Nuprl Lemma : rcos-seq-converges-ext
rcos-seq(n)↓ as n→∞
Proof
Definitions occuring in Statement :
rcos-seq: rcos-seq(n),
converges: x[n]↓ as n→∞
Definitions unfolded in proof :
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
accelerate: accelerate(k;f),
rcos-seq-converges,
increasing-sequence-converges,
rcos-seq-increasing,
rleq_functionality_wrt_implies,
rleq_weakening_rless,
converges-iff-cauchy,
rinv-exp-converges
Lemmas referenced :
rcos-seq-converges,
increasing-sequence-converges,
rcos-seq-increasing,
rleq_functionality_wrt_implies,
rleq_weakening_rless,
converges-iff-cauchy,
rinv-exp-converges
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
rcos-seq(n)\mdownarrow{} as n\mrightarrow{}\minfty{}
Date html generated:
2019_10_30-AM-11_43_11
Last ObjectModification:
2019_04_03-AM-01_08_46
Theory : reals_2
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