(A : pType) (P : pFam A) : loops (psigma P) <~>* psigma (loopsD P). Proof. snrapply Build_pEquiv'. 1: exact (equiv_path_sigma _ _ _)^-1%equiv. reflexivity. 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.