Nuprl Lemma : mdist_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[x,y:X]. (mdist(d;x;y) ∈ ℝ)
Proof
Definitions occuring in Statement :
mdist: mdist(d;x;y),
metric: metric(X),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mdist: mdist(d;x;y),
metric: metric(X)
Lemmas referenced :
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
applyEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectElimination,
isectIsTypeImplies,
universeIsType,
extract_by_obid,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[x,y:X]. (mdist(d;x;y) \mmember{} \mBbbR{})
Date html generated:
2019_10_29-AM-10_57_15
Last ObjectModification:
2019_10_02-AM-09_39_10
Theory : reals
Home
Index