proposition: Lemma mem_1 : forall m (Hm:Sort m) x, In x m -> mem x m = true.
proof: Proof. intros m Hm; induction m as [|[a m]]; intros x H; simpl in *. - destruct H as [? H]; inversion H. - apply In_inv in H; destruct H as [H|H]. + destruct (elim_compare_eq H) as [? Hr]; rewrite Hr; reflexivity. + destruct (X.compare x a); [|reflexivity|apply IHm; inversion_clear Hm; auto]. absurd (In x ((a, m) :: m0)); [|destruct H as [y v]; exists y; constructor 2; auto]. apply Sort_Inf_NotIn with m; [inversion_clear Hm; auto|]. constructor; apply l. Qed.
imports: FMapInterface