Nuprl Lemma : fps-exp_wf
∀[X:Type]
∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[f:PowerSeries(X;r)]. ∀[n:ℕ]. ((f)^(n) ∈ PowerSeries(X;r)) supposing valueall-type(X)
Proof
Definitions occuring in Statement :
fps-exp: (f)^(n),
power-series: PowerSeries(X;r),
deq: EqDecider(T),
nat: ℕ,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fps-exp: (f)^(n),
subtype_rel: A ⊆r B,
crng: CRng,
fps-rng: fps-rng(r),
rng_car: |r|,
pi1: fst(t),
rng: Rng
Lemmas referenced :
rng_nexp_wf,
fps-rng_wf,
crng_wf,
rng_car_wf,
nat_wf,
power-series_wf,
deq_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]
\mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[f:PowerSeries(X;r)]. \mforall{}[n:\mBbbN{}]. ((f)\^{}(n) \mmember{} PowerSeries(X;r))
supposing valueall-type(X)
Date html generated:
2016_05_15-PM-09_52_15
Last ObjectModification:
2015_12_27-PM-04_38_23
Theory : power!series
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