`{Funext} {A : Type} `{IsConnected O A} (C : Type) `{In O C} : C <~> (A -> C) := Build_Equiv _ _ const (isequiv_const_isconnected_inO C). End ConnectedTypes. Section ModalMaps. Context (O : ReflectiveSubuniverse). Global Instance mapinO_isequiv {A B : Type} (f : A -> B) `{IsEquiv _ _ f} : MapIn O f. Proof. intros b; exact _. 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.