Section Transport.
(* Assume that P reaches a halting configuration from (0, 1) after NP steps, show that M is uniformly bounded. *)
Variable NP : nat. (* number of steps  *)
Variable NP_spec : CM.halting P (Nat.iter NP (CM.step P) cm_start).
Definition cm_end := Nat.iter NP (CM.step P) cm_start. (* final configuration *)
Definition CP : nat := CM.value cm_end. (* final counter value *)

Lemma maybe_index_try_run l r z :
maybe_reachable (NP * step_time CP TP) ([§1] ++ l, [§0] ++ [§1] ++ §0^(CP-1) ++ r, '#?0) z.