(** * Addendum to the standard library of Coq *)
Require Export Omega.
Global Obligation Tactic := idtac.
Notation "[ x ; .. ; y ]" := (cons x .. (cons y nil) .. ).
Definition andl {A} (P:A->Prop)(l:list A) : Prop :=
fold_right (fun a res => P a /\ res) True l.
Fixpoint fun_power {A:Type}(n:nat)(f:A->A)(x:A) : A :=
match n with
| 0 => x
| S n' => f (fun_power n' f x)
end.

Lemma fun_power_minus_S : forall A (f:A->A) x m n,
m < n -> f (fun_power (n - S m) f x) = fun_power (n - m) f x.