{A B} : O (A + B) <~> O (O A + O B) := equiv_O_functor_sum (to O A) (to O B).
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.