reserve L for satisfying_DN_1 non empty ComplLLattStr;
reserve x, y, z for Element of L;

theorem Th34:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y being
  Element of L holds ((x + y`)`` + y)` = (y` + y)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y be Element of L;
  set Y = y`, Z = y;
  (((x + Y)` + (Y + Z)`)` + Z)` = (Y + Z)` by Th15;
  hence thesis by Th31;
end;
