Solution
= Solution
Induct on $n$. The initial equation is $0+0=0$ by the <zero> clause. If $0+n=n$, the successor clause gives
$$
0+n^+=(0+n)^+=n^+.
$$
Consequently
$$
\boxed{0+n=n\quad(n\in\omega).}
$$
This proves the left-identity property independently of the right-identity equation built into the recursive definition.