proposition: Lemma hash_swap x : #_L x ++ [#] = # :: #_R x.
proof: Proof. induction x; cbn in *; now try rewrite IHx. Qed.
imports: Bool List Undecidability.PCP.PCP Undecidability.PCP.Util.Facts Undecidability.PCP.Util.PCP_facts Undecidability.Synthetic.Definitions