Commit bd4a6a84 authored by Robbert Krebbers's avatar Robbert Krebbers

Prove `map_fmap_empty_inv`.

parent 4c60de24
......@@ -261,6 +261,11 @@ Proof.
Lemma map_fmap_empty {A B} (f : A B) : f <$> ( : M A) = .
Proof. by apply map_eq; intros i; rewrite lookup_fmap, !lookup_empty. Qed.
Lemma map_fmap_empty_inv {A B} (f : A B) m : f <$> m = m = .
intros Hm. apply map_eq; intros i. generalize (f_equal (lookup i) Hm).
by rewrite lookup_fmap, !lookup_empty, fmap_None.
Lemma map_subset_alt {A} (m1 m2 : M A) :
m1 m2 m1 m2 i, m1 !! i = None is_Some (m2 !! i).
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