proposition: Lemma make_ob_comp_eq {I J K} (ρ : pr1 (pr1 X I)) (f : C^op⟦I,J⟧) (g : C^op⟦J,K⟧) : make_ob _ (# (pr1 X) (f · g) ρ) = make_ob _ (# (pr1 X) g (# (pr1 X) f ρ)).
proof: Proof. exact (maponpaths (make_ob K) (eqtohomot (functor_comp X f g) ρ)). Defined.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf