Nuprl Lemma : mtb-point-cantor_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[mtb:m-TB(X;d)]. ∀[p:X]. (mtb-point-cantor(mtb;p) ∈ mtb-cantor(mtb))
Proof
Definitions occuring in Statement :
mtb-point-cantor: mtb-point-cantor(mtb;p),
mtb-cantor: mtb-cantor(mtb),
m-TB: m-TB(X;d),
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
mtb-point-cantor: mtb-point-cantor(mtb;p),
mtb-cantor: mtb-cantor(mtb),
uall: ∀[x:A]. B[x],
member: t ∈ T,
m-TB: m-TB(X;d),
spreadn: spread3,
pi1: fst(t)
Lemmas referenced :
m-TB_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectElimination,
isectIsTypeImplies,
inhabitedIsType,
extract_by_obid,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[mtb:m-TB(X;d)]. \mforall{}[p:X]. (mtb-point-cantor(mtb;p) \mmember{} mtb-cantor(mtb))
Date html generated:
2019_10_30-AM-06_57_22
Last ObjectModification:
2019_10_02-PM-02_44_07
Theory : reals
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