Especially in boolean algebra, is there a name for a proof that asserts its truthfulness by simply stating all possible combinations of inputs?
It's very hard to describe, but say I had two combination locks, and I wanted to prove they were the same, so I try every combination of numbers with both of the locks and show that they have the same outcome for each combination, thereby proving that they're equal in security (physicality aside)
I was looking at this answer, where what I believe they demonstrate an extension of baye's theorem. The proof is very simple and concise, and they take all possible inputs, and show that all possible outputs for the given inputs match eachother.
Now this undoubtedly proves that the two statements are equal to eachother, but not rigorously, and not with any formal definitions beyond some givens.
What is the formal name for proving something by exhausting all possible conditions in mathematics?
Proof by Cases or Proof by Exhaustion
If you are familiar with the Knights and Knaves puzzles, you'll find that this can be a very powerful proof technique: many people try to sovle Knights and Knaves puzzles by step-by-step reasoning, but considering all possible combinations (akin to a truth-table) will often give on the answer pretty quickly ... and very safely.