{A B : Type} (f : A -> B) `{IsConnMap O _ _ f} `{MapIn O _ _ f} : IsEquiv f. Proof. apply isequiv_contr_map. intros b. apply (contr_trunc_conn O). 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.