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,F} & A<>B & A<>C & A<>D & A<>E & A<>F & B<>C & B<>D & B<>
E & B<>F & C<>D & C<>E & C<>F & D<>E & D<>F & E<>F implies CompF(F,G) = A '/\'
  B '/\' C '/\' D '/\' E
proof
A1: {A,B,C,D,E,F} ={A,B,C,D} \/ {E,F} by ENUMSET1:14
    .={A,B,C,D,F,E} by ENUMSET1:14;
  assume G={A,B,C,D,E,F} & A<>B & A<>C & A<>D & A<>E & A<>F & B<>C & B<>D & B
  <>E & B<>F & C<>D & C<>E & C<>F & D<>E & D<>F & E<>F;
  hence thesis by A1,Th35;
end;
