theorem Th25:
  (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 Th18
    .= (a1-b1)*x1+(a2*x2-b2*x2) by Th11
    .= (a1-b1)*x1+(a2-b2)*x2 by Th11;
end;
