$14\mathrm{.}8$: Kleene Star Construction

Kleene star construction. Suppose we change the $\backslash$lambda $-$NFA construction of Section $14\mathrm{.}8$ as follows. If i and f are the initial and final states respectively of the $\backslash$lambda $-$NFA for R$,$ we add new initial state s and new final state t$,$ make f non$-$final, and add $\backslash$lambda $-$moves from s to i$,$ from s to t$,$ from f to i$,$ and from f to t$.($So we replace the one from i to f in the book$$s construction with one from s to t$.)$ Then the resulting $\backslash$lambda $-$NFA has language L$($R$)*,$ and it obeys rules $(1),(2),$ and $(3).$