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 = 1 & a = 0 implies b = 1 or b = -1
  proof
    assume that
A1: a^2 + b^2 = 1 and
A2: a = 0;
    b^2 = 1^2 by A1,A2;
    hence thesis by SQUARE_1:40;
  end;
