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
  (x,y) to_power 2 = x\y\y
proof
  consider f such that
A1: (x,y) to_power 2 = f.2 & f.0 = x and
A2: for j st j < 2 holds f.(j + 1) = f.j \ y by Def1;
  1<1+1 by NAT_1:13;
  then f.(1+1) = f.(0+1) \y by A2;
  hence thesis by A1,A2,NAT_1:3;
end;
