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_equiv2_stronger2__all_equiv : forall l1 l2,
all_equiv l1 -> all_equiv l2 ->
stronger l1 l2 -> stronger l2 l1 ->
all_equiv (l1++l2).