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

theorem
  for x,y,z being Element of G_Quaternion holds x+y = y+x & (x+y)+z = x+(y+z) &
  x+(0.G_Quaternion) = x by RLVECT_1:def 3,def 4;
