Nuprl Lemma : free-dlwc-point-subtype
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[Cs:T ⟶ fset(fset(T))].
(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])) ⊆r Point(free-dist-lattice(T; eq)))
Proof
Definitions occuring in Statement :
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
free-dist-lattice: free-dist-lattice(T; eq),
lattice-point: Point(l),
fset: fset(T),
deq: EqDecider(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B
Lemmas referenced :
subtype_rel_sets,
fset_wf,
and_wf,
assert_wf,
fset-antichain_wf,
fset-all_wf,
fset-contains-none_wf,
deq_wf,
free-dlwc-point,
free-dl-point
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
productElimination,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[Cs:T {}\mrightarrow{} fset(fset(T))].
(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])) \msubseteq{}r Point(free-dist-lattice(T; eq)))
Date html generated:
2020_05_20-AM-08_48_24
Last ObjectModification:
2015_12_28-PM-01_59_00
Theory : lattices
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