Demonstration quietly removed top of building (4)
I believe the answer is:
roof
'top of building' is the definition.
(a roof covers a building)
'demonstration quietly removed' is the wordplay.
'demonstration' becomes 'proof' (I've seen this in another clue).
'quietly' becomes 'p' (p for piano and quiet).
'removed' indicates named letters should be taken away.
'proof' with 'p' taken out is 'ROOF'.
(Other definitions for roof that I've seen before include "Top covering of structure" , "House's top" , "It could be slated" , "Topmost part" , "Topping structure" .)