Break the ice after a canteen is discovered (9)

I believe the answer is:

cafeteria

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'canteen is discovered' is the definition.
I can't tell whether this defines the answer.

'break the ice after a' is the wordplay.
'break' indicates anagramming the letters.
'ice'+'after'='iceafter'
'iceafter' is an anagram of 'cafeteri'.
'cafeteri'+'a'='CAFETERIA'

Can you help me to learn more?

(Other definitions for cafeteria that I've seen before include "where food is served" , "where food can be picked up" , "cheap restaurant" , "place of refreshment" , "eating-place" .)

I've seen this clue in The Irish Independent.

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