Nuprl Lemma : series-converges_wf
∀[x:ℕ ⟶ ℝ]. (Σn.x[n]↓ ∈ ℙ)
Proof
Definitions occuring in Statement :
series-converges: Σn.x[n]↓,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
series-converges: Σn.x[n]↓,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
real_wf,
series-sum_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
applyEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[x:\mBbbN{} {}\mrightarrow{} \mBbbR{}]. (\mSigma{}n.x[n]\mdownarrow{} \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_57_51
Last ObjectModification:
2015_12_28-AM-01_09_07
Theory : reals
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