Nuprl Lemma : metric_wf
∀[X:Type]. (metric(X) ∈ Type)
Proof
Definitions occuring in Statement :
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,
metric: metric(X),
and: P ∧ Q,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
real_wf,
rleq_wf,
int-to-real_wf,
req_wf,
radd_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
functionEquality,
hypothesisEquality,
extract_by_obid,
hypothesis,
productEquality,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. (metric(X) \mmember{} Type)
Date html generated:
2019_10_29-AM-10_50_54
Last ObjectModification:
2019_10_02-AM-09_32_54
Theory : reals
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