Nuprl Lemma : lattice-0_wf
∀[l:BoundedLatticeStructure]. (0 ∈ Point(l))
Proof
Definitions occuring in Statement :
lattice-0: 0,
bounded-lattice-structure: BoundedLatticeStructure,
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-0: 0,
bounded-lattice-structure: BoundedLatticeStructure,
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,
guard: {T},
lattice-point: Point(l)
Lemmas referenced :
subtype_rel_self,
bounded-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,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
hypothesisEquality,
axiomEquality
Latex:
\mforall{}[l:BoundedLatticeStructure]. (0 \mmember{} Point(l))
Date html generated:
2020_05_20-AM-08_24_11
Last ObjectModification:
2015_12_28-PM-02_03_28
Theory : lattices
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