reserve Y for non empty set,
  G for Subset of PARTITIONS(Y),
  A,B,C,D,E,F for a_partition of Y;

theorem
  G={A,B,C,D,E} & A<>E & B<>E & C<>E & D<>E implies CompF(E,G) = A '/\'
  B '/\' C '/\' D
proof
  assume that
A1: G={A,B,C,D,E} and
A2: A<>E & B<>E & C<>E & D<>E;
  {A,B,C,D,E}={A,B,C} \/ {D,E} by ENUMSET1:9;
  then G={A,B,C,E,D} by A1,ENUMSET1:9;
  hence thesis by A2,Th24;
end;
