Definition inj_on_list {A B} (l : list A) (f : A -> B) :=
forall x y, In x l -> In y l -> f x = f y -> x = y.
Definition subset_rel {X} (sub lst : list X) : Prop :=
forall x,
In x sub ->
In x lst.
(*** NoDup general lemmas ***)

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