reserve X for BCI-algebra;
reserve I for Ideal of X;
reserve a,x,y,z,u for Element of X;
reserve f,f9,g for sequence of  the carrier of X;
reserve j,i,k,n,m for Nat;

theorem Th6:
  (0.X,0.X) to_power n=0.X
proof
  defpred P[set] means for m holds m=$1 & m<= n implies (0.X,0.X) to_power m =
  0.X;
A1: for k st P[k] holds P[k+1] by Th5;
A2: P[0] by Th1;
  for n holds P[n] from NAT_1:sch 2(A2,A1);
  hence thesis;
end;
