theorem Th26:
  (a1*x1+a2*x2+a3*x3)-(b1*x1+b2*x2+b3*x3)=(a1-b1)*x1+(a2-b2)*x2+( a3-b3)*x3
proof
  thus (a1*x1+a2*x2+a3*x3)-(b1*x1+b2*x2+b3*x3) = ((a1*x1+a2*x2)-(b1*x1+b2*x2))
  +(a3*x3-b3*x3) by Th18
    .= ((a1-b1)*x1+(a2-b2)*x2)+(a3*x3-b3*x3) by Th25
    .= (a1-b1)*x1+(a2-b2)*x2+(a3-b3)*x3 by Th11;
end;
