proposition: Lemma is_nat_trans_ψ_from_comps : is_nat_trans ψ_source ψ_target (λ A (f : yoneda_objects_ob D X (L A)), θ A · # G f · ρ).
proof: Proof. intros A B h; apply funextfun; intro f; cbn. rewrite functor_comp, !assoc. assert (θ_nat_trans_ax := nat_trans_ax θ); simpl in θ_nat_trans_ax. now rewrite <- θ_nat_trans_ax. Qed.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.Adamek UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.whiskering