Nuprl Lemma : fps-elim_wf
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[x:X]. (fps-elim(x) ∈ PowerSeries(X;r) ⟶ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-elim: fps-elim(x),
power-series: PowerSeries(X;r),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-elim: fps-elim(x),
crng: CRng,
rng: Rng,
subtype_rel: A ⊆r B,
power-series: PowerSeries(X;r)
Lemmas referenced :
ifthenelse_wf,
bag-deq-member_wf,
rng_car_wf,
rng_zero_wf,
fps-coeff_wf,
bag_wf,
power-series_wf,
crng_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
applyEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[x:X].
(fps-elim(x) \mmember{} PowerSeries(X;r) {}\mrightarrow{} PowerSeries(X;r))
Date html generated:
2016_05_15-PM-09_53_05
Last ObjectModification:
2015_12_27-PM-04_37_56
Theory : power!series
Home
Index