Canonical Structure Pullback1_to_Pullback :=
  Build_Pullback Prf_pb1_law1 Prf_pb1_law2 Prf_pb1_law3 Prf_pb1_law4.Definition Fpulb_ob (x : PULB) :=
  match x return (Ob C) with
  | P1 => a
  | P2 => b
  | P3 => c
  end.

Lemma Fpulb_map_law : forall x y : PULB_ob, Map_law (Fpulb_mor (x:=x) (y:=y)).