theorem Th21:
  a*(b1*x1+b2*x2) = (a*b1)*x1+(a*b2)*x2
proof
  thus a*(b1*x1+b2*x2) = a*(b1*x1)+a*(b2*x2) by EUCLID_4:6
    .= (a*b1)*x1+a*(b2*x2) by EUCLID_4:4
    .= (a*b1)*x1+(a*b2)*x2 by EUCLID_4:4;
end;
