proposition: Lemma filtered_has_pair_cocones {J : category} (filtered : is_filtered J) (d : diagram pair_graph J) : ∃ z : J, cocone d z.
proof: Proof. exact(filtered pair_graph d is_finite_graph_pair). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.covyoneda UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.FiniteSets UniMath.CategoryTheory.Limits.StandardDiagrams