Inspired by a statement about Extended Frege proof systems by Jain and Jin (FOCS 2022) we prove that: - there is a p-time binary relation $\approx$ between circuits that implies their logical equivalence, - the relation $\approx$ implies that each of the two circuits can be rewritten into the other one by possibly deleting some gates and adding at most seven new gates, - if the equivalence $C \equiv D$ has a size $s$ proof in an Extended Frege or a Circuit Frege proof system then there is a chain of circuits $E_i$ $$ C = E_0 \approx \dots \approx E_t = D $$ with $t \le s^{O(1)}$.

翻译：受Jain与Jin（FOCS 2022）关于扩展弗莱格证明系统的一个论断启发，我们证明了：- 存在一个p时间二元关系$\approx$，该关系定义于电路之间且蕴涵其逻辑等价性；- 关系$\approx$意味着两个电路中的每一个均可通过可能删除若干门电路并添加至多七个新门电路重写为另一个；- 若等价性$C \equiv D$在扩展弗莱格或电路弗莱格证明系统中具有规模为$s$的证明，则存在一条电路链$E_i$ $$ C = E_0 \approx \dots \approx E_t = D $$ 其中$t \le s^{O(1)}$。