(* * Copying Machines and Helper functions for verifying machines using [CopySymbols] ane [MoveToSymbol] *)
From Undecidability Require Export TM.Compound.CopySymbols TM.Compound.MoveToSymbol.
Local Generalizable All Variables.
Set Default Proof Using "Type".
(* Don't simplify [skipn (S n) xs]; only, if the number and the lists are constructors *)
Local Arguments skipn { A } !n !l.
Local Arguments plus : simpl never.
Local Arguments mult : simpl never.

Corollary CopySymbols_correct_moveright ls m rs x rs' t2:
(forall x, List.In x rs -> stop x = false) ->
stop x = true ->
CopySymbols_Fun stop (tape_move_right' ls m (rs ++ x :: rs'), t2) =
(midtape (rev rs ++ m :: ls) x rs',
midtape (rev rs ++ left t2) x (skipn (|rs|) (right t2))).