
theorem Th20:
  for K, L being non empty OrthoLattStr st the OrthoLattStr of K =
  the OrthoLattStr of L & K is de_Morgan holds L is de_Morgan
proof
  let K, L be non empty OrthoLattStr;
  assume that
A1: the OrthoLattStr of K = the OrthoLattStr of L and
A2: K is de_Morgan;
  for x, y being Element of L holds x "/\" y = (x` "\/" y`)`
  proof
    let x, y be Element of L;
    reconsider x9 = x, y9 = y as Element of K by A1;
A3: x` = x9` & y` = y9` by A1,Th18;
    x "/\" y = x9 "/\" y9 by A1
      .= (x9` "\/" y9`)` by A2,ROBBINS1:def 23
      .= (x` "\/" y`)` by A1,A3,Th18;
    hence thesis;
  end;
  hence thesis by ROBBINS1:def 23;
end;
