
theorem Th30:
  for L being RelStr holds L is lower-bounded iff L opp is upper-bounded
proof
  let L be RelStr;
  thus L is lower-bounded implies L opp is upper-bounded
  proof
    given x being Element of L such that
A1: x is_<=_than the carrier of L;
    take x~;
    thus thesis by A1,Th8;
  end;
  given x being Element of L opp such that
A2: x is_>=_than the carrier of L opp;
  take ~x;
  thus thesis by A2,Th9;
end;
