{A : Type} `{IsConnMap O _ _ (const_tt A)} : IsConnected O A. Proof. refine (isconnected_equiv O (hfiber (const_tt A) tt) (equiv_sigma_contr _) _). 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.