reserve a,b,c,d,e,f for Real,
        g           for positive Real,
        x,y         for Complex,
        S,T         for Element of REAL 2,
        u,v,w       for Element of TOP-REAL 3;

theorem
  Sum sqr (T - S) = Sum sqr (S - T)
  proof
    Sum (sqr (T - S)) = |. T - S .|^2 by TOPREAL9:5
                     .= |. S - T .|^2 by EUCLID:18;
    hence thesis by TOPREAL9:5;
  end;
