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

theorem
  for P
  for s being State of SCM+FSA,
      I being keeping_0 parahalting really-closed
  Program of SCM+FSA, a being read-write Int-Location st I does not destroy a
  holds Comput(P +* (I ";" SubFrom(a,intloc 0)),
   Initialize Initialized s,
   LifeSpan(P +* (I ";" SubFrom(a,intloc 0)),
  Initialize Initialized s)).a = s.a - 1
proof let P;
  let s be State of SCM+FSA;
  let I be keeping_0 parahalting really-closed Program of SCM+FSA;
  let a be read-write Int-Location;
  assume
A1: I does not destroy a;
  set s0 = Initialized s;
  set s1 = Initialize s0,
      P1 = P +* (I ";" SubFrom(a,intloc 0));
A2: not a in dom Start-At(0,SCM+FSA) by SCMFSA_2:102;
  IExec(I ";" SubFrom(a,intloc 0),P,s).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 SCMFSA6B:11
    .= Comput(P +* I, (Initialize s0),0).a - 1
    by A1,Th52
    .= (Initialize s0).a - 1
    .= s0.a - 1 by A2,FUNCT_4:11;
  hence Comput(P1, s1,LifeSpan(P1,s1)).a = s0.a - 1 by Th50
    .= s.a - 1 by SCMFSA_M:37;
end;
