proposition: Theorem sub_diag : ∀ n, qeq (n - n) 0.
proof: Proof. intros n. destruct n as [n| ]; [ simpl | reflexivity ]. unfold Qeq; simpl. rewrite Z.mul_1_r. rewrite Z.mul_opp_l, Z.add_opp_r. apply Z.sub_diag. Qed.
imports: Utf8 QArith Misc