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(* as published by the Free Software Foundation; either version 2.1   *)
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(*                                                                    *)
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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.                       *)
(*                                                                    *)
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(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
Require Export Qhomographic_Qpositive_to_Qpositive.
Definition quadratic_top_more (a b c d e f g h : Z) :=
(e <= a)%Z /\ (f <= b)%Z /\ (g <= c)%Z /\ (h < d)%Z \/
(e <= a)%Z /\ (f <= b)%Z /\ (g < c)%Z /\ (h <= d)%Z \/
(e <= a)%Z /\ (f < b)%Z /\ (g <= c)%Z /\ (h <= d)%Z \/
(e < a)%Z /\ (f <= b)%Z /\ (g <= c)%Z /\ (h <= d)%Z.

Lemma quadratic_top_more_3 :
forall a b c d e f g h : Z,
(0 < e + f + g + h)%Z ->
(a - e + (b - f) + (c - g) + (d - h) < a + b + c + d)%Z.