formalize-informal-proof

To convert an informal mathematical proof into Lean 4 code, you translate natural-language steps into formal lemmas and tactics, selecting required imports and building Lean structures to ensure machine-checked correctness.

Formal verification is the process of validating mathematical proofs using a proof assistant like Lean 4 to guarantee gap-free, machine-checked correctness for rigorous proof development.

Yes, you can use natural-language textbook proofs for formal verification by mapping informal steps to formal lemmas and tactics, outlining the Lean structure and identifying required imports.

The best way to structure a Lean proof from informal mathematics is to outline the Lean structure first, identify necessary imports, then systematically map informal proof steps to formal lemmas and tactics.

Yes, specifying imports is required when formalizing proofs in Lean 4 to load necessary mathematical structures and lemmas for validating the complete, gap-free proof.

An informal proof may fail formal verification in Lean if there are logical gaps in the informal steps, missing imports, or incorrect mapping to formal Lean lemmas and tactics during the translation process.