proposition: Lemma Qabs_diff_Qle_condition x y r: Qabs (x - y) <= r <-> x - r <= y <= x + r.
proof: Proof. intros. unfold Qminus. rewrite Qabs_Qle_condition. rewrite <- (Qplus_le_l (-r) (x+-y) (y+r)). rewrite <- (Qplus_le_l (x+-y) r (y-r)). setoid_replace (-r + (y + r)) with y by ring. setoid_replace (r + (y - r)) with y by ring. setoid_replace (x + - y + (y + r)) with (x + r) by ring. setoid_replace (x + - y + (y - r)) with (x - r) by ring. intuition. Qed.
imports: QArith Qreduction