T},
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
ring_p: IsRing(T;plus;zero;neg;times;one),
group_p: IsGroup(T;op;id;inv),
monoid_p: IsMonoid(T;op;id),
assoc: Assoc(T;op),
ident: Ident(T;op;id),
infix_ap: x f y
Lemmas referenced :
bag-lub_wf,
atom-deq_wf,
fps-add_wf,
fps-support_wf,
power-series_wf,
mv-polynomial_wf,
crng_wf,
not_wf,
sub-bag_wf,
bag_wf,
rng_car_wf,
rng_plus_wf,
sub-bag-lub,
rng_zero_wf,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
crng_properties,
rng_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairEquality,
extract_by_obid,
isectElimination,
atomEquality,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
setElimination,
rename,
because_Cache,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
lambdaFormation,
independent_functionElimination,
dependent_functionElimination,
inlFormation,
voidElimination,
inrFormation,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
independent_isectElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[r:CRng]. \mforall{}[p,q:mv-polynomial(r)]. (mvp-add(r;p;q) \mmember{} mv-polynomial(r))
Date html generated:
2018_05_21-PM-10_17_24
Last ObjectModification:
2017_07_26-PM-06_36_00
Theory : power!series
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