proposition: Lemma inf_iff : forall x l, Inf x l <-> inf x l = true.
proof: Proof. intros x l; split; intro H. - destruct H; simpl in *. + reflexivity. + rewrite <- compare_lt_iff in H; rewrite H; reflexivity. - destruct l as [|y ys]; simpl in *. + constructor; fail. + revert H; case_eq (X.compare x y); try discriminate; []. intros Ha _. rewrite compare_lt_iff in Ha. constructor; assumption. Qed.
imports: MSetInterface OrdersFacts OrdersLists