Lemma cwcmf (cmf : cmonfunctor) : wmonfunctor_to_cmonfunctor (cmonfunctor_to_wmonfunctor cmf) = cmf. Proof. repeat (use total2_paths_f) ; try (apply idpath) ; try (repeat (apply funextsec ; intro) ; apply homset_property). rewrite transportf_const. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesReordered. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories. Import BifunctorNotations.