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 Th26:
  a is finite-period & ord a = n implies a|^n = 0.X
proof
  assume a is finite-period & ord a = n;
  then a|^n in BCK-part(X) by Def5;
  then ex x being Element of X st x = a|^n & 0.X<=x;
  then
A1: 0.X\a|^n = 0.X;
  a|^n in AtomSet(X) by Th13;
  then ex y being Element of X st y = a|^n & y is atom;
  hence thesis by A1;
end;
