reconsider A = {} as Subset-Family of {} by XBOOLE_1:2;
A is a_partition of {}

proof

thus union A = {} ; :: according to EQREL_1:def 6 :: thesis: for A being Subset of {} st A in A holds
( A <> {} & ( for B being Subset of {} holds
( not B in A or A = B or A misses B ) ) )
thus for A being Subset of {} st A in A holds
( A <> {} & ( for B being Subset of {} holds
( not B in A or A = B or A misses B ) ) ) ; :: thesis: verum

end;

hence {} is a_partition of {} ; :: thesis: verum