Nuprl Lemma : metric-leq_wf
∀[X:Type]. ∀[d1,d2:metric(X)]. (d1 ≤ d2 ∈ ℙ)
Proof
Definitions occuring in Statement :
metric-leq: d1 ≤ d2,
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,
metric-leq: d1 ≤ d2,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
rleq_wf,
mdist_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d1,d2:metric(X)]. (d1 \mleq{} d2 \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-11_06_50
Last ObjectModification:
2019_10_02-AM-09_48_21
Theory : reals
Home
Index