Section lemma.
Context {X : Type}.
Context {Hr : registered X}.
Context {Hcmp : computable (@enc X _)}.
Definition apply_encs_to (s : term) k := ((Vector.fold_left (fun s n => ext L.app s (ext (@enc X _) (var n))) s (many_vars k))).
End lemma.

Lemma L_bool_computable_can_closed k R:
L_bool_computable_closed R <-> L_bool_computable (k:=k) R.