proposition: Lemma is_precategory_data_from_prebicat_and_ob: is_precategory precategory_data_from_bicat_and_ob.
proof: Proof. use make_is_precategory. - intros a b f; apply id2_left. - intros a b f; apply id2_right. - intros a b c d f g h; apply vassocr. - intros a b c d f g h; apply pathsinv0; apply vassocr. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.CategoryTheory.whiskering UniMath.Bicategories.Core.Bicat