Commit be74ad29 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Prove f <$> to_gmap x X = to_gmap (f x) X.

parent 700a60a0
......@@ -159,6 +159,12 @@ Proof.
elem_of_singleton; destruct (decide (i = j)); intuition.
Lemma fmap_to_gmap `{Countable K} {A B} (f : A B) (X : gset K) (x : A) :
f <$> to_gmap x X = to_gmap (f x) X.
apply map_eq; intros j. rewrite lookup_fmap, !lookup_to_gmap.
by simplify_option_eq.
Lemma to_gmap_dom `{Countable K} {A B} (m : gmap K A) (y : B) :
to_gmap y (dom _ m) = const y <$> m.
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