From Undecidability.StackMachines.Util Require Import Nat_facts List_facts.
Local Definition rt_rt1n := @clos_rt_rt1n_iff Config.
Definition terminal (M: SMN) (X: Config) : Prop :=
forall (Y: Config), not (step M X Y).

Lemma stepI {M: SMN} {X Y: Config} v w l r l' r' x y : X = (l ++ v, r ++ w, x) -> Y = (l' ++ v, r' ++ w, y) ->
In ((l, r, x), (l', r', y)) M -> step M X Y.