Nuprl Lemma : free-dma-point-subtype
∀[T:Type]. ∀[eq:EqDecider(T)]. (Point(free-DeMorgan-lattice(T;eq)) ⊆r Point(free-DeMorgan-algebra(T;eq)))
Proof
Definitions occuring in Statement :
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
lattice-point: Point(l),
deq: EqDecider(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
free-dma-point,
subtype_rel_self,
lattice-point_wf,
free-DeMorgan-lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
cumulativity,
hypothesisEquality,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
universeEquality,
because_Cache,
independent_isectElimination,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)].
(Point(free-DeMorgan-lattice(T;eq)) \msubseteq{}r Point(free-DeMorgan-algebra(T;eq)))
Date html generated:
2020_05_20-AM-08_56_27
Last ObjectModification:
2015_12_28-PM-01_55_16
Theory : lattices
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