Nuprl Lemma : fps-div_wf
∀[X:Type]
∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[x:|r|]. ∀[f,g:PowerSeries(X;r)]. ((f÷g) ∈ PowerSeries(X;r))
supposing valueall-type(X)
Proof
Definitions occuring in Statement :
fps-div: (f÷g),
power-series: PowerSeries(X;r),
deq: EqDecider(T),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
crng: CRng,
rng_car: |r|
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fps-div: (f÷g),
subtype_rel: A ⊆r B,
power-series: PowerSeries(X;r),
crng: CRng,
rng: Rng
Lemmas referenced :
fps-div-coeff_wf,
bag_wf,
rng_car_wf,
power-series_wf,
crng_wf,
deq_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
applyEquality,
functionEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]
\mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[x:|r|]. \mforall{}[f,g:PowerSeries(X;r)]. ((f\mdiv{}g) \mmember{} PowerSeries(X;r))
supposing valueall-type(X)
Date html generated:
2016_05_15-PM-09_48_47
Last ObjectModification:
2015_12_27-PM-04_40_43
Theory : power!series
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