The shape of a direct proof

1. 01Let $n$ be an even integer.Assumption
2. 02Then $n = 2k$ for some integer $k$.Definition of even
3. 03So $n + 2 = 2k + 2 = 2(k + 1)$.Factor out $2$
4. 04Since $k + 1$ is an integer, $n + 2$ is even. $\blacksquare$Definition of even