proposition: Lemma is_precategory_base_precategory_data : is_precategory (base_precategory_data C D).
proof: Proof. apply make_is_precategory. - intros F₀ G₀. cbn. intros γ. apply funextsec. intros x. apply id_left. - intros F₀ G₀. cbn. intros γ. apply funextsec. intros x. apply id_right. - intros F₀ G₀ H₀ K₀. cbn. intros γ θ μ. apply funextsec. intros x. apply assoc. - intros F₀ G₀ H₀ K₀. cbn. intros γ θ μ. apply funextsec. intros x. apply assoc'. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.UnivalenceAxiom UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions