What are some proof tools that you use very frequently?
I don't mean contradiction, induction, etc. Rather, more granular techniques that keep coming up again and again. I also don't mean famous results per-se, unless they are themselves common stepping stones to other results.
I know this is a bit of a silly question to ask because it's hard to set the threshold beyond which something becomes a legitimate technique. Obviously deriving bounds on a quantity is too generic to qualify, but on the other end there's some very niche stuff that not too many people might find useful.
I guess the goal here is a little toolbox, if you will, of tools that you find yourself using repeatedly, and that might be useful to a broad audience.