proposition: Lemma remove_spec2 m x y {Hm:Ok m} : ~X.eq x y -> find y (remove x m) = find y m.
proof: Proof. induction m as [|(k,e') m IH]; simpl; trivial. inversion_clear Hm. case X.compare_spec; simpl; intros E E'; try rewrite IH; auto. case X.compare_spec; simpl; trivial; try MX.order. intros. rewrite <- E in H0,H1. clear E E'. destruct (find y m) eqn:F; trivial. apply find_spec in F; trivial. SortLt. MX.order. Qed.
imports: Coq(OrdersFacts OrdersLists)