Goal:
    A : Type  P : nat → A → Type  l : list A  f : nat → A → A  n : nat
  ============================
   (Alli P n l
    → (∀ (n : nat) (x : A), P n x → f n x = x) → mapi_rec f l n = l)


DEBUG:Going to execute:
induction 1; simpl; f_equal