
theorem Th15:  :: Proposition 2 6H
  for R being non empty RelStr,
      X, Y being Subset of R st
    X c= Y holds UAp X c= UAp Y
  proof
    let R be non empty RelStr;
    let X, Y be Subset of R;
    assume
A1: X c= Y;
    let y be object;
    assume y in UAp X; then
    consider z being Element of R such that
A2: z = y & Class (the InternalRel of R, z) meets X;
    Class (the InternalRel of R, z) meets Y by A1,A2,XBOOLE_1:63;
    hence thesis by A2;
  end;
