Definition lt := Rlt.Definition le := Rle.Definition compare := Rcompare.#[global]
 Instance lt_strorder : StrictOrder Rlt.#[global]
 Instance lt_compat : Proper (Logic.eq==>Logic.eq==>iff) Rlt.

Lemma le_lteq : forall x y, x <= y <-> x < y \/ x = y.