proposition: Lemma strict_bicat_to_two_cat_laws (B : strict_bicat) : two_cat_laws (strict_bicat_to_two_cat_category B).
proof: 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.
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