proposition: Lemma is_filtered_kfinite_subsets (X : hSet) : is_filtered (kfinite_subsets_category X).
proof: Proof. intros g d gfinite. apply hinhpr. simple refine(_ ,, _). - exact(kfinite_subtype_union (dob d) (finite_vertexset gfinite)). - use make_cocone. + apply subtype_union_containedIn. + abstract(red; intros ; apply funextsec; intro ; apply funextsec; intro ; apply squash_path). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.Sets UniMath.MoreFoundations.QuotientSet UniMath.MoreFoundations.Subtypes UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Filtered UniMath.CategoryTheory.Limits.StandardDiagrams UniMath.CategoryTheory.Categories.HSET.Core UniMath.Combinatorics.FiniteSets UniMath.Combinatorics.KFiniteTypes UniMath.Combinatorics.KFiniteSubtypes