proposition: Proposition is_cartesian_indexed_cat_factorisation_commutes : is_cartesian_indexed_cat_factorisation · # (Φ $ g) ff · indexed_cat_comp Φ f g yy = hh.
proof: Proof. unfold is_cartesian_indexed_cat_factorisation. rewrite !assoc'. etrans. { do 2 apply maponpaths. rewrite !assoc. apply maponpaths_2. rewrite <- functor_comp. rewrite z_iso_after_z_iso_inv. rewrite functor_id. apply idpath. } rewrite id_left. rewrite z_iso_after_z_iso_inv. apply id_right. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.IndexedCategories.IndexedCategory