Nuprl Lemma : cosine-approx-for-small-ext
∀a:{2...}. ∀N:ℕ+. ∀x:{x:ℝ| |x| ≤ (r1/r(a))} . (∃z:ℤ [(|cosine(x) - (r(z)/r(2 * N))| ≤ (r(2)/r(N)))])
Proof
Definitions occuring in Statement :
cosine: cosine(x),
rdiv: (x/y),
rleq: x ≤ y,
rabs: |x|,
rsub: x - y,
int-to-real: r(n),
real: ℝ,
int_upper: {i...},
nat_plus: ℕ+,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
set: {x:A| B[x]} ,
multiply: n * m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
cosine-approx-for-small,
cosine-approx-lemma-ext
Lemmas referenced :
cosine-approx-for-small,
cosine-approx-lemma-ext
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{}. \mforall{}x:\{x:\mBbbR{}| |x| \mleq{} (r1/r(a))\} . (\mexists{}z:\mBbbZ{} [(|cosine(x) - (r(z)/r(2 * N))| \mleq{} (r(2)/r(N)))]\000C)
Date html generated:
2019_10_29-AM-10_37_49
Last ObjectModification:
2019_02_08-PM-01_56_56
Theory : reals
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