Lemma sigma_disp_cat_monoidal_laws : disp_monoidal_laws sigma_disp_cat_monoidal_data. Proof. repeat split ; try (intro ; intros) ; use total2_paths_f ; try (apply E_prop). - etrans. { apply (disp_monoidal_leftunitornat DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_leftunitoriso DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_leftunitoriso DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_rightunitornat DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_rightunitoriso DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_rightunitoriso DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_associatornatleft DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_associatornatright DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_associatornatleftright DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_associatoriso DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_associatoriso DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_triangleidentity DM). } apply pathsinv0, pr1_transportf. - etrans. { apply (disp_monoidal_pentagonidentity DM). } apply pathsinv0, pr1_transportf. 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Sigma. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. 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.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Examples.Fullsub. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.