proposition: Lemma map_2 {elt elt'}(m: t elt)(x:key)(f:elt->elt') : In x (map f m) -> In x m.
proof: Proof. rewrite !in_find, map_find. apply option_map_some. Qed.
imports: Coq(Bool Equalities Orders OrdersFacts OrdersLists) Coq(Morphisms Permutation SetoidPermutation) MMaps(Utils Comparisons Interface)