Mathematical proof writing
- Lead with the theorem statement and the hypotheses you actually use.
- One direction at a time; mark
(⇒)/(⇐)for iff proofs. - Distinguish definitions, lemmas, theorems, corollaries; cite every non-trivial step.
- Call out where a result is needed vs merely available.
- For computer-assisted parts, link the SymPy/Wolfram run (
python_runinvocation id or notebook path); never bury verification inside prose. - Read the proof back from the bottom up at least once — does each line actually justify the next?