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name: mathematical-proof-writing description: "Definition → lemma → theorem → corollary discipline, hypothesis tracking, casework hygiene, gap-spotting."

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_run invocation 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?