Nuprl Lemma : converges-to-infinity_wf
∀[x:ℕ ⟶ ℝ]. (lim n →∞.x[n] = ∞ ∈ ℙ)
Proof
Definitions occuring in Statement :
converges-to-infinity: lim n →∞.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 :
converges-to-infinity: lim n →∞.x[n] = ∞,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_plus_wf,
all-large_wf,
rleq_wf,
int-to-real_wf,
nat_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[x:\mBbbN{} {}\mrightarrow{} \mBbbR{}]. (lim n \mrightarrow{}\minfty{}.x[n] = \minfty{} \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_39_53
Last ObjectModification:
2015_12_28-AM-00_58_47
Theory : reals
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