Nuprl Lemma : fun-series-converges-absolutely_wf

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


Proof




Definitions occuring in Statement :  fun-series-converges-absolutely: Σn.f[n; x]↓ absolutely for x ∈ I rfun: I ⟶ℝ interval: Interval nat: uall: [x:A]. B[x] prop: 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-absolutely: Σn.f[n; x]↓ absolutely for x ∈ I so_lambda: λ2y.t[x; y] label: ...$L... t rfun: I ⟶ℝ so_apply: x[s1;s2] subtype_rel: A ⊆B prop:
Lemmas referenced :  fun-series-converges_wf rabs_wf rfun_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 applyEquality 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{}  absolutely  for  x  \mmember{}  I  \mmember{}  \mBbbP{})



Date html generated: 2016_05_18-AM-09_56_20
Last ObjectModification: 2015_12_27-PM-11_08_03

Theory : reals


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