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 Th14:
  (a|^(n+1))` = (a|^n)`\a
proof
A1: a|^n in AtomSet(X) by Th13;
  (a|^(n+1))` =( a\(a |^ n )`)` by Th2
    .=a`\(a |^ n )`` by BCIALG_1:9
    .=a`\(a |^ n ) by A1,BCIALG_1:29;
  hence thesis by BCIALG_1:7;
end;
