Nuprl Lemma : fps-scalar-mul_wf
∀[X:Type]. ∀[r:CRng]. ∀[c:|r|]. ∀[f:PowerSeries(X;r)]. ((c)*f ∈ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-scalar-mul: (c)*f,
power-series: PowerSeries(X;r),
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,
fps-scalar-mul: (c)*f,
infix_ap: x f y,
crng: CRng,
rng: Rng,
subtype_rel: A ⊆r B,
power-series: PowerSeries(X;r)
Lemmas referenced :
rng_times_wf,
fps-coeff_wf,
bag_wf,
rng_car_wf,
power-series_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[r:CRng]. \mforall{}[c:|r|]. \mforall{}[f:PowerSeries(X;r)]. ((c)*f \mmember{} PowerSeries(X;r))
Date html generated:
2016_05_15-PM-09_51_04
Last ObjectModification:
2015_12_27-PM-04_38_44
Theory : power!series
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