The Properties of Instructions of SCM over Ring

The papers [16], [9], [11], [12], [15], [19], [2], [3], [5], [6], [4], [1], [20], [21], [17], [8], [7], [13], [18], [14], and [10] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: R denotes a good ring, r denotes an element of the carrier of R, a, b denote Data-Locations of R, i1, i2, i3 denote instruction-locations of SCM(R), I denotes an instruction of SCM(R), s1, s2 denote states of SCM(R), T denotes an instruction type of SCM(R), and k denotes a natural number. Let us note that Z is infinite. One can verify that INT.Ring is infinite and good. Let us mention that there exists a 1-sorted structure which is strict and infinite. Let us mention that there exists a ring which is strict, infinite, and good. We now state the proposition (1) ObjectKind(a) = the carrier of R. Let R be a good ring, let l1, l2 be Data-Locations of R, and let a, b be elements of R. Then [l1 7−→ a, l2 7−→ b] is a finite partial state of SCM(R). We now state a number of propositions: (2) a / ∈ the instruction locations of SCM(R). (3) a 6= ICSCM(R). (4) Data-LocSCM 6= the instruction locations of SCM(R). (5) For every object o of SCM(R) holds o = ICSCM(R) or o ∈ the instruction locations of SCM(R) or o is a Data-Location of R. (6) If i2 6= i3, then Next(i2) 6= Next(i3).