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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                                                     *)
(** -- These are arithmetic operations on signed Stern-Brocot numbers Qplus_lazy :: [Char] -> [Char] -> [Char] Qplus_lazy = Qquadratic 0 1 1 0 0 0 0 1 Qmult_lazy :: [Char] -> [Char] -> [Char] Qmult_lazy = Qquadratic 1 0 0 0 0 0 0 1 Qdiv_lazy :: [Char] -> [Char] -> [Char] Qdiv_lazy = Qquadratic 0 1 0 0 0 0 1 0 Qminus_lazy :: [Char] -> [Char] -> [Char] Qminus_lazy = Qquadratic 0 1 (-1) 0 0 0 0 1 *)
Require Export Qhomographic.
Require Export quadraticAcc_Qquadratic_sign.

Lemma Qquadratic_sg_denom_nonzero_always :
forall (k e f g h : Z) (p1 p2 : Qpositive),
k <> 0%Z ->
(0 < e)%Z ->
(0 < f)%Z ->
(0 < g)%Z ->
(0 < h)%Z ->
Qquadratic_sg_denom_nonzero (k * e) (k * f) (k * g) (k * h) p1 p2.