Nuprl Lemma : ratio-dist_wf
∀[a,p:ℕ]. ∀[b,q:ℕ+]. ∀[m:ℕ]. (|a/b - p/q| < 1/m ∈ ℙ)
Proof
Definitions occuring in Statement :
ratio-dist: |a/b - p/q| < 1/m,
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
ratio-dist: |a/b - p/q| < 1/m,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
nat_plus: ℕ+,
subtype_rel: A ⊆r B
Lemmas referenced :
less_than_wf,
absval_wf,
subtract_wf,
nat_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
multiplyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[a,p:\mBbbN{}]. \mforall{}[b,q:\mBbbN{}\msupplus{}]. \mforall{}[m:\mBbbN{}]. (|a/b - p/q| < 1/m \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-04_43_20
Last ObjectModification:
2015_12_27-PM-02_39_30
Theory : general
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