(** A library of Bellantoni-Cook functions on bitstrings without numerical interpretation *)
(** * Swapping of two arguments  - arities: (2, 0) *)
Definition inv_e (e : BC) : BC :=
comp 2 0 e (proj 2 0 1 :: proj 2 0 0 :: nil) nil.
(** * Conversion from arities (1, 1) to (2, 0) *)
Definition from_11_to_20 (e : BC) : BC :=
comp 2 0 e (proj 2 0 0 :: nil) (proj 2 0 1 :: nil).

Lemma from_11_to_20_correct e v1 v2 :
sem e [v1] [v2] = sem (from_11_to_20 e) [v1 ; v2] nil.