#[deprecated(since="8.16",note="Use Rabs_inv.")]
Notation Rabs_Rinv := Rabs_Rinv_depr.

(* Specifications: *)
Lemma Rabs_Ropp : forall x:R, Rabs (- x) = Rabs x.
Lemma Rabs_triang : forall a b:R, Rabs (a + b) <= Rabs a + Rabs b.
Lemma Rabs_triang_inv : forall a b:R, Rabs a - Rabs b <= Rabs (a - b).
Lemma Rabs_triang_inv2 : forall a b:R, Rabs (Rabs a - Rabs b) <= Rabs (a - b).
Lemma Rabs_def1 : forall x a:R, x < a -> - a < x -> Rabs x < a.
Lemma Rabs_def2 : forall x a:R, Rabs x < a -> x < a /\ - a < x.
Lemma RmaxAbs : forall (p q:R) r, p <= q -> q <= r -> Rabs q <= Rmax (Rabs p) (Rabs r).
Lemma Rabs_Zabs : forall z:Z, Rabs (IZR z) = IZR (Z.abs z).
Lemma abs_IZR : forall z, IZR (Z.abs z) = Rabs (IZR z).
Lemma Ropp_Rmax : forall x y, - Rmax x y = Rmin (-x) (-y).
Lemma Ropp_Rmin : forall x y, - Rmin x y = Rmax (-x) (-y).
Lemma Rmax_assoc : forall a b c, Rmax a (Rmax b c) = Rmax (Rmax a b) c.
Lemma Rminmax : forall a b, Rmin a b <= Rmax a b.
Lemma Rmin_assoc : forall x y z, Rmin x (Rmin y z) = Rmin (Rmin x y) z.