Nuprl Lemma : lattice-less_wf
∀[l:LatticeStructure]. ∀[a,b:Point(l)]. (a < b ∈ ℙ)
Proof
Definitions occuring in Statement :
lattice-less: a < b,
lattice-point: Point(l),
lattice-structure: LatticeStructure,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-less: a < b,
prop: ℙ
Lemmas referenced :
and_wf,
lattice-le_wf,
not_wf,
equal_wf,
lattice-point_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[l:LatticeStructure]. \mforall{}[a,b:Point(l)]. (a < b \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-08_43_02
Last ObjectModification:
2015_12_28-PM-02_01_50
Theory : lattices
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