apply Qabs_case.
- auto.
- apply (Qopp_le_compat x 0).
Qed.

(* Specifications: *)
Lemma Zabs_Qabs : forall n d, (Z.abs n#d)==Qabs (n#d).
Lemma Qabs_opp : forall x, Qabs (-x) == Qabs x.
Lemma Qabs_triangle : forall x y, Qabs (x+y) <= Qabs x + Qabs y.
Lemma Qabs_Qmult : forall a b, Qabs (a*b) == (Qabs a)*(Qabs b).
Lemma Qabs_Qinv : forall q, Qabs (/ q) == / (Qabs q).
Lemma Qabs_Qminus x y: Qabs (x - y) = Qabs (y - x).
Lemma Qle_Qabs : forall a, a <= Qabs a.
Lemma Qabs_triangle_reverse : forall x y, Qabs x - Qabs y <= Qabs (x - y).
Lemma Qabs_Qle_condition x y: Qabs x <= y <-> -y <= x <= y.
Lemma Qabs_Qlt_condition: forall x y : Q,
Qabs x < y <-> -y < x < y.
Lemma Qabs_diff_Qle_condition x y r: Qabs (x - y) <= r <-> x - r <= y <= x + r.
Lemma Qabs_diff_Qlt_condition x y r: Qabs (x - y) < r <-> x - r < y < x + r.
Lemma Qabs_ge: forall r s : Q, r <= s -> r <= Qabs s.
Lemma Qabs_gt: forall r s : Q, r < s -> r < Qabs s.