Corollary upd_Znth_eq' : forall {A}{d: Inhabitant A} x (l1 l2 : list A) i (Hi : 0 <= i < Zlength l1)
  (Hlen : Zlength l1 = Zlength l2)
  (Heq : forall j, 0 <= j < Zlength l1 -> j <> i -> Znth j l1 = Znth j l2),
  upd_Znth i l1 x = upd_Znth i l2 x.

Lemma remove_from_NoDup : forall {A} {A_eq : EqDec A} (x : A) l1 l2, NoDup (l1 ++ x :: l2) -> remove A_eq x (l1 ++ x :: l2) = l1 ++ l2.