This is a very elegant proof pattern and its widely used in mathematical proofs.

Theorem: There is no largest integer.

a couple of comments

a. If N is an integer and M is an integer then M+N is an integer - the integers are closed under addition

b. If N and M are integers then N > M if and only if N-M > 0

These properties are directly from the definition of the integers

Proof: (by contradiction)

Suppose that N is the largest integer. Then N+1 is an integer too (from a) but N+1 is greater than N from b. So N is not the largest integer. QED!:thumbsup: