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(*                                                                    *)
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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)            		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Functor.
Set Implicit Arguments.
Unset Strict Implicit.
(* (x|G) *)
Section comma_def.
Variables (A X : Category) (G : Functor A X) (x : X).
Structure Com_ob : Type :=  {Ob_com_ob : A; Mor_com_ob : x --> G Ob_com_ob}.
Section com_arrow_def.
Variable axf bxg : Com_ob.
Definition Com_law (h : Ob_com_ob axf --> Ob_com_ob bxg) :=
Mor_com_ob bxg =_S Mor_com_ob axf o FMor G h.
Structure > Com_arrow : Type :=
{Mor_com_arrow : Ob_com_ob axf --> Ob_com_ob bxg;
Prf_com_law :> Com_law Mor_com_arrow}.
(*** rewrite rules ***)
(* *)
Definition Equal_com_arrow (h h' : Com_arrow) :=
Mor_com_arrow h =_S Mor_com_arrow h'.

Lemma Equal_com_arrow_equiv : Equivalence Equal_com_arrow.
Canonical Structure Com_arrow_setoid : Setoid := Equal_com_arrow_equiv.