Crossword Genius

Building proposition at school (8)

Ross

I believe the answer is:

premises

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'building' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'proposition at school' is the wordplay.
'proposition' becomes 'premise' (premise is a kind of proposition).
'at school' becomes 's' (I can't explain this - if you can you should believe this answer much more).
'premise'+'s'='PREMISES'

Can you help me to learn more?

(Other definitions for premises that I've seen before include "Buildings occupied by businesses" , "Places of business" , "Building, place of business" , "States" , "Property" .)

I've seen this clue in The Irish Times.
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