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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	                  Universal Arrows                  		     *)
(*									     *)
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(*									     *)
(*                            A.SAIBI   May 95				     *)
(*									     *)
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Require Export CatProperty.
Require Export Functor.
Set Implicit Arguments.
Unset Strict Implicit.
Section ua_def.
Variables (A B : Category) (b : B) (G : Functor A B).
Section isua_def.
Variables (a : A) (u : b --> G a).
Section ua_laws.
Variable diese : forall a' : A, (b --> G a') -> (a --> a').
Definition UA_eq (a' : A) (f : b --> G a') (g : a --> a') :=
u o FMor G g =_S f.
Definition UA_law1 := forall (a' : A) (f : b --> G a'), UA_eq f (diese f).
Definition UA_law2 :=
forall (a' : A) (f : b --> G a') (g : a --> a'),
UA_eq f g -> g =_S diese f.
End ua_laws.
Structure IsUA : Type :=
{UA_diese : forall a' : A, (b --> G a') -> (a --> a');
Prf_isUA_law1 : UA_law1 UA_diese;
Prf_isUA_law2 : UA_law2 UA_diese}.
Variable t : IsUA.
(* f=g => f# = g# *)

Lemma Diese_map : forall a' : A, Map_law (UA_diese t (a':=a')).
End isua_def.