
theorem
  for L being antisymmetric reflexive with_suprema RelStr for A being
  Subset of L holds A c= A "\/" A
proof
  let L be antisymmetric reflexive with_suprema RelStr, A be Subset of L;
  let q be object;
  assume
A1: q in A;
  then reconsider A1 = A as non empty Subset of L;
  reconsider q1 = q as Element of A1 by A1;
  q1 <= q1;
  then q1 = q1 "\/" q1 by YELLOW_0:24;
  hence thesis;
end;
