proposition: Lemma Qcabs_close : forall x y r, Qcabs (x - y) <= r -> Qcabs x <= Qcabs y + r.
proof: Proof. intros x y r Hle. rewrite Qcle_minus_iff. replace (Qcabs y + r + - Qcabs x) with (r + - (Qcabs x - Qcabs y)) by ring. rewrite <- Qcle_minus_iff. transitivity (Qcabs (x - y)). apply Qcabs_triangle_reverse. easy. Qed.
imports: Qreduction ClassicalRealizability.Qccomplement