Proof by exhaustion, also known as proof by cases, perfect induction, or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases and each case is checked to see if the proposition in question holds. A proof by exhaustion contains two stages:
- A proof that the cases are exhaustive; i.e., that each instance of the statement to be proved matches the conditions of (at least) one of the cases.
- A proof of each of the cases.
In the Curry–Howard isomorphism, proof by exhaustion and case analysis are related to ML-style pattern matching.
Read more about Proof By Exhaustion: Example, Number of Cases
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