theorem
  [:T1,T2:] is finite-ind implies [:T2,T1:] is finite-ind & ind [:T1,T2
  :] = ind [:T2,T1:]
proof
  assume
A1: [:T1,T2:] is finite-ind;
  per cases;
  suppose
A2: T1 is empty or T2 is empty;
    then ind[:T1,T2:]=-1 by Th6;
    hence thesis by A2,Th6;
  end;
  suppose
    T1 is non empty & T2 is non empty;
    then [:T1,T2:],[:T2,T1:]are_homeomorphic by YELLOW12:44;
    hence thesis by A1,Lm9;
  end;
end;
