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: member: t ∈ T universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T metric-leq: d1 ≤ d2 prop: 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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