{A B : Type} `{In O A} (f : A -> B) `{O_inverts f} : IsEquiv (to O B o f) := isequiv_homotopic (O_functor f o to O A) (to_O_natural f).
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.