Require Export List.
Require Lt.
Definition all_equiv (l: list Prop) :=
forall x y, In x l -> In y l -> (x <-> y).
Definition all_equiv'_aux (l: list Prop) : Prop.
Definition all_equiv' (l: list Prop) : Prop.
*)
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 incl_preserves_stronger : forall l1 l2 l1' l2',
incl l1 l1' -> incl l2 l2' -> stronger l1' l2' -> stronger l1 l2.