reserve Y for non empty set,
  G for Subset of PARTITIONS(Y),
  A,B,C,D,E,F for a_partition of Y;
reserve Y for non empty set,
  G for Subset of PARTITIONS(Y),
  A, B, C, D, E, F, J, M for a_partition of Y,
  x,x1,x2,x3,x4,x5,x6,x7,x8,x9 for set;

theorem Th59:
  G={A,B,C,D,E,F,J,M} & A<>B & A<>C & A<>D & A<>E & A<>F & A<>J &
A<>M & B<>C & B<>D & B<>E & B<>F & B<>J & B<>M & C<>D & C<>E & C<>F & C<>J & C
  <>M & D<>E & D<>F & D<>J & D<>M & E<>F & E<>J & E<>M & F<>J & F<>M & J<>M
  implies CompF(F,G) = A '/\' B '/\' C '/\' D '/\' E '/\' J '/\' M
proof
  {A,B,C,D,E,F,J,M} ={A,B,C,D} \/ {E,F,J,M} by ENUMSET1:25
    .={A,B,C,D} \/ ({E,F} \/ {J,M}) by ENUMSET1:5
    .={A,B,C,D} \/ ({F,E,J,M}) by ENUMSET1:5
    .={A,B,C,D,F,E,J,M} by ENUMSET1:25;
  hence thesis by Th58;
end;
