Lemma pair_cocone_commutes {J : category} {d : diagram pair_graph J} {j : J} (cc : cocone d j) (e : edge pair_src pair_dst) : dmor d e · coconeIn cc pair_dst = coconeIn cc pair_src. Proof. exact(coconeInCommutes cc pair_src pair_dst e). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.FiniteSets.