(** However, when the dependencies are equal, [JMeq (P p) x (P q) y] is as strong as [eq_dep U P p x q y] (this uses [JMeq_eq]) *)

Lemma JMeq_eq_dep :
forall (U:Type) (P:U->Prop) p q (x:P p) (y:P q),
p = q -> JMeq x y -> eq_dep U P p x q y.