Nuprl Lemma : lattice-join_wf
∀[l:LatticeStructure]. ∀[a,b:Point(l)]. (a ∨ b ∈ Point(l))
Proof
Definitions occuring in Statement :
lattice-join: a ∨ b,
lattice-point: Point(l),
lattice-structure: LatticeStructure,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-join: a ∨ b,
lattice-structure: LatticeStructure,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
lattice-point: Point(l)
Lemmas referenced :
subtype_rel_self,
lattice-point_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
lemma_by_obid,
isectElimination,
universeEquality,
functionEquality,
hypothesisEquality,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[l:LatticeStructure]. \mforall{}[a,b:Point(l)]. (a \mvee{} b \mmember{} Point(l))
Date html generated:
2020_05_20-AM-08_23_33
Last ObjectModification:
2015_12_28-PM-02_03_50
Theory : lattices
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