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

theorem Th23:
  (c1 - c2) * c3 = c1 * c3 - c2 * c3
proof
  (c1 - c2) * c3=c1 * c3 + (-c2) * c3 by Th18;
  hence thesis by Th20;
end;
