Nuprl Lemma : rational-approx-property-ext
∀x:ℝ. ∀n:ℕ+. (|x - (x within 1/n)| ≤ (r1/r(n)))
Proof
Definitions occuring in Statement :
rational-approx: (x within 1/n),
rdiv: (x/y),
rleq: x ≤ y,
rabs: |x|,
rsub: x - y,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
rleq_functionality,
rational-approx-property,
member: t ∈ T
Lemmas referenced :
rational-approx-property,
rleq_functionality
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}x:\mBbbR{}. \mforall{}n:\mBbbN{}\msupplus{}. (|x - (x within 1/n)| \mleq{} (r1/r(n)))
Date html generated:
2018_05_22-PM-01_33_21
Last ObjectModification:
2018_05_21-AM-00_08_13
Theory : reals
Home
Index