Nuprl Lemma : i-approx-of-compact
∀I:Interval. (icompact(I) ⇒ (∀n:ℕ+. (i-approx(I;n) = I ∈ Interval)))
Proof
Definitions occuring in Statement :
icompact: icompact(I),
i-approx: i-approx(I;n),
interval: Interval,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
icompact: icompact(I),
i-finite: i-finite(I),
i-closed: i-closed(I),
interval: Interval,
isl: isl(x),
outl: outl(x),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
bor: p ∨bq,
bfalse: ff,
and: P ∧ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
i-approx: i-approx(I;n),
rccint: [l, u],
false: False,
prop: ℙ
Lemmas referenced :
subtype_rel_product,
real_wf,
top_wf,
subtype_rel_union,
nat_plus_wf,
icompact_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
sqequalRule,
independent_pairEquality,
inlEquality,
hypothesisEquality,
voidEquality,
because_Cache,
applyEquality,
lemma_by_obid,
isectElimination,
unionEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
voidElimination,
isect_memberEquality
Latex:
\mforall{}I:Interval. (icompact(I) {}\mRightarrow{} (\mforall{}n:\mBbbN{}\msupplus{}. (i-approx(I;n) = I)))
Date html generated:
2016_05_18-AM-08_46_47
Last ObjectModification:
2015_12_27-PM-11_46_53
Theory : reals
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