Relocability for SCM over Ring

For simplicity, we use the following convention: i, j, k denote natural numbers, n denotes a natural number, N denotes a set with non empty elements, S denotes a standard IC-Ins-separated definite non empty non void AMI over N , l denotes an instruction-location of S, and f denotes a finite partial state of S. Next we state the proposition (1) N ≈ the instruction locations of S. Let us consider N , S. Observe that the instruction locations of S is infinite. We now state the proposition (2) ilS(i) + j = ilS(i + j). Let N be a set with non empty elements, let S be a standard IC-Ins-separated definite non empty non void AMI over N , let l1 be an instruction-location of S, and let k be a natural number. The functor l1− ′ k yields an instruction-location of S and is defined as follows: (Def. 1) l1 − ′ k = ilS(locnum(l1) − ′ k). We now state a number of propositions: (3) l − 0 = l.