reserve q,r,c,c1,c2,c3 for Quaternion;
reserve x1,x2,x3,x4,y1,y2,y3,y4 for Real;
reserve z for Element of R_Quaternion;

theorem
  -z = (-1_R_Quaternion) * z
proof
  reconsider z9=z as Element of QUATERNION by Def10;
  thus -z = (-1q) * z9 by Th19
    .= (-1_R_Quaternion) * z by Def10;
end;
