Definition strictness_from_univalent_2_1 {B : bicat} (HB : is_univalent_2_1 B) : strictness_structure B. Proof. repeat use tpair. - refine (λ _ _ f, isotoid_2_1 HB (lunitor f ,, _)). is_iso. - refine (λ _ _ f, isotoid_2_1 HB (runitor f ,, _)). is_iso. - refine (λ _ _ _ _ f g h, isotoid_2_1 HB (lassociator f g h ,, _)). is_iso. - abstract (cbn ; intros ; rewrite idtoiso_2_1_isotoid_2_1 ; apply idpath). - abstract (cbn ; intros ; rewrite idtoiso_2_1_isotoid_2_1 ; apply idpath). - abstract (cbn ; intros ; rewrite idtoiso_2_1_isotoid_2_1 ; apply idpath). Defined.
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.