Goal:
  
  A : Type
  B : Type
  f : nat -> A -> option B
  a : A
  l : list A
  i : nat
  t : B
  n : nat
  l0 : list B
  IHl : nth_error l0 i = Some t ->
        ∑ x : A, nth_error l i = Some x /\ f (i + S n)%nat x = Some t
  b : B
  Heq : f n a = Some b
  Heq' : map_option_out (mapi_rec f l (S n)) = Some l0
  ============================
   (nth_error l0 i = Some t ->
    ∑ x : A, nth_error l i = Some x /\ f (S (i + n)) x = Some t)


DEBUG:Going to execute:
t