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.

Lemma subset_rel_get_cand_bs : forall `{C :Config} lst p lvl pos_map, subset_rel (get_cand_bs lst p lvl pos_map) lst.