During an exercise for college, given two NFA's, $A_1\text{ and }A_2$ that accept the languages $L_1\text{ and }L_2$, I've built a NFA, $M$ that accepts the language $L_1*L_2$ (concatenation).
The formal NFA description is: $M = (Q, \Sigma, \delta, q_0, F)$ where
- $Q = Q_1 \cup Q_2$
- $\Sigma\ $ is the same
- $q_0 = q_0\ (\text{of }A_1)$
- $F= F\ (\text{of }A_2)$
- $\delta = \delta\ (\text{of }A_1)\cup \delta\ (\text{of }A_2)$
- and for each state $q \in F\text{ of }L_1, \delta(q,\epsilon)= q_0\text{ of }L_2$
Now I need to formally prove that $L(M) = L(A1) * L(A2)$. Can I get a direction to start from?
Thanks in advance