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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	                      Comma Category (x|G) : Projection		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Comma.
Set Implicit Arguments.
Unset Strict Implicit.
(* Functor Projection *)
Section comma_proj_def.
Variables (A X : Category) (G : Functor A X) (x : X).
Definition Comma_proj_ob (a : Com_ob G x) := Ob_com_ob a.
Section comma_proj_map_def.
Variable a b : Com_ob G x.
Definition Comma_proj_mor (f : a --> b) := Mor_com_arrow f.

Lemma Comma_proj_map_law : Map_law Comma_proj_mor.
Definition Comma_proj_map := Build_Map Comma_proj_map_law.