Proof by exhaustion

[2] In the Curry–Howard isomorphism, proof by exhaustion and case analysis are related to ML-style pattern matching.

The statement can also be proved by exhaustion by listing out every year in which the Summer Olympics were held, and checking that every one of them can be divided by four.

In addition to being less elegant, the proof by exhaustion will also require an extra case each time a new Summer Olympics is held.

For example, rigorously solving a chess endgame puzzle might involve considering a very large number of possible positions in the game tree of that problem.

A proof with a large number of cases leaves an impression that the theorem is only true by coincidence, and not because of some underlying principle or connection.