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

theorem Th49:
  for s being State of SCM+FSA, I being Program of SCM+FSA st I
  is_halting_on Initialized s,P holds
   (for a being read-write Int-Location holds
IExec(I,P,s).a = Comput(P +* I,Initialize Initialized s,
 (LifeSpan(P +* I, Initialize Initialized s))).a) &
  for f being FinSeq-Location
  holds IExec(I,P,s).f = Comput(P +* I,Initialize Initialized s,
  LifeSpan(P +* I,Initialize Initialized s)).f
proof
  let s be State of SCM+FSA;
  let I be Program of SCM+FSA;
  set s0 = Initialized s;
  set s1 = Initialize s0,
      P1 = P +* I;
  assume I is_halting_on s0,P;
  then
A1: P1 halts_on s1;
  hereby
    let a be read-write Int-Location;
    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;
  end;
  let f be FinSeq-Location;
  thus IExec(I,P,s).f = (Result(P1,s1)).f by MEMSTR_0:44
    .= (Result(P1,s1)).f
    .= Comput(P1, s1,LifeSpan(P1,s1)).f by A1,EXTPRO_1:23;
end;
