(* * 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.

(* TODO: ~> Base *)
Lemma pair_inv (X Y : Type) (x1 x2 : X) (y1 y2 : Y) :
(x1, y1) = (x2, y2) -> x1 = x2 /\ y1 = y2.