reserve m for Nat;
reserve P for Instruction-Sequence of SCM+FSA;

theorem
  for s being State of SCM+FSA
  for P being Instruction-Sequence of SCM+FSA,
  I being really-closed Program of SCM+FSA st I is_halting_on s,P
   holds Directed I is_pseudo-closed_on s,P by Lm2;
