{A B : Type} (f g : A -> B) (h : f == g) : IsConnMap O f -> IsConnMap O g. Proof. intros ? b. exact (isconnected_equiv O (hfiber@{i i} f b) (equiv_hfiber_homotopic@{i i i} f g h 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.