(O' O : ReflectiveSubuniverse) `{O <= O', O' <= Sep O} {Y X : Type} (f : Y -> X) `{IsConnected O' Y} `{IsConnMap O _ _ f} : IsConnected O' X. Proof. apply isconnected_conn_map_to_unit. apply (OO_cancelR_conn_map O' O f (const_tt _)). Defined.
Require Import HoTT.Basics HoTT.Types. Require Import HFiber Extensions Limits.Pullback. Require Import Modality Accessible Modalities.Localization.