As the usage of theorem prover technology expands, so too does the reliance on correctness of the tools. Metamath Zero is a verification system that aims for simplicity of logic and implementation, without compromising on efficiency of verification. It is formally specified in its own language, and supports a number of translations to and from other proof languages. This paper describes the abstract logic of Metamath Zero, essentially a multi-sorted first order logic, as well as the binary proof format and the way in which it can ensure essentially linear time verification while still being concise and efficient at scale. Metamath Zero currently holds the record for fastest verification of the $\mathtt{set .mm}$ Metamath library of proofs in ZFC (including 71 of Wiedijk's 100 formalization targets), at less than 200 ms. Ultimately, we intend to use it to verify the correctness of the implementation of the verifier down to binary executable, so it can be used as a root of trust for more complex proof systems.

中文翻译：

---

Metamath 零：笛卡尔定理证明者

随着定理证明器技术的使用范围扩大，对工具正确性的依赖也在扩大。Metamath Zero 是一个验证系统，旨在简化逻辑和实现，同时不影响验证效率。它以自己的语言正式指定，并支持与其他证明语言之间的许多翻译。本文描述了 Metamath Zero 的抽象逻辑，本质上是一个多排序的一阶逻辑，以及二进制证明格式和它可以确保本质上线性时间验证的方式，同时在规模上仍然简洁高效。Metamath Zero 目前保持着 ZFC 中 $\mathtt{set .mm}$ 元数学证明库的最快验证记录（包括 Wiedijk 的 100 个形式化目标中的 71 个），不到 200 毫秒。最终，