Nuprl Lemma : mk-metric-space_wf
∀[X:Type]. ∀[d:metric(X)]. (X with d ∈ MetricSpace)
Proof
Definitions occuring in Statement :
mk-metric-space: X with d,
metric-space: MetricSpace,
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,
mk-metric-space: X with d,
metric-space: MetricSpace
Lemmas referenced :
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
dependent_pairEquality_alt,
hypothesisEquality,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. (X with d \mmember{} MetricSpace)
Date html generated:
2019_10_29-AM-11_08_52
Last ObjectModification:
2019_10_02-AM-09_50_05
Theory : reals
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