proposition: Lemma split_idempotent_is_idempotent {c : C} (e : split_idempotent c) : is_idempotent e.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors