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].

(* The following theorems are used to build a morphism from Z to R and prove its properties in ZCoeff.v. They are not used in RingMicromega.v. *)
(* Surprisingly, multiplication is needed to prove the following theorem *)
Theorem Ropp_neg_pos : forall n : R, - n < 0 <-> 0 < n.