and by the construction of wherever constrains a state in F.

If (and thus is not in F ), then with leads to an accepting state in N' iff it leads to an accepting state in N ( by the construction of N' and N ).

Also, if ( , thus w is accepted by N' iff w is accepted by N (iff )

If (and, thus in M we load in F ), thus is accepted by both N' and N .

Let . If w cannot lead to in N , then . (Since can add transitions to get an accept state). So there is no harm in making an accept state in N'.

Ex: Consider the following NFA with - transition.