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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                                                     *)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export Integral_domain_cat.
Require Export Ring_facts.
Require Export Classical_Prop.
(** Title "Basic properties of  integral domains." *)
Section Lemmas.
Variable R : INTEGRAL_DOMAIN.

Lemma INTEGRAL_DOMAIN_prop_rev :
forall x y : R,
~ Equal x (monoid_unit R) ->
~ Equal y (monoid_unit R) -> ~ Equal (ring_mult x y) (monoid_unit R).