(* TODO: why core? *)

(* Specifications: *)
Lemma Ropp_lt_gt_contravar : forall r1 r2, r1 < r2 -> - r1 > - r2.
#[global]
Hint Resolve Ropp_le_ge_contravar: real.
Lemma Ropp_ge_le_contravar : forall r1 r2, r1 >= r2 -> - r1 <= - r2.
#[global]
Hint Resolve Rmult_lt_compat_r : core.
Lemma Rmult_gt_compat_r : forall r r1 r2, r > 0 -> r1 > r2 -> r1 * r > r2 * r.
#[global]
Hint Resolve Rmult_le_compat_l: real.
Lemma Rmult_le_compat_r :
forall r r1 r2, 0 <= r -> r1 <= r2 -> r1 * r <= r2 * r.