{A B : Type} `{In O B} (f : A -> B) `{O_inverts f} : IsEquiv (O_rec (O := O) f). Proof. rapply (cancelL_isequiv (C:=O B) (to O B)). rapply (isequiv_homotopic (O_functor f) (fun x => (O_rec_postcompose_to_O f x)^)). 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.