Nuprl Lemma : fps-deriv_wf
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[f:PowerSeries(X;r)]. ∀[x:X]. (df/dx ∈ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-deriv: df/dx,
power-series: PowerSeries(X;r),
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-deriv: df/dx,
infix_ap: x f y,
crng: CRng,
rng: Rng,
subtype_rel: A ⊆r B,
nat: ℕ,
power-series: PowerSeries(X;r)
Lemmas referenced :
rng_times_wf,
int-to-ring_wf,
bag-count_wf,
nat_wf,
cons-bag_wf,
bag_wf,
subtype_rel_self,
power-series_wf,
crng_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
addEquality,
natural_numberEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[f:PowerSeries(X;r)]. \mforall{}[x:X]. (df/dx \mmember{} PowerSeries(X;r))
Date html generated:
2018_05_21-PM-10_16_01
Last ObjectModification:
2018_05_19-PM-04_17_09
Theory : power!series
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