Canonical Structure PULB_mor_setoid := Build_Setoid Equal_PULB_mor_equiv.(* composition *)

Definition Comp_PULB_mor (a b c : PULB_ob) (f : PULB_mor_setoid a b) :=
  match
    f in (PULB_mor p p0) return (PULB_mor_setoid p0 c -> PULB_mor_setoid p c)
  with
  | IP1 => 
      (* IP1 *) 
      match c as p return (PULB_mor P1 p -> PULB_mor P1 p) with
      | P1 =>
          (* P1 *)  fun _ => IP1 
                    (* P2 *) 
      | P2 => fun _ => F12
              (* P3 *) 
      | P3 =>
          fun g => PULB_13_rect (fun _ : PULB_mor P1 P3 => PULB_mor P1 P3) g
      end
      (* IP1 *) 
  | IP2 =>
      match c as p return (PULB_mor P2 p -> PULB_mor P2 p) with
      | P1 => 
          (* P1 *) 
          fun g =>
          PULB_21_rect (fun _ : PULB_mor P2 P1 => PULB_mor P2 P1) g
          (* P2 *) 
      | P2 => fun _ => IP2
              (* P3 *) 
      | P3 =>
          fun g => PULB_23_rect (fun _ : PULB_mor P2 P3 => PULB_mor P2 P3) g
      end
      (* IP3 *) 
  | IP3 =>
      match c as p return (PULB_mor P3 p -> PULB_mor P3 p) with
      | P1 =>
          (* P1 *) 
          fun g =>
          PULB_31_rect (fun _ : PULB_mor P3 P1 => PULB_mor P3 P1) g 
          (* P2 *) 
      | P2 => fun _ => F32
              (* P3 *) 
      | P3 => fun _ => IP3
      end
      (* F12  *) 
  | F12 =>
      match c as p return (PULB_mor P2 p -> PULB_mor P1 p) with
      | P1 =>
          (* P1 *) 
          fun g =>
          PULB_21_rect (fun _ : PULB_mor P2 P1 => PULB_mor P1 P1) g
          (* P2 *) 
      | P2 => fun _ => F12
              (* P3 *) 
      | P3 =>
          fun g => PULB_23_rect (fun _ : PULB_mor P2 P3 => PULB_mor P1 P3) g
      end
      (* F32  *) 
  | F32 =>
      match c as p return (PULB_mor P2 p -> PULB_mor P3 p) with
      | P1 =>
          (* P1 *) 
          fun g =>
          PULB_21_rect (fun _ : PULB_mor P2 P1 => PULB_mor P3 P1) g
          (* P2 *) 
      | P2 => fun _ => F32
              (* P3 *) 
      | P3 =>
          fun g => PULB_23_rect (fun _ : PULB_mor P2 P3 => PULB_mor P3 P3) g
      end
  end.

Lemma Comp_PULB_congl : Congl_law Comp_PULB_mor.