If the proof of a theorem is not immediately apparent, it may be because you are trying the wrong approach. Below are some effective methods of proof that might aim you in the right direction.
1. Proof by obviousness
"The proof is so clear that it need not be mentioned."
2. Proof by general agreement
"All in favor?..."
3. Proof by imagination
"Well, we'll pretend it's true..."
4. Proof by convenience
"It would be very nice if it were true, so..."
5. Proof by necessity
"It had better be true, or the entire structure of mathematics would crumble to the ground."
6. Proof by plausibility
"It sounds good, so it must be true."
7. Proof by intimidation
"Don't be stupid; of course it's true!"
8. Proof by lack of sufficient time
"Because of the time constraint, I'll leave the proof to you."
9. Proof by postponement
"The proof for this is long and arduous, so it is given to you in the appendix."
10. Proof by accident
"Hey, what have we here?!"
11. Proof by insignificance
"Who really cares anyway?"
12. Proof by plagiarism
"As we see on page 289,..."
13. Proof by clever variable choice
"Let A be the number such that this proof works..."
14. Proof by divine word
"...And the Lord said, 'Let it be true,' and it was true."
15. Proof by hasty generalization
"Well, it works for 17, so it works for all reals."
16. Proof by avoidance
"Limit of proof by postponement as it approaches infinity."
17. Proof by design
"If it's not true in today's math, invent a new system in which it is."