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 all_equiv3_stronger3__all_equiv : forall l1 l2 l3, l1 <> nil -> l2 <> nil -> l3 <> nil -> all_equiv l1 -> all_equiv l2 -> all_equiv l3 -> stronger l1 l2 -> stronger l2 l3 -> stronger l3 l1 -> all_equiv (l1++l2++l3).