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

theorem Th51:
  for s being State of SCM+FSA,
      I being really-closed Program of SCM+FSA, a
  being Int-Location,k being Element of NAT
   st I is_halting_on Initialized s,P & I does not destroy a
 holds IExec(I,P,s).a = Comput(P +* I, (Initialize Initialized s),k).a
proof
  let s be State of SCM+FSA;
  let I be really-closed Program of SCM+FSA;
  let a be Int-Location;
  let k be Element of NAT;
  set s0 = Initialized s;
  set s1 = Initialize s0,
      P1 = P +* I;
  assume I is_halting_on Initialized s,P;
  then
A1: P1 halts_on s1;
  assume
A2: I does not destroy a;
  thus IExec(I,P,s).a = (Result(P1,s1)).a by MEMSTR_0:44
    .= (Result(P1,s1)).a
    .= Comput(P1, s1,LifeSpan(P1,s1)).a by A1,EXTPRO_1:23
    .= s0.a by A2,SCMFSA7B:21
    .= Comput(P +* I, (Initialize s0),k).a by A2,SCMFSA7B:21;
end;
