Nuprl Lemma : fps-restrict_wf
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[f:PowerSeries(X;r)]. ∀[d:bag(X)].
(fps-restrict(eq;r;f;d) ∈ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-restrict: fps-restrict(eq;r;f;d),
power-series: PowerSeries(X;r),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-restrict: fps-restrict(eq;r;f;d),
power-series: PowerSeries(X;r),
crng: CRng,
rng: Rng
Lemmas referenced :
ifthenelse_wf,
deq-sub-bag_wf,
rng_car_wf,
fps-coeff_wf,
rng_zero_wf,
bag_wf,
power-series_wf,
crng_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[f:PowerSeries(X;r)]. \mforall{}[d:bag(X)].
(fps-restrict(eq;r;f;d) \mmember{} PowerSeries(X;r))
Date html generated:
2016_05_15-PM-09_56_42
Last ObjectModification:
2015_12_27-PM-04_36_08
Theory : power!series
Home
Index