Section Forall2.
(** [Forall2]: stating that elements of two lists are pairwise related. *)
Variables A B : Type.
Variable R : A -> B -> Prop.
Inductive Forall2 : list A -> list B -> Prop :=
| Forall2_nil : Forall2 [] []
| Forall2_cons : forall x y l l',
R x y -> Forall2 l l' -> Forall2 (x::l) (y::l').
Hint Constructors Forall2 : core.

Theorem Forall2_app : forall l1 l2 l1' l2',
Forall2 l1 l1' -> Forall2 l2 l2' -> Forall2 (l1 ++ l2) (l1' ++ l2').