Definition Id_PA (x : PA_ob) :=
  match x as x' return (PA_mor x' x') with
  | PA1 => (* PA1 *)  PA_I1 
      (* PA2 *) 
  | PA2 => PA_I2
  end.

(* Specifications: *)
Lemma Idl_PA : Idl_law Comp_PA Id_PA.
Lemma Idr_PA : Idr_law Comp_PA Id_PA.