Lemma strict_bicat_to_two_cat_laws (B : strict_bicat) : two_cat_laws (strict_bicat_to_two_cat_category B). Proof. repeat split. - intros ; apply id2_left. - intros ; apply id2_right. - intros ; apply vassocr. - intros ; apply lwhisker_id2. - intros ; apply id2_rwhisker. - intros ; apply lwhisker_vcomp. - intros ; apply rwhisker_vcomp. - intros ; apply vcomp_whisker. - intros ; cbn. rewrite !idto2mor_idtoiso. rewrite !idtoiso_plunitor. apply vcomp_lunitor. - intros ; cbn. rewrite !idto2mor_idtoiso. rewrite !idtoiso_prunitor. apply vcomp_runitor. - intros ; cbn. rewrite !idto2mor_idtoiso. rewrite !idtoiso_plassociator. apply lwhisker_lwhisker. - intros ; cbn. rewrite !idto2mor_idtoiso. rewrite !idtoiso_plassociator. apply rwhisker_lwhisker. - intros ; cbn. rewrite !idto2mor_idtoiso. rewrite !idtoiso_plassociator. apply rwhisker_rwhisker. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.TwoCategories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.TransportLaws.