Nuprl Lemma : mdist-nonneg
∀[X:Type]. ∀[d:metric(X)]. ∀[x,y:X]. (r0 ≤ mdist(d;x;y))
Proof
Definitions occuring in Statement :
mdist: mdist(d;x;y),
metric: metric(X),
rleq: 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,
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
sq_stable__rleq,
int-to-real_wf,
le_witness_for_triv,
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,
natural_numberEquality,
hypothesis,
applyEquality,
hypothesisEquality,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
lambdaEquality_alt,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
functionIsTypeImplies,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[x,y:X]. (r0 \mleq{} mdist(d;x;y))
Date html generated:
2019_10_29-AM-10_57_36
Last ObjectModification:
2019_10_02-AM-09_39_27
Theory : reals
Home
Index