Question:

Formally prove the correctness of the union construction as follows. Let M1 and M2 be the two $\displaystyle \lambda$-NFA's constructed for R1 and R2 and let N be the $\displaystyle \lambda$-NFA constructed so that L(N) = R1 + R2. Let w be a string such that $\displaystyle \Delta_{N}^{*}(\iota,w,f)$. Prove that either $\displaystyle \Delta_{M_{1}}^{*}(\iota_{1},w,f_{1})$ or $\displaystyle \Delta_{M_{2}}^{*}(\iota_{2},w,f_{2})$. Use induction on all strings w.

Not only do I have no idea what to do, I don't even know what this is asking. Any push in the right direction would be helpful.

Thanks.