Nuprl Lemma : mtb-cantor-map_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[cmplt:mcomplete(X with d)]. ∀[mtb:m-TB(X;d)]. ∀[p:mtb-cantor(mtb)].
(mtb-cantor-map(d;cmplt;mtb;p) ∈ X)
Proof
Definitions occuring in Statement :
mtb-cantor-map: mtb-cantor-map(d;cmplt;mtb;p),
mtb-cantor: mtb-cantor(mtb),
m-TB: m-TB(X;d),
mcomplete: mcomplete(M),
mk-metric-space: X with d,
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mtb-cantor-map: mtb-cantor-map(d;cmplt;mtb;p),
guard: {T},
prop: ℙ
Lemmas referenced :
m-regularize-mcauchy,
cauchy-mlimit_wf,
m-regularize_wf,
mtb-seq_wf,
mtb-cantor_wf,
m-TB_wf,
mcomplete_wf,
mk-metric-space_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
hypothesis,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[cmplt:mcomplete(X with d)]. \mforall{}[mtb:m-TB(X;d)]. \mforall{}[p:mtb-cantor(mtb)].
(mtb-cantor-map(d;cmplt;mtb;p) \mmember{} X)
Date html generated:
2019_10_30-AM-07_05_11
Last ObjectModification:
2019_10_09-AM-09_21_27
Theory : reals
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