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(*                                                                    *)
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(* GNU General Public License for more details.                       *)
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(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(* BIBLI *)
(* fichier de bibliotheque*)
Require Export Arith.
Require Export Omega.
Global Set Asymmetric Patterns.
Section SEPAR.
(* lorsque l'egalite est decidable sur un ensemble *)

(* Specifications: *)
Lemma eq_bool_dec : forall b : bool, {b = true} + {b = false}.
Lemma case_ineq :
forall (E F : Set) (eq_E_dec : eq_dec E) (x x' : E) (y z : F),
x <> x' -> match eq_E_dec x x' with
| left _ => y
| right _ => z
end = z.
Lemma eq_couple_dec :
forall (E F : Set) (eq_E_dec : eq_dec E) (eq_F_dec : eq_dec F)
(x1 x2 : E) (y1 y2 : F), {x1 = x2 /\ y1 = y2} + {x1 <> x2 \/ y1 <> y2}.