Section Classes.
Context {A : Type}.
Context {dec : EquivDec.EqDec A (@eq A)}.
intros.
eapply Coq.Logic.Eqdep_dec.UIP_dec. apply EquivDec.equiv_dec.
Qed.
eapply Coq.Logic.Eqdep_dec.UIP_dec. apply EquivDec.equiv_dec.
Qed.

Lemma inj_pair2 :
forall (P:A -> Type) (p:A) (x y:P p),
existT P p x = existT P p y -> x = y.