Lemma is_cocone_mor_filtered_cocone_morphism {Y : SET} (cc : cocone d Y) : is_cocone_mor (filtered_cocone) cc (filtered_cocone_morphism cc). Proof. intro; apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.QuotientSet. Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Filtered. Require Import UniMath.CategoryTheory.Limits.StandardDiagrams. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.Combinatorics.KFiniteTypes. Require Import UniMath.Combinatorics.KFiniteSubtypes.