### Nuprl Lemma : fun-series-converges_wf

`∀[I:Interval]. ∀[f:ℕ ⟶ I ⟶ℝ].  (Σn.f[n;x]↓ for x ∈ I ∈ ℙ)`

Proof

Definitions occuring in Statement :  fun-series-converges: `Σn.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-series-converges: `Σn.f[n; x]↓ for x ∈ I` so_lambda: `λ2x y.t[x; y]` label: `...\$L... t` rfun: `I ⟶ℝ` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s1;s2]` subtype_rel: `A ⊆r B` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  fun-converges_wf rsum_wf int_seg_subtype_nat false_wf rfun_wf int_seg_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 lambdaEquality natural_numberEquality setElimination rename applyEquality addEquality independent_isectElimination independent_pairFormation lambdaFormation hypothesis setEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality because_Cache

Latex:
\mforall{}[I:Interval].  \mforall{}[f:\mBbbN{}  {}\mrightarrow{}  I  {}\mrightarrow{}\mBbbR{}].    (\mSigma{}n.f[n;x]\mdownarrow{}  for  x  \mmember{}  I  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-09_55_04
Last ObjectModification: 2015_12_27-PM-11_08_16

Theory : reals

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