Nuprl Lemma : free-dml-deq_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. (free-dml-deq(T;eq) ∈ EqDecider(Point(free-DeMorgan-lattice(T;eq))))
Proof
Definitions occuring in Statement :
free-dml-deq: free-dml-deq(T;eq),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
lattice-point: Point(l),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
top: Top,
free-dml-deq: free-dml-deq(T;eq),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
free-dl-point,
deq-fset_wf,
fset_wf,
union-deq_wf,
strong-subtype-deq-subtype,
assert_wf,
fset-antichain_wf,
strong-subtype-set2,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
unionEquality,
hypothesisEquality,
applyEquality,
setEquality,
independent_isectElimination,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. (free-dml-deq(T;eq) \mmember{} EqDecider(Point(free-DeMorgan-lattice(T;eq))))
Date html generated:
2020_05_20-AM-08_53_48
Last ObjectModification:
2015_12_28-PM-01_56_52
Theory : lattices
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