(** [eq_dep U P p x q y] is strictly finer than [JMeq (P p) x (P q) y] *)

(* Specifications: *)
Lemma eq_dep_JMeq :
forall (U: Type) (P: U -> Type) p x q y, eq_dep U P p x q y -> JMeq x y.
Lemma eq_dep_strictly_stronger_JMeq :
exists (U: Type) (P: U -> Type) p q x y, JMeq x y /\ ~ eq_dep U P p x q y.