proposition: Lemma map_fmap_alt {A B} (f : A → B) (m : M A) : f <$> m = omap (λ x, Some (f x)) m.
proof: Proof. apply map_eq. intros i. rewrite lookup_fmap, lookup_omap. destruct (m !! i); done. Qed.
imports: Coq(Permutation) stdpp(options)