reserve u,v,x,y,z,X,Y for set;
reserve r,s for Real;
reserve N for non empty ConjNormAlgStr;
reserve a,a1,a2,b,b1,b2 for Element of N;

theorem Th8:
  for a being Element of N_Real holds a*a = ||.a.||^2
  proof
    let a be Element of N_Real;
    reconsider x = a as Element of REAL;
    thus a*a = x^2
    .= ||.a.||^2 by COMPLEX1:75;
  end;
