Nuprl Lemma : msep_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[x,y:X]. (x # y ∈ ℙ)
Proof
Definitions occuring in Statement :
msep: x # y,
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
msep: x # y
Lemmas referenced :
rless_wf,
int-to-real_wf,
mdist_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[x,y:X]. (x \# y \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-11_00_23
Last ObjectModification:
2019_10_02-AM-09_41_43
Theory : reals
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