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

theorem Th22:
  for s being State of SCM+FSA, I being Program of SCM+FSA st
  Directed I is_pseudo-closed_on s,P holds
   DataPart Result(P +* (I ";" Stop SCM+FSA),
   Initialize s) =
  DataPart Comput(P +* I, (Initialize s),
  pseudo-LifeSpan(s,P,Directed I))
proof
  let s be State of SCM+FSA;
  set D = Data-Locations SCM+FSA;
  let I be Program of SCM+FSA;
  set I0 = Directed I;
  set I1 = I ";" Stop SCM+FSA;
  set s2 = Initialize s,
      P2 = P +* I;
  set s10 = Initialize s,
      P10 = P+*I1;
  set k = pseudo-LifeSpan(s,P,I0);
  assume
A1: I0 is_pseudo-closed_on s,P;
  then
A2: DataPart Comput(P2, s2,k) = DataPart Comput(P10, s10,k) by Th21;
  I1 is_halting_on s,P by A1,Th21;
  then
A3: P10 halts_on s10;
  LifeSpan(P10,s10) = k by A1,Th21;
  hence thesis by A2,A3,EXTPRO_1:23;
end;
