proposition: Lemma sigma_disp_cat_monoidal_laws : disp_monoidal_laws sigma_disp_cat_monoidal_data.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.DisplayedCats.Examples.Sigma UniMath.CategoryTheory.PrecategoryBinProduct 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.Symmetric UniMath.CategoryTheory.Monoidal.Examples.Fullsub UniMath.CategoryTheory.Monoidal.Structure.Symmetric