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

theorem Th49:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
being Element of L holds (x` + ((y + x)`` + (y + z))`)` + (y + z) = (y + x)``+
  (y + z)
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  set X = (y + x)`, Y = (y + z), Z = x;
  (((X + Y)` + Z)` + (X` + Y)`)` + Y = X` + Y by Th48;
  hence thesis by Th46;
end;
