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The carbanion part of the phosphonium ylid acts as the nucleophile, and attacks the cabonyl group of the cyclohexanone. This generates a negatively charged oxygen that can then attack the positively charged phosphorus, giving a four-membered ring called an oxaphosphetane.
This ring structure is unstable and can collapse in a way that forms two double bonds. The mechanism is concerted and gives the alkene which is the product, together with a phosphine oxide which provides the thermodynamic driving force.
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