Representation Theorem for Stacks

In this paper i is a natural number and x is a set. Let A be a set and let s1, s2 be finite sequences of elements of A. Then s1s2 is an element of A∗. Let A be a set, let i be a natural number, and let s be a finite sequence of elements of A. Then s i is an element of A∗. The following two propositions are true: (1) ∅ i = ∅. (2) Let D be a non empty set and s be a finite sequence of elements of D. Suppose s 6= ∅. Then there exists a finite sequence w of elements of D and there exists an element n of D such that s = 〈n〉 a w. The scheme IndSeqD deals with a non empty set A and a unary predicate P, and states that: For every finite sequence p of elements of A holds P[p] provided the following conditions are met: • P[εA], and