Inductive nth_split (a : B) (l : list B) : Set :=
    Nth_Split_Intro :
      forall l1 l2 : list B, l = l1 ++ a :: l2 -> nth_split a l.Inductive nth_split (a : B) (l : list B) : Set :=
    Nth_Split_Intro :
      forall l1 l2 : list B, l = l1 ++ a :: l2 -> nth_split a l.

(* Specifications: *)
Lemma my_nth_split : forall (n : nat) (l : list B) (a : B), my_nth n l a -> nth_split a l.
Lemma in_nth : forall (a : B) (l : list B), In a l -> exists n : nat, my_nth n l a.