Nuprl Lemma : fps-degree-bound_wf
∀[r:CRng]. ∀[f:PowerSeries(r)]. ∀[d:ℕ]. (fps-degree-bound(r;f;d) ∈ ℙ)
Proof
Definitions occuring in Statement :
fps-degree-bound: fps-degree-bound(r;f;d),
power-series: PowerSeries(X;r),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
atom: Atom,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-degree-bound: fps-degree-bound(r;f;d),
so_lambda: λ2x.t[x],
uimplies: b supposing a,
nat: ℕ,
subtype_rel: A ⊆r B,
prop: ℙ,
crng: CRng,
rng: Rng,
so_apply: x[s]
Lemmas referenced :
uall_wf,
bag_wf,
isect_wf,
less_than_wf,
bag-size_wf,
equal_wf,
rng_car_wf,
fps-coeff_wf,
rng_zero_wf,
nat_wf,
power-series_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atomEquality,
hypothesis,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[f:PowerSeries(r)]. \mforall{}[d:\mBbbN{}]. (fps-degree-bound(r;f;d) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-10_03_08
Last ObjectModification:
2015_12_27-PM-04_34_24
Theory : power!series
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