Lemma rel0_impl a b (Hab : rel0 a b) : from_cobase_eqrel a b. Proof. use Hab. clear Hab. intro H; simpl. destruct H as [f Hf]. generalize (toforallpaths _ _ _ (coconeInCommutes cc (pr1 a) (pr1 b) f) (pr2 a)). unfold compose, from_cobase; simpl; intro H. rewrite <- H. rewrite <- Hf. apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Sets. 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.Coproducts. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Pushouts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.MoreFoundations.Subtypes.