Variation [1] discusses @
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White 11 makes a first eye, a and b being miai. White 13 threatens to kill the corner in a capturing race: see variation [2]. Hence Black 14 connects. White 15 makes the second eye. If she omits it, Black at c or 15 destroys the second eye.
[1]
If Black 8 at here, White wins the capturing race. Losing four moves with a to d, she still has 7 liberties left to attack, while Black has only three to defend (he'll have to react to one).
[2]
a to f are theoretically Black's semeai liberties (he's on the defence), but to c or d (atari) and a (two eyes) he has to react, which leaves him with 4 liberties. White has already 6 at the circled points (minus g to connect) so she clearly wins the race.