Section hoas.
Definition mu' := Eval cbn -[enc] in rho (λ mu P n, (P n) (!!K n) (λ Sn, mu P Sn) (!!(ext S) n)).
End hoas.
unfold mu'; Lproc.
Qed.
Hint Resolve mu'_proc : LProc.

(* TODO: mu' sound*)
Lemma mu'_sound v n: proc v -> mu' P (ext (n:nat)) == v ->
(forall n', n' < n -> P (ext n') == ext false) ->
exists n0, n0 >= n /\ P (ext n0) == ext true /\ v == ext n0
/\ forall n', n' < n0 -> P (ext (n':nat)) == ext false.