### 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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