If $x+y$ is not greater than $z$ it must be either less than $z$, or equal to $z$, so $x+y \leq z$
**Edited** (in response to OP's comment) to clarify for future readers:
The negation applies just to the logic; it has nothing to do with arithmetic. The negation of "greater than" is "not greater than". For numbers, "not greater than" is exactly the same as "less than or equal to". The fact that there's arithmetic on the left hand side is irrelevant.