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Greaves is making her tournament debut and hit three 180s on her way to victory over the Dutchwoman at the O2.
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She will now face last year's champion Mikuru Suzuki after she beat Russia's Anastasia Dobromyslova in the last women's match of the night session.
Corrine Hammond beat Laura Turner 2-0 in the other women's quarter-final match in the early session.
She will face Lisa Ashton for a place in the final after the top seed beat Lorraine Winstanley 2-0 in the first of the evening games.
In the men's side of the tournament second seed Jim Williams made short work of Ryan Hogarth, hammering his opponent 4-0 on his way through to the quarter-finals.
Meanwhile in first evening game for the men Mario Vandenbogaerde hammered Dennie Olde Kalter 4-1.