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(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                 Coq V6.1                                 *)
(*                               Oct 1st 1996                               *)
(*                                                                          *)
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(*                                    Map.v                                 *)
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(*****************************************************************************)
(*          Projet Coq - Calculus of Inductive Constructions V5.10           *)
(*****************************************************************************)
(*                                                                           *)
(*          General Algebra : Maps                                           *)
(*                                                                           *)
(*          Peter Aczel, Dec. 92                                             *)
(*          rev. Gerard Huet,  Aug. 1993                                     *)
(*                                                                           *)
(*****************************************************************************)
Require Export Setoid.
Set Implicit Arguments.
Unset Strict Implicit.
(* The set of maps between two Setoid *)
Section maps.
Variable A B : Setoid.
Definition Map_law (f : A -> B) := forall x y : A, x =_S y -> f x =_S f y.
Structure > Map : Type :=  {Ap :> A -> B; Pres :> Map_law Ap}.
(*** rewrite rule ***)

(* Specifications: *)
Lemma Pres1 : forall (m : Map) (x y : A), x =_S y -> m x =_S m y.
Definition Ext (f g : Map) := forall x : A, f x =_S g x.