Ltac le_equal := rewrite Rle_lt_eq; right; try reflexivity; try assumption.
Ltac le_elim H := rewrite Rle_lt_eq in H; destruct H as [H | H].

(* Times and order *)
Theorem Rtimes_pos_pos : forall n m : R, 0 < n -> 0 < m -> 0 < n * m.
Proof (SORtimes_pos_pos sor).