Section MirrorTape.
Variable (n : nat) (sig : Type).
Definition mirror_tape (t : tape sig) : tape sig :=
match t with
| niltape _ => niltape _
| leftof r rs => rightof r rs
| rightof l ls => leftof l ls
| midtape ls m rs => midtape rs m ls
end.
Definition mirror_move (D : move) : move := match D with | Nmove => Nmove | Lmove => Rmove | Rmove => Lmove end.

Lemma tape_left_move_right (t : tape sig) (x : sig) :
current t = Some x -> left (tape_move_right t) = x :: left t.