(A B : Type) : O_monad_strength A B o functor_prod idmap (to O B) == to O (A*B). Proof. intros [a b]. unfold O_monad_strength, functor_prod. simpl. revert a; apply ap10. nrapply O_rec_beta. Qed.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.