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 .| = |.c1.|*|.c2.|
proof
  thus |.(c1.|.c2).| =(|.c1.|)*(|.c2*'.|) by QUATERNI:87
    .=|.c1.|*|.c2.| by QUATERNI:73;
end;
