Nuprl Lemma : partition_wf
∀[I:Interval]. partition(I) ∈ Type supposing icompact(I)
Proof
Definitions occuring in Statement :
partition: partition(I),
icompact: icompact(I),
interval: Interval,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
partition: partition(I),
prop: ℙ
Lemmas referenced :
list_wf,
real_wf,
partitions_wf,
icompact_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[I:Interval]. partition(I) \mmember{} Type supposing icompact(I)
Date html generated:
2016_05_18-AM-08_55_21
Last ObjectModification:
2015_12_27-PM-11_38_39
Theory : reals
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