`{Funext} (A : Type) (F : A -> pType) (n : nat) : iterated_loops n (pproduct F) <~>* pproduct (iterated_loops n o F). Proof. induction n. 1: reflexivity. refine (loops_pproduct_commute _ _ o*E _). rapply (emap loops). exact IHn. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import HFiber Factorization Truncations.Core Truncations.Connectedness HProp. Require Import Pointed.Core Pointed.pEquiv. Require Import WildCat. Require Import Spaces.Nat.Core.