reserve Y for non empty set,
  a for Function of Y,BOOLEAN,
  G for Subset of PARTITIONS(Y),
  P,Q for a_partition of Y;

theorem Th9:
  for Y being set, R being Relation of Y st R is_reflexive_in Y holds
    Y = field R
proof
  let Y be set, R be Relation of Y;
  assume R is_reflexive_in Y;
  hence Y c= field R by Th8;
  field R c= Y \/ Y by RELSET_1:8;
  hence thesis;
end;
