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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*		                                 			     *)
(*	     The Special Adjoint Functor Theorem (Freyd's Theorem)	     *)
(*                      ( The Solution Set Condition )                       *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Functor.
Set Implicit Arguments.
Unset Strict Implicit.
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(* Solution Set Condition *)
(**************************)
Section ssc2_def.
Variables (A X : Category) (G : Functor A X) (x : X).
Structure Cond2 (I : Type) (l : I -> A) (f : forall i : I, x --> G (l i))
(a : A) (h : x --> G a) : Type :=
{Cond2_i : I;
Cond2_t : l Cond2_i --> a;
Prf_Cond2_law : h =_S f Cond2_i o FMor G Cond2_t}.
Structure SSC2 : Type :=
{SSC2_I : Type;
SSC2_a : SSC2_I -> A;
SSC2_f : forall i : SSC2_I, x --> G (SSC2_a i);
SSC2_p : forall (a : A) (h : x --> G a), Cond2 SSC2_f h}.
Variables (s : SSC2) (a : A) (h : x --> G a).
Definition SSC2_i := Cond2_i (SSC2_p s h).
Definition SSC2_t := Cond2_t (SSC2_p s h).

Lemma Prf_SSC2_law : h =_S SSC2_f SSC2_i o FMor G SSC2_t.
End ssc2_def.