proposition: Lemma add_neq_in_iff m x y e : ~ K.eq x y -> (In y (add x e m) <-> In y m).
proof: Proof. split; intros (e',H0); exists e'. - now apply add_3 with x e. - now apply add_2. Qed.
imports: Coq(Bool Equalities Orders OrdersFacts OrdersLists) Coq(Morphisms Permutation SetoidPermutation) MMaps(Utils Comparisons Interface)