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(*                                                                    *)
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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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(*									     *)
(*	                   Full SubCategory                   		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Category.
Set Implicit Arguments.
Unset Strict Implicit.
Section fscat.
Variables (C : Category) (I : Type) (a : I -> C).
Definition FSC_mor_setoid (i j : I) := a i --> a j.
(* composition *)
Definition Comp_FSC (i j l : I) :
Map2 (FSC_mor_setoid i j) (FSC_mor_setoid j l) (FSC_mor_setoid i l) :=
Op_comp (a i) (a j) (a l).

(* Specifications: *)
Lemma Assoc_FSC : Assoc_law Comp_FSC.
Definition Id_FSC (i : I) := Id (a i).