Nuprl Lemma : i-approx-rep2
∀I:Interval. ∀n:ℕ+. ∃a,b:ℝ. (i-approx(I;n) = [a, b] ∈ Interval)
Proof
Definitions occuring in Statement :
i-approx: i-approx(I;n),
rccint: [l, u],
interval: Interval,
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Lemmas referenced :
i-closed-finite-rep,
i-approx_wf,
i-approx-closed,
i-approx-finite,
nat_plus_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
because_Cache
Latex:
\mforall{}I:Interval. \mforall{}n:\mBbbN{}\msupplus{}. \mexists{}a,b:\mBbbR{}. (i-approx(I;n) = [a, b])
Date html generated:
2016_05_18-AM-08_48_44
Last ObjectModification:
2015_12_27-PM-11_45_27
Theory : reals
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