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Proof

(related to Corollary: Reduction of $\epsilon$-NFA to DFA)

• First, reduce a given $\epsilon$-NFA to an NFA according to theorem about the reduction of epsilon-nfa to nfa.
• Now, reduce the resulting NFA to a DFA according to the Rabin-Scott theorem.
• This shows the set inclusion $\mathcal L(\epsilon-\operatorname{NFA})\subseteq\mathcal L(\operatorname{DFA}).$
• The other set inclusion $\mathcal L(\operatorname{DFA})\subseteq\mathcal L(\epsilon-\operatorname{NFA})$ is trivial.
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References

Bibliography

1. Erk, Katrin; Priese, Lutz: "Theoretische Informatik", Springer Verlag, 2000, 2nd Edition
2. Hoffmann, Dirk: "Theoretische Informatik, 3. Auflage", Hanser, 2015