Nuprl Lemma : cosine-approx-lemma-ext
∀a:{2...}. ∀N:ℕ+. (∃k:ℕ [(N ≤ (a^((2 * k) + 2) * ((2 * k) + 2)!))])
Proof
Definitions occuring in Statement :
fact: (n)!,
exp: i^n,
int_upper: {i...},
nat_plus: ℕ+,
nat: ℕ,
le: A ≤ B,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
multiply: n * m,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
cosine-approx-lemma
Lemmas referenced :
cosine-approx-lemma
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}a:\{2...\}. \mforall{}N:\mBbbN{}\msupplus{}. (\mexists{}k:\mBbbN{} [(N \mleq{} (a\^{}((2 * k) + 2) * ((2 * k) + 2)!))])
Date html generated:
2019_10_29-AM-10_34_03
Last ObjectModification:
2019_02_08-PM-01_39_01
Theory : reals
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