theorem Th23:
  (a1*x1+a2*x2)+(b1*x1+b2*x2)=(a1+b1)*x1+(a2+b2)*x2
proof
  thus (a1*x1+a2*x2)+(b1*x1+b2*x2) = (a1*x1+b1*x1)+(a2*x2+b2*x2) by Th16
    .= (a1+b1)*x1+(a2*x2+b2*x2) by EUCLID_4:7
    .= (a1+b1)*x1+(a2+b2)*x2 by EUCLID_4:7;
end;
