proposition: Lemma two_cat_to_prebicat_laws (C : two_cat) : prebicat_laws (two_cat_to_prebicat_data C).
proof: Proof. repeat split. - intros. apply TwoCategories.id2_left. - intros. apply TwoCategories.id2_right. - intros. apply TwoCategories.vassocr. - intros. apply TwoCategories.lwhisker_id2. - intros. apply TwoCategories.id2_rwhisker. - intros. apply TwoCategories.lwhisker_vcomp. - intros. apply TwoCategories.rwhisker_vcomp. - intros. apply TwoCategories.vcomp_lunitor. - intros. apply TwoCategories.vcomp_runitor. - intros. apply TwoCategories.lwhisker_lwhisker. - intros. apply TwoCategories.rwhisker_lwhisker. - intros. apply TwoCategories.rwhisker_rwhisker. - intros. apply TwoCategories.vcomp_whisker. - intros ; cbn. etrans. { apply idto2mor_comp. } rewrite pathsinv0r. apply idpath. - intros ; cbn. etrans. { apply idto2mor_comp. } rewrite pathsinv0l. apply idpath. - intros ; cbn. etrans. { apply idto2mor_comp. } rewrite pathsinv0r. apply idpath. - intros ; cbn. etrans. { apply idto2mor_comp. } rewrite pathsinv0l. apply idpath. - intros ; cbn. etrans. { apply idto2mor_comp. } rewrite pathsinv0r. apply idpath. - intros ; cbn. etrans. { apply idto2mor_comp. } rewrite pathsinv0l. apply idpath. - intros ; cbn. etrans. { apply maponpaths. apply idto2mor_rwhisker. } etrans. { apply idto2mor_comp. } refine (!_). etrans. { apply idto2mor_lwhisker. } refine (!_). apply maponpaths. apply (homset_property C). - intros ; cbn. etrans. { apply maponpaths. apply idto2mor_rwhisker. } etrans. { do 2 apply maponpaths_2. apply idto2mor_lwhisker. } etrans. { apply maponpaths_2. apply idto2mor_comp. } etrans. { apply idto2mor_comp. } refine (!_). etrans. { apply idto2mor_comp. } refine (!_). apply maponpaths. apply (homset_property C). 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