Section pb1_diese_def.
Variables (r : C) (t1 : r --> G P1) (t2 : r --> G P3).
Hypothesis H : Pullback_eq1 (FMor G F12) (FMor G F32) t1 t2.
(* construction de r# *)
Definition Pulb_tau (a : PULB) :=
match a as a' return (Carrier (r --> G a')) with
| P1 => t1
| P2 => t1 o FMor G F12
| P3 => t2
end.
Definition Pulb_cone : Cone r G := Pulb_cone_law.
Definition Pb1_diese : r --> Fibred1_prod := Lim_diese l Pulb_cone.
End pb1_diese_def.

Lemma Prf_pb1_law3 : Pullback_law3 Fibred1_q Pb1_diese.