BCI-homomorphisms

In this paper X is a BCI-algebra and n is an element of N. Let D be a set, let f be a function from N into D, and let n be a natural number. Then f(n) is an element of D. Let G be a non empty BCI structure with 0. The functor BCI-powerG yielding a function from (the carrier of G) × N into the carrier of G is defined as follows: (Def. 1) For every element x of G holds (BCI-powerG)(x, 0) = 0G and for every n holds (BCI-powerG)(x, n+ 1) = x \ (BCI-powerG)(x, n)c.