O (Coeq f g) <~> O (Coeq (O_functor f) (O_functor g)) := Build_Equiv _ _ (O_functor coeq_cmp) _.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.