Nuprl Lemma : fps-slice_wf
∀[X:Type]. ∀[r:CRng]. ∀[n:ℤ]. ∀[f:PowerSeries(X;r)]. ([f]_n ∈ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-slice: [f]_n,
power-series: PowerSeries(X;r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type,
crng: CRng
Definitions unfolded in proof :
power-series: PowerSeries(X;r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-slice: [f]_n,
subtype_rel: A ⊆r B,
nat: ℕ,
crng: CRng,
rng: Rng
Lemmas referenced :
ifthenelse_wf,
eq_int_wf,
bag-size_wf,
nat_wf,
rng_car_wf,
rng_zero_wf,
bag_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
intEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[r:CRng]. \mforall{}[n:\mBbbZ{}]. \mforall{}[f:PowerSeries(X;r)]. ([f]\_n \mmember{} PowerSeries(X;r))
Date html generated:
2016_05_15-PM-09_49_13
Last ObjectModification:
2015_12_27-PM-04_40_39
Theory : power!series
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