Proof-like flow of thinking

Learning proof is just learning how to think logically, and completely.
As a researcher in FM, proving thing is just like eating, it is part and parcel of everyday job. Thus to make it easy, one would have to learnt it, digest it, make use of it FREQUENTLY, and hopefully master it.
After thousand of years of human history, some of the common pattern of thinking/proofing is known to be powerful, and it is used to tackle many important problems again and again.

Proof By Contradiction
This proof method is somewhat surprising yet very extremely powerful.
Basically we assume something is false, get a consequences from that which we can REVERT IT EASILY.

Proof By Structural Induction