Modifying Addresses of Instructions of SCMFSA

Let N be a non empty set with non empty elements and let S be an AMI over N . One can check that every finite partial state of S is finite. Let N be a non empty set with non empty elements and let S be an AMI over N . One can verify that there exists a finite partial state of S which is programmed. Next we state the proposition (1) Let N be a non empty set with non empty elements, and let S be a definite AMI over N , and let p be a programmed finite partial state of S. Then rng p ⊆ the instructions of S. Let N be a non empty set with non empty elements, let S be a definite AMI over N , and let I, J be programmed finite partial states of S. Then I+·J is a programmed finite partial state of S. Next we state the proposition (2) Let N be a non empty set with non empty elements, and let S be a definite AMI over N , and let f be a function from the instructions of S into the instructions of S, and let s be a programmed finite partial state of S. Then dom(f · s) = dom s.