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_goto_1_far {l r m n X Y z T} : (NP * step_time CP TP + 2) <= T -> G + (CP+1) <= m ->
maybe_reachable T (l, §0^m ++ r, goto n X Y) z.