(** Export the theory of injective dependent elimination *)

  Module EqdepTheory := EqdepTheory(Eq_rect_eq).Scheme eq_indd := Induction for eq Sort Prop.

Lemma subset_eq_compat : forall (U:Type) (P:U->Prop) (x y:U) (p:P x) (q:P y), x = y -> exist P x p = exist P y q.