proposition: Lemma tape_local_l_move_left (t : tape sig) (x : sig) (xs : list sig) : tape_local_l t = x :: xs -> tape_local_l (tape_move_left t) = xs.
proof: Proof. intro H. destruct t eqn:E; cbn in *; try congruence. inv H. destruct xs; cbn; auto. Qed.
imports: Undecidability.Shared.Libs.PSL.Vectors.Vectors Undecidability.TM.TM