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 stronger2__stronger_left : forall l1 l1' l2, stronger l1 l2 -> stronger l1' l2 -> stronger (l1++l1') l2.