
theorem Th21:
  for K, L being non empty OrthoLattStr st the OrthoLattStr of K =
  the OrthoLattStr of L & K is involutive holds L is involutive
proof
  let K, L be non empty OrthoLattStr;
  assume that
A1: the OrthoLattStr of K = the OrthoLattStr of L and
A2: K is involutive;
  for x being Element of L holds x`` = x
  proof
    let x be Element of L;
    reconsider x9 = x as Element of K by A1;
    x` = x9` by A1,Th18;
    then x`` = x9`` by A1,Th18
      .= x by A2;
    hence thesis;
  end;
  hence thesis;
end;
