Lemma chain_mor_right {C : category} {c : chain C} {i j} (Hij : i < j) (HSij : S i < j) : dmor c (idpath (S i)) · chain_mor c HSij = chain_mor c Hij. Proof. induction j as [|j IHj]. - destruct (negnatlthn0 _ Hij). - simpl. destruct (natlehchoice4 _ _ Hij). + destruct (natlehchoice4 _ _ HSij). * now rewrite <- (IHj h h0), assoc. * destruct p; simpl. destruct (natlehchoice4 _ _ h); [destruct (isirreflnatlth _ h0)|]. apply cancel_postcomposition, maponpaths, isasetnat. + destruct p, (isirreflnatlth _ HSij). Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Initial.