Section MPCP_PCP.
Local Definition card := card nat.
Local Definition string := string nat.
Local Notation "x / y" := (x, y).
Variable R : list (card).
Variable x0 y0 : string.
Definition Sigma := sym (x0/y0 :: R).
Definition R_Sigma : sym R <<= Sigma.

Lemma hash_swap x :
#_L x ++ [#] = # :: #_R x.