On the Instructions of SCM FSA 1 Artur

The articles [18], [10], [11], [12], [22], [5], [14], [3], [6], [20], [7], [8], [9], [4], [19], [1], [2], [23], [24], [17], [16], [13], [21], and [15] provide the terminology and notation for this paper. For simplicity, we use the following convention: a, b are integer locations, f is a finite sequence location, i1, i2, i3 are instruction-locations of SCMFSA, T is an instruction type of SCMFSA, and k is a natural number. Next we state two propositions: (1) For every function f and for all sets a, A, b, B, c, C such that a 6= b and a 6= c holds (f+·(a7−→ . A)+·(b7−→ . B)+·(c7−→ . C))(a) = A. (2) For all sets a, b holds 〈a〉 +· (1, b) = 〈b〉. Let l1, l2 be integer locations and let a, b be integers. Then [l1 7−→ a, l2 7−→ b] is a finite partial state of SCMFSA. One can prove the following propositions: (3) a / ∈ the instruction locations of SCMFSA. (4) f / ∈ the instruction locations of SCMFSA. (5) Data-LocSCMFSA 6= the instruction locations of SCMFSA. (6) Data-LocSCMFSA 6= the instruction locations of SCMFSA. (7) Let o be an object of SCMFSA. Then (i) o = ICSCMFSA , or (ii) o ∈ the instruction locations of SCMFSA, or (iii) o is an integer location or a finite sequence location. (8) If i2 6= i3, then Next(i2) 6= Next(i3). (9) a:=b = 〈1, 〈a, b〉〉. (10) AddTo(a, b) = 〈2, 〈a, b〉〉.