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(*                                                                    *)
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(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	                       Products                   		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Limit.
Require Export Discr.
Require Export Products.
Set Implicit Arguments.
Unset Strict Implicit.
(* Foncteur de I~ (cate'gorie discrete obtenue a` partir de I) vers C *)
Section products_limit_def.
Variables (C : Category) (I : Type) (a : I -> C).
Definition FunDiscr_ob (i : Discr I) := a i.
Definition FunDiscr_arrow (i j : Discr I) (f : i --> j) :=
match f in (Discr_mor d d0) return (Carrier (a d --> a d0)) with
| Build_Discr_mor k => Id (a k)
end.

(* Specifications: *)
Lemma FunDiscr_map_law :
forall i j : I, Map_law (FunDiscr_arrow (i:=i) (j:=j)).