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.

Lemma mu'_complete n0 : P (ext n0) == ext true
-> (forall n', n' < n0 -> P (ext n') == ext false)
-> mu' P (ext 0) == ext n0.