Lemma trivial_disp_prebicat_laws : disp_prebicat_laws trivial_displayed_data. Proof. repeat apply make_dirprod; red; cbn; intros. - etrans. { apply id2_left. } apply transportf_trivial. - etrans. { apply id2_right. } apply transportf_trivial. - etrans. { apply vassocr. } apply transportf_trivial. - etrans. { apply lwhisker_id2. } apply transportf_trivial. - etrans. { apply id2_rwhisker. } apply transportf_trivial. - etrans. { apply lwhisker_vcomp. } apply transportf_trivial. - etrans. { apply rwhisker_vcomp. } apply transportf_trivial. - etrans. { apply vcomp_lunitor. } apply transportf_trivial. - etrans. { apply vcomp_runitor. } apply transportf_trivial. - etrans. { apply lwhisker_lwhisker. } apply transportf_trivial. - etrans. { apply rwhisker_lwhisker. } apply transportf_trivial. - etrans. { apply rwhisker_rwhisker. } apply transportf_trivial. - etrans. { apply vcomp_whisker. } apply transportf_trivial. - etrans. { apply lunitor_linvunitor. } apply transportf_trivial. - etrans. { apply linvunitor_lunitor. } apply transportf_trivial. - etrans. { apply runitor_rinvunitor. } apply transportf_trivial. - etrans. { apply rinvunitor_runitor. } apply transportf_trivial. - etrans. { apply lassociator_rassociator. } apply transportf_trivial. - etrans. { apply rassociator_lassociator. } apply transportf_trivial. - etrans. { apply runitor_rwhisker. } apply transportf_trivial. - etrans. { apply lassociator_lassociator. } apply transportf_trivial. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.