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

theorem Th5:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds ((x + y)` + ((z + x)` + y)`)` = y
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  set u = the Element of L;
  set U = (y` + (y + u)`)`;
  ((x + y)` + ((z + x)` + (((y + y`)` + y)` + (y + U)`)`)`)` = y by Th4;
  hence thesis by Def1;
end;
