
theorem Th7:
  for R being non empty RelStr,
      X being Subset of R
  for x being set st x in UAp X holds
    Class (the InternalRel of R, x) meets X
proof
  let R be non empty RelStr,
      X be Subset of R;
  let x be set;
  assume x in UAp X;
  then ex x1 being Element of R st
  x = x1 & Class (the InternalRel of R, x1) meets X;
  hence thesis;
end;
