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.Inductive PO : Type :=
       Definition_of_PO :
         forall (C : Carrier) (R : Rel), Non_empty U C -> Order U R -> PO.

Theorem Carrier_of : PO -> Carrier.