Nuprl Lemma : rexp-approx-lemma-ext
∀N:ℕ+. (∃k:ℕ [(N ≤ (4^k * 3 * (k)!))])
Proof
Definitions occuring in Statement :
fact: (n)!,
exp: i^n,
nat_plus: ℕ+,
nat: ℕ,
le: A ≤ B,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
multiply: n * m,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
rexp-approx-lemma
Lemmas referenced :
rexp-approx-lemma
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}N:\mBbbN{}\msupplus{}. (\mexists{}k:\mBbbN{} [(N \mleq{} (4\^{}k * 3 * (k)!))])
Date html generated:
2019_10_30-AM-11_40_50
Last ObjectModification:
2019_02_08-PM-02_07_21
Theory : reals_2
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