Nuprl Lemma : mcompact_wf
∀[X:Type]. ∀[d:metric(X)]. (mcompact(X;d) ∈ Type)
Proof
Definitions occuring in Statement :
mcompact: mcompact(X;d),
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
mcompact: mcompact(X;d),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
metric_wf,
m-TB_wf,
mk-metric-space_wf,
mcomplete_wf
Rules used in proof :
universeEquality,
instantiate,
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
universeIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. (mcompact(X;d) \mmember{} Type)
Date html generated:
2019_10_30-AM-07_06_22
Last ObjectModification:
2019_10_25-PM-01_14_13
Theory : reals
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