Nuprl Lemma : decidable__i-closed
∀I:Interval. Dec(i-closed(I))
Proof
Definitions occuring in Statement :
i-closed: i-closed(I),
interval: Interval,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
interval: Interval,
i-closed: i-closed(I),
member: t ∈ T,
isl: isl(x),
outl: outl(x),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
bor: p ∨bq,
bfalse: ff,
uall: ∀[x:A]. B[x],
assert: ↑b,
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
interval_wf,
assert_wf,
isl_wf,
real_wf,
true_wf,
btrue_wf,
decidable__cand,
decidable__assert
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
cut,
lemma_by_obid,
hypothesis,
unionElimination,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}I:Interval. Dec(i-closed(I))
Date html generated:
2016_05_18-AM-08_18_56
Last ObjectModification:
2015_12_27-PM-11_57_11
Theory : reals
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