Lemma monnattrans_to_monoidal_section_strongunit : smonoidal_strongunit V dialgebra_disp_monoidal (smonoidal_preserves_unit V dialgebra_disp_monoidal monnattrans_to_monoidal_section_data). Proof. use tpair. - cbn. unfold dialgebra_disp_unit. do 2 rewrite functor_id. rewrite id_left, id_right. cbn in ismnt_unit. rewrite <- ismnt_unit. rewrite assoc. apply pathsinv0. etrans. { apply cancel_postcomposition. apply (z_iso_after_z_iso_inv (_,,fmonoidal_preservesunitstrongly Fm)). } apply id_left. - split; apply base_disp_cells_isaprop. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.MonoidalSections. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Displayed.MonoidalFunctorLifting. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations. Section FromMonoidalSection. End FromMonoidalSection.