(A : Type) : @O_functor A A idmap == idmap. Proof. refine (O_indpaths _ _ _); intros x. apply O_rec_beta. 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.