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

Home Index