proposition: Lemma find_spec m x e {Hm:Ok m}: find x m = Some e <-> MapsTo x e m.
proof: Proof. induction m as [|(k,e') m IH]; simpl. - split. discriminate. inversion 1. - inversion_clear Hm. unfold MapsTo in *. rewrite InA_cons, eqke_def. case X.compare_spec; intros. + split. injection 1 as ->; auto. intros [(_,<-)|IN]; trivial. SortLt. MX.order. + split. discriminate. intros [(E,<-)|IN]; trivial; try SortLt; MX.order. + rewrite IH; trivial. split; auto. intros [(E,<-)|IN]; trivial. MX.order. Qed.
imports: Coq(OrdersFacts OrdersLists)