Nuprl Lemma : mul_comm_fps
∀[X:Type]
∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[a,b:PowerSeries(X;r)]. ((a*b) = (b*a) ∈ 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],
universe: Type,
equal: s = t ∈ T,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fps-rng: fps-rng(r),
rng_car: |r|,
pi1: fst(t),
rng_times: *,
pi2: snd(t),
infix_ap: x f y
Lemmas referenced :
crng_times_comm,
fps-rng_wf,
crng_wf,
deq_wf,
valueall-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]
\mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[a,b:PowerSeries(X;r)]. ((a*b) = (b*a))
supposing valueall-type(X)
Date html generated:
2020_05_20-AM-09_05_38
Last ObjectModification:
2020_01_31-PM-03_03_59
Theory : power!series
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