Ltac le_less := rewrite Rle_lt_eq; left; try assumption.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].

Theorem Rtimes_nonneg_nonneg : forall n m : R, 0 <= n -> 0 <= m -> 0 <= n * m.