Qed.
(* Theorems to simplify the hyp 0 ? x * y and x * y ? 0 where ? is < > <= >= *)

(* Specifications: *)
Theorem Rle_sign_pos_pos_rev: forall x y: R, (0 < x -> 0 <= x * y -> 0 <= y)%R.
intros x y H1 H2; case (Rle_or_lt 0 y); auto with real.
Theorem Zle_sign_pos_pos_rev: forall x y: Z, (0 < x -> 0 <= x * y -> 0 <= y)%Z.
intros x y H1 H2; case (Zle_or_lt 0 y); auto with zarith.
Theorem Rle_sign_pos_pos_rev: forall x y: R, (0 < x -> 0 <= x * y -> 0 <= y)%R.
intros x y H1 H2; case (Rle_or_lt 0 y); auto with real.