(******************************************  Copied From Coq.Logic.JMeq.  No longer involving JMeq_eq, which is potentially inconsistenty with homotopy type theory.  TODO: let reflexivity, symmetry and transitivity work again.  ******************************************)
Definition JMeq {A:Type} (x:A) {B:Type} (y: B): Prop :=
{H: @eq Type A B | @eq_rect Type A (fun T: Type => T) x B H = y}.

Lemma JMeq_trans :
forall {A: Type} {B: Type} {C:Type} {x:A} {y:B} {z:C}, JMeq x y -> JMeq y z -> JMeq x z.