(X : Type) `{IsHSet X} (f : PreIdempotent X) : Splitting f. Proof. simple refine (Build_RetractOf X { x : X & f x = x } (fun x => (f x ; isidem f x)) pr1 _ ; _). - intros [x p]; simpl. apply path_sigma with p; simpl. apply path_ishprop. - simpl. intros x; reflexivity. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import HFiber Constant. Require Import Truncations.Core Modalities.Modality. Require Import Homotopy.IdentitySystems.