reserve z1,z2,z3,z4,z for Quaternion;

theorem
  (z1-z2)*z3=(z2-z1)*(-z3)
proof
 (z2-z1)*(-z3)=z2*(-z3)-z1*(-z3) by QUATERN2:23
    .=-(z2*z3)-z1*(-z3) by QUATERN2:21
    .=-(z2*z3)-(-(z1*z3)) by QUATERN2:21
    .=z1*z3-z2*z3;
  hence thesis by QUATERN2:23;
end;
