Proof Explanation Tool — illustrative example

INPUT
Explain why the sum of two even integers is even.

RESULT
An even integer can be written as 2 times an integer. Let the two numbers be 2m and 2n, where m and n are integers. Their sum is 2m + 2n = 2(m + n). Since m + n is an integer, the sum is divisible by 2 and is therefore even.

REVIEW
Explain why each step follows, including the assumptions being used. Restating symbolic lines in words is not enough to clarify a proof.

This is a teaching example, not a live execution record.