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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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(* 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 Zring.
Require Export Fraction_field.
(* Check fraction_cfield. *)

Lemma Z_one_diff_zero : ~ Equal (ring_unit ZZ) (monoid_unit ZZ).
(* Goal: not (@Equal (sgroup_set (monoid_sgroup (group_monoid (abelian_group_group (ring_group (cring_ring (idomain_ring ZZ))))))) (ring_unit (cring_ring (idomain_ring ZZ))) (@monoid_unit (monoid_sgroup (group_monoid (abelian_group_group (ring_group (cring_ring (idomain_ring ZZ)))))) (monoid_on_def (group_monoid (abelian_group_group (ring_group (cring_ring (idomain_ring ZZ)))))))) *)
simpl in |- *.
(* Goal: not (@eq Z (ring_unit Zr_aux) Z0) *)
unfold not in |- *; intros.
(* Goal: False *)
inversion H.
Qed.

Definition Q := fraction_cfield Z_one_diff_zero Zzero_dec.
