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 Rplus_le_lt_mono : forall n m p q : R, n <= m -> p < q -> n + p < m + q.