Definition all_equiv' (l: list Prop) : Prop.
induction l; [exact True|].
exact ((last l a -> a) /\ all_equiv'_aux (a::l)).
Defined.
(* Definition all_equiv' (l: list Prop) : Prop. *)

Lemma all_equiv__equiv : forall l, all_equiv l <-> all_equiv' l.
Definition stronger (l1 l2 : list Prop) :=
forall x y, In x l1 -> In y l2 -> (x -> y).