Their argument shows that because the system is deterministic, every cell surrounded entirely by zeros or ones must then become a zero. Likewise, any perfect rule can never make the ratio of ones go above formula_1 if it was below (or vice versa). They then show that any assumed perfect rule will either cause an isolated one that pushed the ratio over formula_1 to be cancelled out or, if the ratio of ones is less than formula_1, will cause an isolated one to introduce spurious ones into a block of zeros causing the ratio of ones to be become greater than formula_1.