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
  (c1+c2).|.c3 = c1.|.c3 + c2.|.c3 by Th18;
