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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   *)
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(* 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.                       *)
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(* 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                                                     *)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export Classical_Prop.
Require Export Parts.
(** Title "Complement, images." *)
Comments "We define here complement of a part, image of a part by a map.".
Section Complement1.
Variable E : Setoid.

Lemma not_in_comp_l :
forall (E : Setoid) (A : part_set E) (x y : E),
~ in_part x A -> Equal y x -> ~ in_part y A.