(* 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        *)
(*****************************************************************************)
(*									     *)
(*	                         Limits                  		     *)
(*									     *)
(*****************************************************************************)
(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
(*****************************************************************************)
Require Export Const.
Require Export CoUniversalArrow.
Require Export Ntransformation.
Set Implicit Arguments.
Unset Strict Implicit.
Section def_cone.
Variables (J C : Category) (c : C) (F : Functor J C).
SubClass Cone := NT (Const J c) F.
Definition Cones := NT_setoid (Const J c) F.
Section cone_nt.
Variable T : forall a : J, c --> F a.
Definition Cone_law :=
forall (i j : J) (g : i --> j), T j =_S T i o FMor F g.

Lemma Prf_Cone_nt_law : Cone_law -> NT_law (F:=Const J c) T.
Coercion Prf_Cone_nt_law : Cone_law >-> NT_law.