Verify Sequential Statements

Check each statement and subproof in order and log all local issues.

Input Contract

Assume:

• Proof is markdown text.
• The proof is written in good mathematical order.
• Statement contains the target theorem statement and its hypotheses.

Do not split the proof with utility code. Read the markdown in order and use its own structure.

Procedure

1. Extract the assumptions and hypotheses from Statement before checking the proof.
2. Iterate through the statements/subproofs in the order they appear in the markdown.
3. For each item, determine a location key:
   • use the displayed theorem/lemma/claim heading if present,
   • otherwise use a local textual locator such as proof paragraph 2.
4. Check local reasoning:
   • Is the inference valid?
   • Are assumptions stated and sufficient?
   • Is each theorem application valid in context?
   • Are there skipped or hand-wavy steps?