(** *** Sign of multiplication *)

(* Specifications: *)
Lemma Rmult_lt_0_compat : forall r1 r2, 0 < r1 -> 0 < r2 -> 0 < r1 * r2.
Lemma Rmult_gt_0_compat : forall r1 r2, r1 > 0 -> r2 > 0 -> r1 * r2 > 0.
Lemma Rmult_neg_pos : forall r1 r2, r1 < 0 -> r2 > 0 -> r1 * r2 < 0.
Lemma Rmult_pos_neg : forall r1 r2, r1 > 0 -> r2 < 0 -> r1 * r2 < 0.
Lemma Rmult_neg_cases :
forall r1 r2, r1 * r2 < 0 -> (r1 > 0 /\ r2 < 0) \/ (r1 < 0 /\ r2 > 0).