Checklist for finding and writing proofs

• Be sure you have a clear statement to prove
• Understand what you're proving
  • Figure out the logical structure.
  • Rephrase the statement in several logically equivalent ways.
  • Make sure you know the definitions of the mathematical terms.
  • Think about what theorems, concepts, etc. that involve those terms.
• Decide how you might prove it
  • Which proof techniques seem likely? Best?
  • What can you assume? What is your goal?
• Find the proof
  • Compare what you can assume with the theorems and definitions you know.
  • Figure out what theorems would get you to your goal.
  • Stuck? Try an alternative proof technique.
  • Still stuck? See if you can prove the theorem is false.
• Write rough draft, check for logical errors
  • Did you use all of the hypotheses?
  • Did you assume the conclusion? (This is bad.)
  • Are there clear steps in your proof that lead directly to the conclusion?
  • Does each step follow logically from the previous one?
  • Are the steps consistently sized?
• Write first draft
  • Check that you just prove one thing. If necessary, prove some propositions or lemmas first.
  • Check for content.
  • Check spelling, punctuation, grammar, and writing style.
  • Check for readability - format, spacing, visual appeal.
• Write the final draft
  • Be sure to state the theorem you're proving.
  • Be sure to leave room in the margins and between proofs for my comments.