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

theorem Th22:
  G={A,B,C,D,E} & A<>B & B<>C & B<>D & B<>E implies CompF(B,G) = A
  '/\' C '/\' D '/\' E
proof
  assume that
A1: G={A,B,C,D,E} and
A2: A<>B & B<>C & B<>D & B<>E;
  {A,B,C,D,E}={A,B} \/ {C,D,E} by ENUMSET1:8;
  then G={B,A,C,D,E} by A1,ENUMSET1:8;
  hence thesis by A2,Th21;
end;
