(A : Type) {B : Type} (f : A -> B) `{IsEquiv _ _ f} : IsConnected O A -> IsConnected O B. Proof. intros ?; refine (contr_equiv (O A) (O_functor O f)). 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.