reserve X for BCI-algebra;
reserve n for Nat;
reserve x,y for Element of X;
reserve a,b for Element of AtomSet(X);
reserve m,n for Nat;
reserve i,j for Integer;

theorem Th21:
  (x|^n)` = ((x``)|^n)`
proof
  set b=(x``)|^n;
  x`` in AtomSet(X) by BCIALG_1:34;
  then reconsider b as Element of AtomSet(X) by Th13;
  0.X in AtomSet(X) & x|^n in BranchV(b) by Th20;
  hence thesis by BCIALG_1:37;
end;
