Opaque Normalize_e.
(** Def 1 of (Rose) *)
Definition Succ_e : Cobham :=
Rec
(Comp 0 (Succ true) [Zero])
(Comp 2 (Succ true) [Proj 2 0])
(Comp 2 (Succ false) [Proj 2 1])
(Comp 1 (Succ true) [Proj 1 0]).

(* Specifications: *)
Lemma arity_Succ : arity Succ_e = ok_arity 1.
Lemma length_Succ : forall l,
length (Sem Succ_e l) <= length (Sem (Comp 1 (Succ true) [Proj 1 0]) l).
Lemma le_1_length_Succ v :
1 <= length (Sem Succ_e [v]).
Lemma le_length_Succ v :
length v <= length (Sem Succ_e [v]).
Lemma Succ_length v :
length (Sem Succ_e v) <= S (length (hd nil v)).
Lemma rec_bounded_Succ :
rec_bounded Succ_e.
Lemma Succ_correct : forall l,
bs2nat (Sem Succ_e l) = 1 + bs2nat (hd nil l).