Module Ident <: OrderedTypeFull
with Definition t := positive
with Definition lt := Plt
with Definition compare := fun x y => Pcompare x y Eq
with Definition le := Ple.
Definition t := positive.
Definition eq : t -> t -> Prop := @Logic.eq positive.
Definition eq_equiv: Equivalence eq := @eq_equivalence t. (*apply eq_equivalence. Qed.*)
Definition lt : t -> t -> Prop := Plt.
apply Positive_as_OT.lt_compat. Qed.
Definition compare: t -> t -> comparison := fun x y => Pcompare x y Eq.

Lemma compare_spec: forall p q : t, CompSpec Logic.eq lt p q (compare p q).