{A B C : Type} (f : A -> B) (g : B -> C) `{IsEquiv _ _ g} `{IsConnMap O _ _ (g o f)} : IsConnMap O f. Proof. intros b. srefine (isconnected_equiv' O (hfiber (g o f) (g b)) _ _). exact (equiv_inverse (equiv_functor_sigma_id (fun a => equiv_ap g (f a) b))). 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.