proposition: Lemma modNat_divides : forall x p, modNat x p = O -> exists k, (x = k * p)%nat.
proof: Proof. intuition. destruct (modNat_correct x p). rewrite H in H0. econstructor. rewrite Nat.add_0_r in H0. eauto. Qed.
imports: Arith micromega.Lia Coq.NArith.BinNat