Commit 4f68d8a9 authored by Ralf Jung's avatar Ralf Jung Committed by Robbert Krebbers
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show a Proper instance for dom

parent 4978faed
......@@ -119,6 +119,17 @@ Proof.
eauto using (empty_finite (C:=D)), (union_finite (C:=D)),
(singleton_finite (C:=D)).
Global Instance dom_proper `{!Equiv A} : Proper ((@{M A}) ==> ()) (dom D).
intros m1 m2 EQm. apply elem_of_equiv. intros i.
rewrite !elem_of_dom, EQm. done.
(** If [D] has Leibniz equality, we can show an even stronger result. This is a
common case e.g. when having a [gmap K A] where the key [K] has Leibniz equality
(and thus also [gset K], the usual domain) but the value type [A] does not. *)
Global Instance dom_proper_L `{!Equiv A, !LeibnizEquiv D} :
Proper ((@{M A}) ==> (=)) (dom D) | 0.
Proof. intros ???. unfold_leibniz. by apply dom_proper. Qed.
Context `{!LeibnizEquiv D}.
Lemma dom_empty_L {A} : dom D (@empty (M A) _) = .
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