PROOF BY CASES
AN ARGUMENT MADE IN CAPITAL LETTERS IS CORRECT. THEREFORE, SIMPLY RESTATE THE PROPOSITION YOU ARE TRYING TO PROVE IN CAPITAL LETTERS, AND IT WILL BE CORRECT.
Of course, you have to be careful which letters you use as variable names in stating your result -- you can only use one of a, α, and A, for example.
And some of them are methods of proof that are actually used:
Proof by Diagram
Reducing problems to diagrams with lots of arrows. Particularly common in category theory.
And here's an interesting point about mathematical writing:
Proof by TeX
The proof is typeset using TeX or LaTeX, preferably using one of the AMS or ACM stylesheets. When laid out so professionally, it can't possibly have any flaws.