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
  a^2 + b^2 is negative implies a = 0 & b = 0
  proof
    assume
A1: a^2 + b^2 is negative;
    0 <= a * a & 0 <= b * b by XREAL_1:63;
    hence thesis by A1;
  end;
