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 Th8:
  for R being Relation, Y being set st R is_reflexive_in Y holds Y c= field R
proof
  let R be Relation, Y be set such that
A1: R is_reflexive_in Y;
  let x be object;
  assume x in Y;
  then [x,x] in R by A1;
  hence thesis by RELAT_1:15;
end;
