Nuprl Lemma : sine-approx-lemma-bad-ext
∀a:{2...}. ∀N:ℕ. (∃k:ℕ [(N ≤ (a^((2 * k) + 3) * ((2 * k) + 3)!))])
Proof
Definitions occuring in Statement :
fact: (n)!,
exp: i^n,
int_upper: {i...},
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,
sine-approx-lemma-bad,
decidable__le,
decidable__and,
decidable__not,
decidable__less_than',
decidable__implies,
decidable__false,
any: any x,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
sine-approx-lemma-bad,
lifting-strict-decide,
istype-void,
strict4-decide,
lifting-strict-less,
decidable__le,
decidable__and,
decidable__not,
decidable__less_than',
decidable__implies,
decidable__false
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
isect_memberEquality_alt,
voidElimination,
independent_isectElimination
Latex:
\mforall{}a:\{2...\}. \mforall{}N:\mBbbN{}. (\mexists{}k:\mBbbN{} [(N \mleq{} (a\^{}((2 * k) + 3) * ((2 * k) + 3)!))])
Date html generated:
2019_10_29-AM-10_33_12
Last ObjectModification:
2019_02_02-AM-10_37_57
Theory : reals
Home
Index