Fixpoint all_but (i : nat) {A} (l : list A) : list A :=
  match i with
    O => tl l
  | S i =>
    match l with
      nil => nil
    | x :: l => x :: all_but i l
    end
  end.

Lemma permutation_all_but {A} i (l : list A) x : nth_error l i = Some x -> Permutation l (x :: all_but i l).