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

theorem Th4:
  - [*x1,x2,x3,x4*] = [*-x1,-x2,-x3,-x4*]
proof
  [*x1,x2,x3,x4*] + [*-x1,-x2,-x3,-x4*]
  =[*x1-x1,x2-x2,x3-x3,x4-x4*] by QUATERNI:def 7
    .=[*In(0,REAL),In(0,REAL)*] by QUATERNI:91
    .=0 by ARYTM_0:def 5;
  hence thesis by QUATERNI:def 8;
end;
