reserve a,b,c,d,x,y,w,z,x1,x2,x3,x4 , X for set;
reserve A for non empty set;
reserve i,j,k for Element of NAT;
reserve a,b,c,d for Real;
reserve y,r,s,x,t,w for Element of RAT+;
reserve z,z1,z2,z3,z4 for Quaternion;
 reserve x for Real;

theorem
  |.z*z.| = |.z*z*'.|
proof
  thus |.z*z.| = |.z.|*|.z.| by Th80
    .= |.z.|*|.z*'.| by Th66
    .= |.z*z*'.| by Th80;
end;
