Section Reduction.
Variables (M1 M2 : SMN) (L R L' R': list Symbol) (X Y: State).
Definition M : SMN := M1 ++ (((L, R, X), (L', R', Y)) ::  M2).
Definition M' : SMN := [((L, R, X), (L', R', Y))] ++ M1 ++ M2.

Lemma simulation {x y} : reachable M' x y <-> reachable M x y.