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_informative : forall a b c d e f g h : Z, {quadratic_top_more a b c d e f g h} + {~ quadratic_top_more a b c d e f g h}.