computed types is relatively complex, they perform quite mechanical
"Finally, they are making their way back on shore where, unfortunately, a lot of them are already dead or dying as they approach the coastlines and get into rougher coastal waters."
They are not just any glasses.，详情可参考谷歌浏览器【最新下载地址】
Abstract:This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.
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然而，这种表面的平静下潜藏着更大的暗流。当前真正的“灰犀牛”，并非地缘冲突本身，而是其可能引发的货币政策剧变。倘若油价因供应中断而持续高企，将进一步固化美国的通胀压力，迫使美联储暂停甚至逆转降息进程。
В тройку крупнейших импортеров российского шоколада за прошлый год вошли Казахстан с импортом на сумму примерно в 300 миллионов долларов, а также Белоруссия (188 миллионов) и Узбекистан (107 миллионов). Другими важными покупателями стали Киргизия, Азербайджан, Армения, Китай, Грузия, Таджикистан и Монголия. Что касается Казахстана, то в 2025 году, отмечало агентство РИА Новости, Россия обеспечила 63 процента потребностей страны в импорте этого лакомства.。关于这个话题，heLLoword翻译官方下载提供了深入分析