
theorem
  for T being non empty 1-sorted holds T is real-membered iff for
  x being Element of T holds x is real
proof
  let T be non empty 1-sorted;
  thus T is real-membered implies for x being Element of T holds x is real;
  assume for x being Element of T holds x is real;
  then for x being object st x in the carrier of T holds x is real;
  then the carrier of T is real-membered by MEMBERED:def 3;
  hence thesis by TOPMETR:def 8;
end;
