proposition: Lemma iterate_compat {f : nat -> nat}(n:nat)(x:nat): iterate f n x = nat_rec (fun _ => nat -> nat) (fun x : nat => x) (fun (_ : nat) (rec : nat -> nat) (x : nat) => f (rec x)) n x.
proof: Proof. induction n; cbn. - reflexivity. - now rewrite IHn. Qed.
imports: Coq(RelationClasses Relations Arith Max Lia) hydras(Exp2) LibHyps(LibHyps) hydras(MoreLibHyps)