Nuprl Lemma : mdist-same
∀[X:Type]. ∀[d:metric(X)]. ∀[x:X]. (mdist(d;x;x) = r0)
Proof
Definitions occuring in Statement :
mdist: mdist(d;x;y),
metric: metric(X),
req: x = y,
int-to-real: r(n),
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
mdist: mdist(d;x;y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
metric: metric(X),
sq_stable: SqStable(P),
implies: P ⇒ Q,
and: P ∧ Q,
squash: ↓T,
guard: {T},
all: ∀x:A. B[x]
Lemmas referenced :
sq_stable__req,
int-to-real_wf,
req_witness,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
applyEquality,
hypothesisEquality,
natural_numberEquality,
hypothesis,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
universeIsType,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[x:X]. (mdist(d;x;x) = r0)
Date html generated:
2019_10_29-AM-10_58_57
Last ObjectModification:
2019_10_02-AM-09_40_35
Theory : reals
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