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