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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.             *)
(*                                                                    *)
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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.                       *)
(*                                                                    *)
(* 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 Automatic Coercions Import.
Set Implicit Arguments.
Unset Strict Implicit.
Require Export Z_group_facts.
(** Title "Universal property of integers." *)
Section Zup1.
Variable R : RING.
Hint Resolve Z_to_group_nat_eq_pos: algebra.
Hint Resolve Z_to_group_nat_unit: algebra.
Hint Resolve Zl1: algebra.
Hint Resolve Zl2: algebra.

Lemma nat_to_group_mult :
forall n m : nat,
Equal (nat_to_group (ring_unit R) (n * m))
(ring_mult (nat_to_group (ring_unit R) n) (nat_to_group (ring_unit R) m)).