reserve n for Nat,
        lambda,lambda2,mu,mu2 for Real,
        x1,x2 for Element of REAL n,
        An,Bn,Cn for Point of TOP-REAL n,
        a for Real;

theorem Th2:
  |.a.| = |.1-a.| implies a = 1/2
  proof
    assume
A1: |.a.| = |.1-a.|;
    |.a.|^2 = a^2 & |.1-a.|^2 = (1-a)^2 by COMPLEX1:75;
    then a^2 = (1-a) * (1-a) by A1,SQUARE_1:def 1
            .= 1 - 2*a + a*a
            .= 1 - 2*a + a^2 by SQUARE_1:def 1;
    hence thesis;
  end;
