Bounding Boxes for Special Sequences in E 2

(6) For every finite sequence g of elements of R such that r ∈ rngg holds (Inc(g))(1)≤ r and r ≤ (Inc(g))(lenInc(g)). (7) Suppose 1 ≤ i and i ≤ lenh and 1 ≤ I and I ≤ width the Go-board of h. Then (the Go-board of h◦ (1, I))1 ≤ (hi)1 and (hi)1 ≤ (the Go-board of h◦ (len the Go-board of h, I))1. (8) Suppose 1 ≤ i and i ≤ lenh and 1 ≤ I and I ≤ len the Go-board of h. Then (the Go-board of h◦ (I,1))2 ≤ (hi)2 and (hi)2 ≤ (the Go-board of h◦ (I,width the Go-board of h))2. (9) Suppose 1 ≤ i and i ≤ len the Go-board of f . Then there exist k, j such that k ∈ dom f and 〈i, j〉 ∈ the indices of the Go-board of f and fk = the Go-board of f ◦ (i, j). (10) Suppose 1 ≤ j and j ≤ width the Go-board of f . Then there exist k, i such that k ∈ dom f and 〈i, j〉 ∈ the indices of the Go-board of f and fk = the Go-board of f ◦ (i, j). 1 The propositions (1) and (2) have been removed.