theorem Th11:
  x in A^f iff ex y st y in A & x in U_FT y
proof
  thus x in A^f implies ex y st y in A & x in U_FT y
  proof
    assume x in A^f;
    then ex y st y = x & ex z st z in A & y in U_FT z;
    hence thesis;
  end;
  assume ex z st z in A & x in U_FT z;
  hence thesis;
end;
