#[global]
Hint Resolve Rmult_le_compat: real.

(* Specifications: *)
Lemma Rmult_le_pos : forall r1 r2, 0 <= r1 -> 0 <= r2 -> 0 <= r1 * r2.
Lemma Rmult_ge_compat :
forall r1 r2 r3 r4,
r2 >= 0 -> r4 >= 0 -> r1 >= r2 -> r3 >= r4 -> r1 * r3 >= r2 * r4.
Lemma Rmult_ge_0_gt_0_lt_compat :
forall r1 r2 r3 r4,
r3 >= 0 -> r2 > 0 -> r1 < r2 -> r3 < r4 -> r1 * r3 < r2 * r4.
Lemma Rmult_gt_0_lt_compat :
forall r1 r2 r3 r4,
r3 > 0 -> r2 > 0 -> r1 < r2 -> r3 < r4 -> r1 * r3 < r2 * r4.