{A B : Type} `{In O A} `{In O B} (f : A -> B) `{O_inverts f} : IsEquiv f. Proof. refine (isequiv_commsq' f (O_functor f) (to O A) (to O B) _). apply to_O_natural. 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.