Nuprl Lemma : fps-mul_wf
∀[X:Type]
∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[f,g:PowerSeries(X;r)]. ((f*g) ∈ PowerSeries(X;r)) supposing valueall-type(X)
Proof
Definitions occuring in Statement :
fps-mul: (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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
crng: CRng,
rng: Rng,
prop: ℙ,
and: P ∧ Q,
fps-mul: (f*g),
so_lambda: λ2x.t[x],
pi1: fst(t),
pi2: snd(t),
so_apply: x[s],
cand: A c∧ B,
subtype_rel: A ⊆r B
Lemmas referenced :
crng_properties,
rng_properties,
rng_all_properties,
ring_p_wf,
rng_car_wf,
rng_plus_wf,
rng_zero_wf,
rng_minus_wf,
rng_times_wf,
rng_one_wf,
rng_plus_comm,
rng_plus_comm2,
power-series_wf,
crng_wf,
deq_wf,
valueall-type_wf,
bag-summation_wf,
bag_wf,
fps-coeff_wf,
bag-partitions_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality,
lambdaEquality,
productEquality,
cumulativity,
applyEquality,
independent_isectElimination,
independent_pairFormation
Latex:
\mforall{}[X:Type]
\mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[f,g:PowerSeries(X;r)]. ((f*g) \mmember{} PowerSeries(X;r))
supposing valueall-type(X)
Date html generated:
2016_05_15-PM-09_47_39
Last ObjectModification:
2015_12_27-PM-04_40_53
Theory : power!series
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