Let N be a$$$-$NFA and let N$$ be the ordinary NFA made from N by the construction of Section $14\mathrm{.}7.$ Let w be a non$-$empty string that is in the language L$($N$),$ and let P be a path from the start state i of N to some final state f of N$,$ where the labels in the letter moves of P$,$ in order, form w$.$ Then P can be broken up into a sequence of paths in N$,$ one for each letter of w$,$ such that each path contains exactly one letter move and the concatenation of these paths, in order, is P$.($The statement doesn$$t mention N$--$ don$$t worry about that.$)$

Is this statement true or false?