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

theorem Th52:
  -(z1+z2)=-z1-z2
proof
A1: -z1-z2=(-1q)*z1-z2 by QUATERN2:19
    .=(-1q)*z1+(-1q)*z2 by QUATERN2:19;
 -(z1+z2)=(-1q)*(z1+z2) by QUATERN2:19
    .=(-1q)*z1+(-1q)*z2 by QUATERN2:17;
  hence thesis by A1;
end;
