`{Funext} {A : Type} (B : A -> Type) : (forall a, In O (B a)) <~> MapIn O (@pr1 A B). Proof. exact (equiv_iff_hprop_uncurried (iff_forall_inO_mapinO_pr1 B)). Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.