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 remove_list_sub_lemma {A} `{EqDec A} : forall (a : A) (sub : list A) (lst : list A),
In a lst ->
In a (remove_list_sub eqb sub lst) \/ In a sub.