Nuprl Lemma : fps-div-property
∀[X:Type]
∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[f,g:PowerSeries(X;r)]. ∀[x:|r|].
(g*(f÷g)) = f ∈ PowerSeries(X;r) supposing (g[{}] * x) = 1 ∈ |r|
supposing valueall-type(X)
Proof
Definitions occuring in Statement :
fps-div: (f÷g),
fps-mul: (f*g),
fps-coeff: f[b],
power-series: PowerSeries(X;r),
empty-bag: {},
deq: EqDecider(T),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
universe: Type,
equal: s = t ∈ T,
crng: CRng,
rng_one: 1,
rng_times: *,
rng_car: |r|
Definitions unfolded in proof :
fps-div: (f÷g)
Lemmas referenced :
fps-div-coeff-property
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[X:Type]
\mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[f,g:PowerSeries(X;r)]. \mforall{}[x:|r|].
(g*(f\mdiv{}g)) = f supposing (g[\{\}] * x) = 1
supposing valueall-type(X)
Date html generated:
2016_05_15-PM-09_48_49
Last ObjectModification:
2015_12_27-PM-04_40_40
Theory : power!series
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