
theorem Th36:
  for L being bounded LATTICE holds L is complemented iff L opp is complemented
proof
  let L be bounded LATTICE;
  thus L is complemented implies L opp is complemented
  proof
    assume
A1: for x being Element of L ex y being Element of L st y is_a_complement_of x;
    let x be Element of L opp;
    consider y being Element of L such that
A2: y is_a_complement_of ~x by A1;
    take y~;
    (~x)~ = ~x;
    hence thesis by A2,Th35;
  end;
  assume
A3: for x being Element of L opp ex y being Element of L opp st y
  is_a_complement_of x;
  let x be Element of L;
  consider y being Element of L opp such that
A4: y is_a_complement_of x~ by A3;
  take ~y;
  (~y)~ = ~y;
  hence thesis by A4,Th35;
end;
