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.|.c2 - c1.|.c3
proof
  c1.|.(c2 - c3)=c1 * (c2*' - c3*') by QUATERNI:56
    .=c1 * c2*' - c1 * c3*' by Th24;
  hence thesis;
end;
