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Deans said on Friday in South Africa that Cooper's surgery on loose cartilage in his knee had been delayed for a few days but he should be able travel in November "so long as he gets in and gets the operation done soon."
Deans said the delay was precautionary while some "grazes" on Cooper's problematic right knee, which he injured at last year's World Cup, healed.
Cooper's recovery from the surgery is expected to take four to six weeks, and the delay threatens his availability for the tour starting on Nov. 10 against France.
But Deans also said other injuries to regular starters meant the Wallabies were "going to have to function with a squad as opposed to a 15."
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Which of the four SA franchises in contention for the Super Rugby quarter-finals will miss out?
Bulls (Top of Africa 1, 11 matches, 32 points)
Stormers (Second in Africa 1, 11 matches, 32 points)
Lions (Bulls (Top of Africa 2, 11 matches, 37 points)
Sharks (Bulls (Second in Africa 2, 12 matches, 35 points)