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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                                                     *)
Require Export Qhomographic_sign.

Lemma sg_pos_2 :
forall (a b c d : Z) (p : Qpositive)
(H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c d p)
(na nb nc nd : Z) (np : Qpositive),
Qhomographic_sign a b c d p H_Qhomographic_sg_denom_nonzero =
(1%Z, (na, (nb, (nc, nd)), np)) ->
{(0 <= na)%Z /\ (0 <= nb)%Z /\ (0 <= nc)%Z /\ (0 <= nd)%Z} +
{(na <= 0)%Z /\ (nb <= 0)%Z /\ (nc <= 0)%Z /\ (nd <= 0)%Z} +
{np = One}.