proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.TwoCategories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Categories.HSET.All UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.TransportLaws