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 Th1:
  (x,y) to_power 0 = x
proof
  ex f st (x,y) to_power 0 = f.0 & f.0 = x & for j st j < 0 holds f.(j + 1
  ) = f.j \ y by Def1;
  hence thesis;
end;
