proposition: Proposition isaprop_conical_colim_enriched (HC : is_univalent C) : isaprop (conical_colim_enriched).
proof: Proof. use invproofirrelevance. intros φ₁ φ₂. use subtypePath. { intro. apply isaprop_is_conical_colim_enriched. } use total2_paths_f. - use (isotoid _ HC). apply iso_between_conical_colim_enriched. - use subtypePath. { intro. repeat (use impred ; intro). apply homset_property. } rewrite pr1_transportf. rewrite transportf_sec_constant. use funextsec. intro j. rewrite transportf_isotoid'. apply is_conical_colim_enriched_map_in. 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