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_5 : forall a b c d e f g h : Z, (0 < e + f + g + h)%Z -> (a - e + (b - f) + (c - g) + (d - h) + e + f + g + h < a + b + c + d + e + f + g + h)%Z.