Crossword Genius

Remains with teacher carrying mattress upstairs (6)

Ross

I believe the answer is:

debris

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'remains' is the definition.
(I've seen this before)

I don't understand how the rest of the clue works.

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(Other definitions for debris that I've seen before include "'Ruins, rubble (6)'" , "Refuse, litter" , "Remains - wreckage" , "Refuse remains" , "Brides with pieces of rubble" .)

I've seen this clue in The Hindu.
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