Definition compare : forall x y, Compare lt eq x y.Definition t := t.Definition eq x y := (x?=y) = Eq.Definition lt x y := (x?=y) = Lt.#[global]
 Instance eq_equiv : Equivalence eq.#[global]
 Instance lt_strorder : StrictOrder lt.

Lemma lt_eq : forall x y z, lt x y -> eq y z -> lt x z.