Nuprl Lemma : lattice-meet-0
∀[l:BoundedLattice]. ∀[x:Point(l)]. (0 ∧ x = 0 ∈ Point(l))
Proof
Definitions occuring in Statement :
bdd-lattice: BoundedLattice,
lattice-0: 0,
lattice-meet: a ∧ b,
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-le: a ≤ b,
subtype_rel: A ⊆r B,
bdd-lattice: BoundedLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
lattice-0-le,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
and_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
bdd-lattice_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalitySymmetry,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
cumulativity,
independent_isectElimination
Latex:
\mforall{}[l:BoundedLattice]. \mforall{}[x:Point(l)]. (0 \mwedge{} x = 0)
Date html generated:
2020_05_20-AM-08_25_55
Last ObjectModification:
2015_12_28-PM-02_02_43
Theory : lattices
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