∈ on `listset` is decidable.

22d4a0cd · Robbert Krebbers · 91a46cc0 · 22d4a0cd
Commit 22d4a0cd authored Feb 20, 2019 by Robbert Krebbers
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theories/listset.v theories/listset.v +6 -1

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--- a/theories/listset.v
+++ b/theories/listset.v
@@ -38,7 +38,12 @@ Proof.
  abstract (by rewrite listset_empty_alt).
 Defined.

-Context `{!EqDecision A}.
+Context `{Aeq : !EqDecision A}.
+
+Global Instance listset_elem_of_dec : RelDecision (∈@{listset A}).
+Proof using Aeq.
+  refine (λ x X, cast_if (decide (x ∈ listset_car X))); done.
+Defined.

 Global Instance listset_intersection: Intersection (listset A) := λ l k,
  let (l') := l in let (k') := k in Listset (list_intersection l' k').