Inductive Forall2' (A B : Type) (R : A -> B -> Type) : list A -> list B -> Type :=
Forall2'_nil : Forall2' R [] []
| Forall2'_cons : forall (x : A) (y : B) (l : list A) (l' : list B),
R x y -> Forall2' R l l' -> Forall2' R (x :: l) (y :: l').

Lemma In_nth:
forall (A : Type) (l : list A) (x d : A) n,
n < length l -> nth n l d = x -> x ∈ l.