Fixpoint remove_list_sub {A} (A_eqb : A -> A -> bool) (sublist : list A) (lst : list A) : list A :=
  match sublist with
  | [] => lst
  | h :: t => remove_list_sub A_eqb t (remove_aux A_eqb lst h)
  end.

Lemma In_remove_aux {A} `{EqDec A} : forall (lst : list A) (x a : A), In x (remove_aux eqb lst a) -> In x lst.