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(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(* definit un tableau a deux dimensions *)
Require Export table.
Unset Standard Proposition Elimination Names.
Section TABLE2.
Variable E F G : Set.
Hypothesis eq_E_dec : eq_dec E.
Hypothesis eq_F_dec : eq_dec F.
Variable t : E -> F -> G.
Variable x0 : E.
Variable y0 : F.
Variable z0 : G.
Definition change_x0y0 :=
change_x0 E (F -> G) eq_E_dec t x0 (change_x0 F G eq_F_dec (t x0) y0 z0).

(* Specifications: *)
Lemma elsewhere2_x : forall x : E, x <> x0 -> change_x0y0 x = t x.
Lemma elsewhere2_y :
forall y : F,
y <> y0 -> (fun x : E => change_x0y0 x y) = (fun x : E => t x y).
Lemma elsewhere2 :
forall (x : E) (y : F), x <> x0 \/ y <> y0 -> change_x0y0 x y = t x y.
Lemma here2 : change_x0y0 x0 y0 = z0.
End TABLE2.