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

theorem Th1:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z, u,
v being Element of L holds ((x + y)` + (((z + u)` + x)` + (y` + (y + v)`)`)`)`
  = y
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z, u, v be Element of L;
  set X = ((z + u)` + x)`, Y = (z + (x` + (x + u)`)`)`;
  set Z = y, U = v;
  (((X + Y)` + Z)` + (X + (Z` + (Z + U)`)`)`)` = Z by Def1;
  hence thesis by Def1;
end;
