Lemma split_idempotent_is_idempotent {c : C} (e : split_idempotent c) : is_idempotent e. Proof. induction (!split_idempotent_is_split e). refine (assoc _ _ _ @ _). refine (maponpaths (λ x, x · _) _). refine (assoc' _ _ _ @ _). refine (maponpaths _ (retraction_is_retraction _) @ _). apply id_right. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.OppositeCategory.Core.