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

theorem
  z3*(z1-z2)=(-z3)*(z2-z1)
proof
 (-z3)*(z2-z1)=(-z3)*z2-(-z3)*z1 by QUATERN2:24
    .=-(z3*z2)-(-z3)*z1 by QUATERN2:20
    .=-(z3*z2)-(-(z3*z1)) by QUATERN2:20
    .=z3*z1-z3*z2;
  hence thesis by QUATERN2:24;
end;
