
theorem Th17:  :: Proposition 2 9LH
  for R being non empty serial RelStr,
      X being Subset of R holds
    LAp X c= UAp X
  proof
    let R be non empty serial RelStr;
    let X be Subset of R;
    let y be object;
    assume y in LAp X; then
    consider z being Element of R such that
A1: z = y & Class (the InternalRel of R, z) c= X;
    Class (the InternalRel of R, z) meets X by XBOOLE_1:69,A1;
    hence thesis by A1;
  end;
