proposition: Lemma quadratic_top_more_5' : forall a b c d e f g h : Z, (0 < a + b + c + d)%Z -> (a + b + c + d + (e - a) + (f - b) + (g - c) + (h - d) < a + b + c + d + e + f + g + h)%Z.
proof: Proof. intros. assert ((a + b + c + d + (e - a) + (f - b) + (g - c) + (h - d))%Z = (0 + e + f + g + h)%Z). abstract ring. rewrite H0. repeat rewrite Zplus_assoc_reverse with (n := (a + b + c + d)%Z). repeat rewrite Zplus_assoc_reverse with (n := 0%Z). apply Zplus_lt_le_compat. assumption. apply Z.le_refl. Qed.
imports: QArithSternBrocot(Merge_Order)