Lemma is_coh_strictness_from_univalent_2_1 {B : bicat} (HB : is_univalent_2_1 B) : is_coh_strictness_structure (strictness_from_univalent_2_1 HB). Proof. split. - intros a b c f g ; cbn. rewrite isotoid_2_1_lwhisker. rewrite isotoid_2_1_rwhisker. rewrite isotoid_2_1_vcomp. apply maponpaths. use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } simpl. refine (!_). apply runitor_rwhisker. - intros v w x y z f g h k ; cbn. rewrite isotoid_2_1_lwhisker. rewrite isotoid_2_1_rwhisker. rewrite !isotoid_2_1_vcomp. apply maponpaths. use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } simpl. rewrite vassocr. apply lassociator_lassociator. 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.