Some Remarks on Finite Sequences on Go-boards

The articles [20], [24], [8], [19], [9], [2], [3], [22], [4], [15], [14], [16], [18], [5], [7], [13], [1], [6], [12], [17], [23], [21], [10], and [11] provide the terminology and notation for this paper. We follow the rules: i, j, k, n denote natural numbers, f denotes a finite sequence of elements of the carrier of E2 T, and G denotes a Go-board. We now state several propositions: (1) Suppose that (i) f is a sequence which elements belong to G, (ii) L(G ◦ (i, j), G ◦ (i, k)) meets L̃(f), (iii) 〈i, j〉 ∈ the indices of G, (iv) 〈i, k〉 ∈ the indices of G, and (v) j ¬ k. Then there exists n such that j ¬ n and n ¬ k and (G ◦ (i, n))2 = inf(proj2◦(L(G ◦ (i, j), G ◦ (i, k)) ∩ L̃(f))). (2) Suppose that (i) f is a sequence which elements belong to G, (ii) L(G ◦ (i, j), G ◦ (i, k)) meets L̃(f), (iii) 〈i, j〉 ∈ the indices of G, (iv) 〈i, k〉 ∈ the indices of G, and