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 NoDup_disjointness: forall {A B} (l1 : list A) (l2 : list A) (f : A -> B) ,
NoDup (List.map f l1) ->
NoDup (List.map f l2) ->
disjoint_list (List.map f l1) (List.map f l2) ->
NoDup (List.map f (l1 ++ l2)).