Notation equiv_eqex_eqdep := eq_sigT_iff_eq_dep (only parsing). (* Compat *)

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