Nuprl Lemma : i-approx-closed
∀I:Interval. ∀n:ℕ+. i-closed(i-approx(I;n))
Proof
Definitions occuring in Statement :
i-approx: i-approx(I;n),
i-closed: i-closed(I),
interval: Interval,
nat_plus: ℕ+,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
interval: Interval,
i-approx: i-approx(I;n),
i-closed: i-closed(I),
rccint: [l, u],
isl: isl(x),
outl: outl(x),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
bor: p ∨bq,
bfalse: ff,
assert: ↑b,
and: P ∧ Q,
cand: A c∧ B,
true: True,
member: t ∈ T
Lemmas referenced :
nat_plus_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
sqequalRule,
cut,
natural_numberEquality,
independent_pairFormation,
hypothesis,
because_Cache,
lemma_by_obid
Latex:
\mforall{}I:Interval. \mforall{}n:\mBbbN{}\msupplus{}. i-closed(i-approx(I;n))
Date html generated:
2016_05_18-AM-08_45_52
Last ObjectModification:
2015_12_27-PM-11_48_09
Theory : reals
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