Module ProofIrrelevanceTheory (M:ProofIrrelevance).
(** Proof-irrelevance implies uniqueness of reflexivity proofs *)
Module Eq_rect_eq.

Lemma eq_rect_eq :
forall (U:Type) (p:U) (Q:U -> Type) (x:Q p) (h:p = p),
x = eq_rect p Q x p h.