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_aux_lemma {A} `{EqDec A} : forall (lst : list A) (a a' : A),
In a' lst ->
In a' (remove_aux eqb lst a) \/ a = a'.