theorem Th147:
  for x,w,y,z holds ((((x | x) | w) | ((z | (y | (y | y))) | w))
  | w) = w | (x | z)
proof
  let x,w,y,z;
  (w | (x | z)) | (w | (x | z)) = ((x | x) | w) | ((z | (y | (y | y))) | w
  ) by Th75;
  hence thesis by Th131;
end;
