Proofs

When writing your own proof or critiquing someone's proof you need to remember the following.
  1. A proof is a presentation.
    1. The theorem should be stated.
    2. The argument type should be stated if not direct (contradiction, cases, etc.)
    3. Any objects or notations should be explained before they are used.
    4. Theorems are never referred to as Lemma 2739 (they have names just like you).
    5. Correct grammar should be used at all times.
    6. The presentation should aid understanding not  hinder it.
  2. A proof is logical.
    1. Every proof starts with the conditions and works logically toward the conclusion.
    2. Every statement has a reason which is explicitely stated.
    3. These reasons must be definitions or previously proven theorems.
    4. Proofs never "assume" anything.
    5. "Let" and "suppose" are not synonyms.