(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(*****************************************************************************)
(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
(*****************************************************************************)
(*									     *)
(*	                       Pullbacks                  		     *)
(*									     *)
(*****************************************************************************)
(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
(*****************************************************************************)
Require Export Limit.
Require Export PULB.
Require Export Pullbacks.
Set Implicit Arguments.
Unset Strict Implicit.
(* Pullbacks *)
Section Fpullback_limit_def.
Variables (C : Category) (G : Functor PULB C).
SubClass Fpullback1 := Limit G.
Variable l : Fpullback1.
Definition Fibred1_prod := Lim l.
Definition Fibred1_p : Fibred1_prod --> G P1 := Limiting_cone l P1.
Definition Fibred1_q : Fibred1_prod --> G P3 := Limiting_cone l P3.

(* Specifications: *)
Lemma Prf_pb1_law1 :
Pullback_law1 (FMor G F12) (FMor G F32) Fibred1_p Fibred1_q.