(A B : Type) : O (A * B) <~> (O A * O B) := Build_Equiv _ _ (O_prod_cmp A 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.