Nuprl Lemma : lattice-le_wf
∀[l:LatticeStructure]. ∀[a,b:Point(l)]. (a ≤ b ∈ Type)
Proof
Definitions occuring in Statement :
lattice-le: a ≤ b,
lattice-point: Point(l),
lattice-structure: LatticeStructure,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-le: a ≤ b,
prop: ℙ
Lemmas referenced :
equal_wf,
lattice-point_wf,
lattice-meet_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[l:LatticeStructure]. \mforall{}[a,b:Point(l)]. (a \mleq{} b \mmember{} Type)
Date html generated:
2020_05_20-AM-08_23_46
Last ObjectModification:
2017_07_28-AM-09_12_32
Theory : lattices
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