(A : Type) : O_monad_mult A o (to O (O A)) == idmap. Proof. apply O_indpaths; intros x; unfold O_monad_mult. exact (O_rec_beta idmap (to O A 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.