Section prodl.
Fixpoint prodl (l : list nat) : nat :=
match l with
| nil => 1
| n :: l' => n * prodl l'
end.
End prodl.
Definition clos_refl {A : Type} (R : A -> A -> Prop) (x y : A) : Prop :=
R x y \/ x = y.
Inductive Exists2 {A B} (R: A -> B -> Prop) : list A -> list B -> Prop :=
| Exists2_cons_hd : forall x xs y ys, R x y -> Exists2 R (x::xs) (y::ys)
| Exists2_cons_tl : forall x xs y ys, Exists2 R xs ys -> Exists2 R (x::xs) (y::ys).
Hint Constructors Exists2.

Lemma app_eq_compat_l {A: Type} (xs ys zs: list A) : ys = zs -> xs ++ ys = xs ++ zs.