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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