Nuprl Lemma : decidable__equal_free-dl
∀[T:Type]. ∀eq:EqDecider(T). ∀x,y:Point(free-dist-lattice(T; eq)). Dec(x = y ∈ Point(free-dist-lattice(T; eq)))
Proof
Definitions occuring in Statement :
free-dist-lattice: free-dist-lattice(T; eq),
lattice-point: Point(l),
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
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,
implies: P ⇒ Q,
guard: {T},
top: Top
Lemmas referenced :
deq-implies,
lattice-point_wf,
free-dist-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,
free-dl-point,
deq-fset_wf,
fset_wf,
strong-subtype-deq-subtype,
assert_wf,
fset-antichain_wf,
strong-subtype-set2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
universeEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
introduction,
setEquality
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}x,y:Point(free-dist-lattice(T; eq)). Dec(x = y)
Date html generated:
2020_05_20-AM-08_45_08
Last ObjectModification:
2015_12_28-PM-02_00_16
Theory : lattices
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