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

(* Specifications: *)
Lemma arity_Pred' : arity Pred'_e = ok_arity 1.
Lemma rec_bounded_Pred' :
rec_bounded Pred'_e.
Lemma Pred'_correct : forall l,
hd nil l = nil \/ bs2nat (hd nil l) <> 0 ->
bs2nat (Sem Pred'_e l) =  bs2nat (hd nil l) - 1.