An Extension of SCM
Andrzej Trybulec, Yatsuka Nakamura, Piotr Rudnicki · 1996
The articles [19], [25], [9], [20], [11], [14], [2], [18], [26], [6], [7], [17], [16], [22], [3], [8], [10], [23], [1], [15], [5], [24], [12], [13], [21], and [4] provide the notation and terminology for this paper. In this paper x will be arbitrary and k will denote a natural number. The subset Data-LocSCMFSA of is defined as follows: (Def. 1) Data-LocSCMFSA = Data-LocSCM. The subset Data∗-LocSCMFSA of is defined as follows: (Def. 2) Data∗-LocSCMFSA = . The subset Instr-LocSCMFSA of is defined as follows: (Def. 3) Instr-LocSCMFSA = Instr-LocSCM. One can check the following observations: ∗ Data∗-LocSCMFSA is non empty, ∗ Data-LocSCMFSA is non empty, and ∗ Instr-LocSCMFSA is non empty. For simplicity we adopt the following convention: J , K are elements of 13, a is an element of Instr-LocSCMFSA, b, c, c1 are elements of Data-LocSCMFSA , and f , f1 are elements of Data ∗-LocSCMFSA . The subset InstrSCMFSA of [: 13, ( ⋃ { , } ∪ ):] is defined by: (Def. 4) InstrSCMFSA = InstrSCM ∪ {〈J, 〈c, f, b〉〉 : J ∈ {9, 10}} ∪ {〈K, 〈c1, f1〉〉 : K ∈ {11, 12}}. The following two propositions are true: (1) InstrSCMFSA = InstrSCM ∪ {〈J, 〈c, f, b〉〉 : J ∈ {9, 10}} ∪ {〈K, 〈c1, f1〉〉 : K ∈ {11, 12}}. (2) InstrSCM ⊆ InstrSCMFSA .