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Set to transpose Great Lake bed (7)

Ross

I believe the answer is:

coterie

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'bed' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how one could define the other.

'set to transpose great lake' is the wordplay.
'set' becomes 'c' (I can't explain this - if you can you should give a lot more credence to this answer).
'transpose' indicates an anagram (I've seen 'transposed' mean this).
'great lake' becomes 'erie' (Erie is one of the Great Lakes).
'to' is an anagram of 'ot'.
'c'+'ot'+'erie'='COTERIE'

Can you help me to learn more?

(Other definitions for coterie that I've seen before include "Exclusive circle of people, clique" , "Set" , "Exclusive circle of people with common purpose" , "EEC trio in exclusive group" , "Small exclusive circle with a common purpose" .)

I've seen this clue in the Sydney Morning Herald.
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