reserve m for Nat;
reserve P,PP,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem
  for s being State of SCM+FSA,
      I being good parahalting really-closed Program
  of SCM+FSA, a being read-write Int-Location st I does not destroy a
holds IExec(I ";" SubFrom(a,intloc 0),P,s).a = s.a - 1
proof
  let s be State of SCM+FSA;
  let I be good parahalting really-closed Program of SCM+FSA;
  let a be read-write Int-Location;
  set I1 = I ";" SubFrom(a,intloc 0);
  set ss = IExec(I1,P,s);
  set s0 = Initialized s;
A1: I is_halting_on s0,P by SCMFSA7B:19;
  assume
A2: I does not destroy a;
  thus ss.a = Exec(SubFrom(a,intloc 0),IExec(I,P,s)).a by SCMFSA6C:6
    .= IExec(I,P,s).a - IExec(I,P,s).intloc 0 by SCMFSA_2:65
    .= IExec(I,P,s).a - 1 by A1,Th54
    .= s0.a - 1 by A2,Th53
    .= s.a - 1 by SCMFSA_M:37;
end;
