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').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').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').

Lemma Forall2_impl (A B : Type) (R1 R2 : A -> B -> Prop) : (forall a b, R1 a b -> R2 a b) -> forall l1 l2, Forall2 R1 l1 l2 -> Forall2 R2 l1 l2.