Definition stronger (l1 l2 : list Prop) :=
  forall x y, In x l1 -> In y l2 -> (x -> y).Definition all_equiv_under (l1 l2 : list Prop) :=
  forall x y z, In x l1 -> In y l2 -> In z l2 -> (x -> (y <-> z)).

Lemma stronger_transitivity : forall l1 l2 l3, stronger l1 l2 -> stronger l2 l3 -> l2 <> nil -> stronger l1 l3.