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(* as published by the Free Software Foundation; either version 2.1   *)
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(*                                                                    *)
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(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* License along with this program; if not, write to the Free         *)
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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	   A Universal Arrow is a Initial Object In Comma Category 	     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Comma.
Require Export UniversalArrow.
Set Implicit Arguments.
Unset Strict Implicit.
Section ua_comma.
Variables (A X : Category) (G : Functor A X) (x : X).
(* Un UA de x vers G est un obj initial dans (x|G) *)
Variable u : UA x G.
Canonical Structure UA_com_ob := Build_Com_ob (UA_mor u).
Section ua_com_arrow_def.
Variable axf : Comma G x.

(* Specifications: *)
Lemma UA_com_law : Com_law (UA_diese u (Mor_com_ob axf)).
Canonical Structure UA_com_arrow := Build_Com_arrow UA_com_law.