Nuprl Lemma : lattice-meet-1
∀[l:BoundedLattice]. ∀[x:Point(l)]. (x ∧ 1 = x ∈ Point(l))
Proof
Definitions occuring in Statement :
bdd-lattice: BoundedLattice,
lattice-1: 1,
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,
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,
guard: {T},
bounded-lattice-axioms: bounded-lattice-axioms(l)
Lemmas referenced :
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 :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
cumulativity,
independent_isectElimination,
isect_memberEquality,
axiomEquality,
because_Cache,
setElimination,
rename,
productElimination
Latex:
\mforall{}[l:BoundedLattice]. \mforall{}[x:Point(l)]. (x \mwedge{} 1 = x)
Date html generated:
2020_05_20-AM-08_26_01
Last ObjectModification:
2015_12_28-PM-02_02_41
Theory : lattices
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