Nuprl Lemma : i-closed_wf
∀[I:Interval]. (i-closed(I) ∈ ℙ)
Proof
Definitions occuring in Statement :
i-closed: i-closed(I),
interval: Interval,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
interval: Interval,
i-closed: i-closed(I),
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
Lemmas referenced :
and_wf,
assert_wf,
isl_wf,
real_wf,
true_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
sqequalRule,
lemma_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I:Interval]. (i-closed(I) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_18_47
Last ObjectModification:
2015_12_27-PM-11_57_30
Theory : reals
Home
Index