Section soundness.
(* We assume a solution to pcp_hand and we build a finite and decidable model of Σbpcp_encode from it *)
Variable (l : list bool) (Hl : lc ⊳ l∕l).
Let n := length l.
Let X := option { m : list bool | length m < S n }.
Fact Σbpcp_model_finite : finite_t X.

Lemma Σbpcp_model_interpreted x y :
fom_rels Σbpcp_model Σbpcp_eq (x##y##ø) <-> x = y.