proposition: Proposition enriched_conical_colim_eq_from_coprod_coequalizers {i j : I} (k : i --> j) : # D k · enriched_conical_colim_in_from_coprod_coequalizers i = enriched_conical_colim_in_from_coprod_coequalizers j.
proof: Proof. unfold enriched_conical_colim_in_from_coprod_coequalizers. rewrite !assoc. rewrite <- enriched_conical_colim_from_coprod_coequalizers_r_in. rewrite <- (enriched_conical_colim_from_coprod_coequalizers_l_in k). rewrite !assoc'. apply maponpaths. refine (!_). exact (enriched_coequalizer_cocone_eq _ _ _ (pr1 (EE _ _ f g))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoequalizers