proposition: Lemma insert_sorted : forall (l:list Z) (x:Z), sorted l -> sorted (insert x l).
proof: Proof. intros l x H; induction H; simpl; auto with sort. - case (Z_le_gt_dec x z); simpl; auto with sort zarith. - revert H H0 IHsorted; simpl; case (Z_le_gt_dec x z2) , (Z_le_gt_dec x z1); simpl; auto with sort zarith. Qed.
imports: List ZArith RelationClasses Morphisms Extraction