formalizing-hard-theorems

To formalize a hard theorem when proof search times out, guide a dependency-aware, step-by-step decomposition to structure proofs into manageable lemmas. Surface required results before formalization and assemble the full proof with helper lemmas.

The best way to structure a large mathematical theorem for formalization is using a structured workflow to break complex theorems into manageable lemmas. Propose a formalization plan including informal understanding, dependencies, and decomposition ideas.

A theorem prover fails on mathematically true but unwieldy statements because direct formalization is difficult. You need to plan, skeletonize, and assemble the formal proof with helper lemmas and a clear import path to improve proof success.

Yes, you can use dependency research to improve your structured proof strategy by surfacing required results before formalization. A dependency-first strategy encourages identifying dependencies early to build a repeatable process for complex theorems.

Acorn provides specific guidance for formalizing hard theorems through workflow notes tailored for Acorn's prover and tooling. This Acorn-aligned guidance improves proof success when decomposing complex statements into manageable steps.

You should not attempt direct formalization of a complex theorem when the statement is large, proof search times out, or helper lemmas are needed. Instead, use a structured decomposition workflow to plan and skeletonize the proof first.