reserve a, b, c, d, x, y, z for Complex;

theorem
  (x + y).|.(x + y) = x.|.x + x.|.y + y.|.x + y.|.y
proof
  (x + y).|.(x + y) = x.|.(x+y) + y.|.(x+y)
    .= x.|.x + x.|.y + y.|.(x+y) by Th34
    .= x.|.x + x.|.y + (y.|.x + y.|.y) by Th34
    .= x.|.x + x.|.y + y.|.x + y.|.y;
  hence thesis;
end;
