Section Partial_orders.
Variable U : Type.
Definition Carrier := Ensemble U.
Definition Rel := Relation U.
Inductive PO : Type :=
Definition_of_PO :
forall (C : Carrier) (R : Rel), Non_empty U C -> Order U R -> PO.
intro H'; elim H'.
intros C R H'0 H'1; exact C.
Defined.

Theorem Rel_of : PO -> Rel.