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 Th47:
  G={A,B,C,D,E,F,J} & A<>B & A<>C & A<>D & A<>E & A<>F & A<>J & B
<>C & B<>D & B<>E & B<>F & B<>J & C<>D & C<>E & C<>F & C<>J & D<>E & D<>F & D<>
J & E<>F & E<>J & F<>J implies CompF(F,G) = A '/\' B '/\' C '/\' D '/\' E '/\'
  J
proof
  {A,B,C,D,E,F,J}={A,B,C,D} \/ {E,F,J} by ENUMSET1:19
    .={A,B,C,D} \/ {F,E,J} by ENUMSET1:58
    .={A,B,C,D,F,E,J} by ENUMSET1:19;
  hence thesis by Th46;
end;
