proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Displayed.TransportLemmas UniMath.CategoryTheory.Monoidal.Structure.Symmetric