{A B : Type} (f : A -> B) {g : A -> B} (p : f == g) `{MapIn O _ _ f} : MapIn O g. Proof. intros b. exact (inO_equiv_inO (hfiber f b) (equiv_hfiber_homotopic f g p 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.