(** **)

(* Specifications: *)
Lemma Comp_PA_congl : Congl_law Comp_PA_mor.
Lemma Comp_PA_congr : Congr_law Comp_PA_mor.
Definition Comp_PA := Build_Comp Comp_PA_congl Comp_PA_congr.
Lemma Assoc_PA : Assoc_law Comp_PA.
Definition Id_PA (x : PA_ob) :=
match x as x' return (PA_mor x' x') with
| PA1 => (* PA1 *)  PA_I1
| PA2 => PA_I2
end.