theorem Th14:
  x - (a1*x1+a2*x2+a3*x3) = x + ((-a1)*x1 + (-a2)*x2 + (-a3)*x3)
proof
  thus x - (a1*x1+a2*x2+a3*x3) = x + (-a1*x1 + -a2*x2 + -a3*x3) by Th8
    .= x + ((-a1)*x1 + -a2*x2 + -a3*x3) by Th3
    .= x + ((-a1)*x1 + (-a2)*x2 + -a3*x3) by Th3
    .= x + ((-a1)*x1 + (-a2)*x2 + (-a3)*x3) by Th3;
end;
