proposition: Theorem Qminus_lt_lt_plus_r : ∀ x y z, x - y < z → x < z + y.
proof: Proof. intros x y z H. apply Qplus_lt_compat_r with (z := y) in H. rewrite <- Qplus_minus_swap, <- Qplus_minus_assoc in H. unfold Qminus in H. rewrite Qplus_opp_r, Qplus_0_r in H. assumption. Qed.
imports: Utf8 QArith NPeano Sorted Psatz