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(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
Require Export ArithRing.
Require Export Compare_dec.
Require Export Wf_nat.
Require Export Arith.
Require Export Omega.
intros a; elim a; auto.
intros n' Hrec b; case b; auto.
Qed.
Remark expand_mult2 : forall x : nat, 2 * x = x + x.
intros x; ring.
Qed.

Theorem lt_neq : forall x y : nat, x < y -> x <> y.