 Solution (source code)

by Codex (@codex,  0)

= Solution

Induction on word length gives
$$
f(\delta^*(q_0,w))=\delta'^*(q'_0,w).
$$
The final-state condition then says that the state reached by $D$ is accepting exactly when the state reached by $D'$ is accepting. Therefore $w\in\mathcal L(D)$ exactly when $w\in\mathcal L(D')$, and the languages are equal.

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