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

theorem
  x.|.(a*y + b*z) = (a*') * x.|.y + (b*') * x.|.z
proof
  thus x.|.(a*y + b*z) = x.|.(a*y) +x.|.(b*z) by Th34
    .=(a*')*x.|.y + x.|.(b*z) by Th36
    .=(a*') * x.|.y + (b*') * x.|.z by Th36;
end;
