From here on, we will use simplified versions of the problem, which are equivalent to the moment when Black has just played into the four-point eye of White's group on the left side in our solution.

Black's guzumi at , followed by , creates two approach-move liberties (), equivalent to one real liberty. Black has three direct liberties (), ...

... so White needs four local moves to take Black's group off the board.

Please note that Black also had four local liberties beforehand (3, 1, , 4), thus the guzumi has not changed the liberties locally.