Nuprl Lemma : mdist-symm
∀[X:Type]. ∀[d:metric(X)]. ∀[x,y:X]. (mdist(d;x;y) = mdist(d;y;x))
Proof
Definitions occuring in Statement :
mdist: mdist(d;x;y),
metric: metric(X),
req: x = y,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
mdist: mdist(d;x;y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
metric: metric(X),
implies: P ⇒ Q
Lemmas referenced :
metric-symmetry,
req_witness,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
applyEquality,
setElimination,
rename,
because_Cache,
independent_functionElimination,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[x,y:X]. (mdist(d;x;y) = mdist(d;y;x))
Date html generated:
2019_10_29-AM-10_57_56
Last ObjectModification:
2019_10_02-AM-09_39_45
Theory : reals
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