(* 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 Coq - Calculus of Inductive Constructions V5.10           *)
(*****************************************************************************)
(*                                                                           *)
(*          Category Theory : Natural Transformations                        *)
(*                                                                           *)
(*          Amokrane Saibi May 1994                                          *)
(*                                                                           *)
(*****************************************************************************)
Require Export Functor.
Require Export Setoid_dup2.
Set Implicit Arguments.
Unset Strict Implicit.
(* Natural Transformations *)
Section nt_def.
Variables (C D : Category) (F G : Functor C D).
Definition NT_law (T : forall a : C, F a --> G a) :=
forall (a b : C) (f : a --> b), FMor F f o T b =_S T a o FMor G f.
Structure > NT : Type :=
{ApNT :> forall a : C, F a --> G a; Prf_NT_law :> NT_law ApNT}.
(*** rewrite rules ***)

Lemma NatCond :
forall (T : NT) (a b : C) (f : a --> b), FMor F f o T b =_S T a o FMor G f.