Nuprl Lemma : fun-converges_wf
∀[I:Interval]. ∀[f:ℕ ⟶ I ⟶ℝ]. (λn.f[n;x]↓ for x ∈ I) ∈ ℙ)
Proof
Definitions occuring in Statement :
fun-converges: λn.f[n; x]↓ for x ∈ I),
rfun: I ⟶ℝ,
interval: Interval,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fun-converges: λn.f[n; x]↓ for x ∈ I),
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
label: ...$L... t,
rfun: I ⟶ℝ,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
exists_wf,
rfun_wf,
fun-converges-to_wf,
real_wf,
i-member_wf,
nat_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
applyEquality,
setEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} I {}\mrightarrow{}\mBbbR{}]. (\mlambda{}n.f[n;x]\mdownarrow{} for x \mmember{} I) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-09_53_29
Last ObjectModification:
2015_12_27-PM-11_08_26
Theory : reals
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