(* This program is free software; you can redistribute it and/or      *)
(* 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 une table a une ou deux dimensions puis la sommation sur la table *)
Require Export finite.
Unset Standard Proposition Elimination Names.
Section TABLE1.
(* une table a lements dans F indexee par E est une fonction de E dans F dans laquelle on ne modifie qu'un terme a la fois *)
Variable E F : Set.
Hypothesis eq_E_dec : eq_dec E.
Variable t : E -> F.
Variable x0 : E.
Variable y0 : F.
Definition change_x0 (x : E) :=
if eq_E_dec x0 x then y0 else t x.

(* Specifications: *)
Lemma here : change_x0 x0 = y0.
Lemma elsewhere : forall x : E, x0 <> x -> change_x0 x = t x.
End TABLE1.