(A B : Type) : O (A * B) -> O A * O B := O_rec (O_prod_unit A B). Global Instance isequiv_O_prod_cmp (A B : Type) : IsEquiv ( A B). Proof. rapply isequiv_O_rec_O_inverts. 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.