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

theorem
  [*x1,x2,x3,x4*] - [*y1,y2,y3,y4*] = [*x1-y1,x2-y2,x3-y3,x4-y4*]
proof
  [*x1,x2,x3,x4*] - [*y1,y2,y3,y4*]
  = [*x1,x2,x3,x4*] + [*-y1,-y2,-y3,-y4*] by Th4
    .= [*x1-y1,x2-y2,x3-y3,x4-y4*] by QUATERNI:def 7;
  hence thesis;
end;
