proposition: Lemma Zle_minus : forall a b : Z, (b <= a)%Z -> (0 <= a - b)%Z.
proof: Proof. intros a b. intros. apply Zplus_le_reg_l with b. unfold Zminus in |- *. rewrite (Zplus_comm a). rewrite (Zplus_assoc b (- b)). rewrite Zplus_opp_r. simpl in |- *. rewrite <- Zplus_0_r_reverse. assumption. Qed.
imports: ZArith EqNat