Nuprl Lemma : i-member-witness
∀I:Interval. ∀r:ℝ. ((r ∈ I) ⇒ (∃n:ℕ+. (r ∈ i-approx(I;n))))
Proof
Definitions occuring in Statement :
i-approx: i-approx(I;n),
i-member: r ∈ I,
interval: Interval,
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
i-member-iff,
i-member_wf,
real_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
hypothesis,
isectElimination
Latex:
\mforall{}I:Interval. \mforall{}r:\mBbbR{}. ((r \mmember{} I) {}\mRightarrow{} (\mexists{}n:\mBbbN{}\msupplus{}. (r \mmember{} i-approx(I;n))))
Date html generated:
2016_05_18-AM-08_40_58
Last ObjectModification:
2015_12_27-PM-11_50_54
Theory : reals
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