reserve i,j,k,n,m for Nat,
        X for set,
        b,s for bag of X,
        x for object;

theorem Th6:
  for x be Element of F_Real st x<>0.F_Real holds
     (power F_Real).(x,n) <> 0.F_Real
proof
  let x be Element of F_Real such that
A1: x<>0.F_Real;
  defpred P[Nat] means (power F_Real).(x,$1) <>0.F_Real;
  (power F_Real).(x,0) = 1_F_Real by GROUP_1:def 7;
  then
A2:P[0];
A3:P[i] implies P[i+1]
  proof
    assume
A4: P[i];
    set i1=i+1;
    (power F_Real).(x,i1) = (power F_Real).(x,i) * x by GROUP_1:def 7;
    hence thesis by A1,A4;
  end;
  P[i] from NAT_1:sch 2(A2,A3);
  hence thesis;
end;
