The Wimbledon champion converted five out of seven break points to secure the win and set up a last-four clash with Ons Jabeur.
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Unseeded Tunisian Jabeur was made to work hard for a victory over Alize Cornet as she shook off an ankle injury in the final set to prevail 1-6 7-5 6-3.
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"At this tournament, I'm the queen of losing the first set and then coming back," Jabeur, who has rallied back from a set down to win three of her four matches in Eastbourne, said.

Romania's Simona Halep reacts while playing Germany's Angelique Kerber during their women's singles quarter-final match at the WTA Nature Valley International tennis tournament in Eastbourne, southern England on June 27, 2019.

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"It's another motivation for me to win, to play better in the second set, but I'm really happy with this win.
"It wasn't easy at the end, I was scared for my ankle, but hopefully everything will be good. I tried to move better, be better on court, and that helped me regain my shots."
World number 10 Aryna Sabalenka faces Kiki Bertens of the Netherlands in another quarter-final on Thursday while former world number one Karolina Pliskova meets Russia's Ekaterina Alexandrova.
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