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

theorem Th13:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z, u
  being Element of L holds ((x + y)` + ((z + x)` + (y` + (u + y)`)`)`)` = y
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z, u be Element of L;
  set U = ((u + z)` + (u + y)`)`;
  ((x + y)` + ((z + x)` + (y` + (y + U)`)`)`)` = y by Th2;
  hence thesis by Th10;
end;
