I believe I've proved that the power semigroup of non-negative integers with addition has a trivial automorphism group. The proof is a bit long, completely elementary and rather unremarkable (as the fact itself probably) so I won't post it here. However, I spent a long time thinking it up. Probably way too long. So I would like to know whether the fact

- is actually a fact;

- is completely trivial;

- follows immediately from a theorem that's maybe not that trivial;

- has any significance.

Added: For a semigroup $(S,\star)$, the power semigroup of $S$, denoted by $P(S)$ is the semigroup of all non-empty subsets of $S$ with the operation $A\star B=\{a\star b\,|\,a\in A,b\in B\}.$