proposition: 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.
proof: Proof. intros. assert ((a - e + (b - f) + (c - g) + (d - h) + e + f + g + h)%Z = (a + b + c + d + 0)%Z). abstract ring. rewrite H0. repeat rewrite Zplus_assoc_reverse with (n := (a + b + c + d)%Z). apply Zplus_le_lt_compat. apply Z.le_refl. assumption. Qed.
imports: QArithSternBrocot(Merge_Order)