Lemma make_disp_symm_braiding_hex1 {B : symmetric M} {c : disp_braiding_data DM B} (p_hex : disp_sym_moncat_laws_tensored_hex c) : disp_braiding_law_hexagon1 DM c. Proof. unfold disp_braiding_law_hexagon1. intro ; intros. set (q := p_hex x y z xx yy zz). set (qq := specialized_transport_lemma _ _ _ _ (! q)). rewrite assoc_disp_var in qq. set (qq' := transportb_transpose_right qq). set (qq'' := specialized_transport_lemma' _ _ _ _ qq'). rewrite assoc_disp in qq''. set (qq''' := transportb_transpose_right qq''). refine (_ @ ! qq'''). clear qq''' qq'' qq' qq q. use transportf_transpose_left. unfold transportb. rewrite ! transport_f_f. apply pathsinv0. use transportf_set. apply homset_property. 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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. 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.TransportLemmas. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.