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
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