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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
(** modulo Modulo Arithmetic.  @author Olga Caprotti and Martijn Oostdijk @version $Revision$ *)
(** (Mod a b n) means (a = b (mod n)) *)
Definition Mod (a b : Z) (n : nat) :=
exists q : Z, a = (b + Z_of_nat n * q)%Z.

Lemma mod_plus_compat :
forall (a b c d : Z) (n : nat),
Mod a b n -> Mod c d n -> Mod (a + c) (b + d) n.