{X Y : pType} (f : X ->* Y) n (x y : iterated_loops n.+1 X) : fmap (iterated_loops n.+1) f (x @ y) = fmap (iterated_loops n.+1) f x @ fmap (iterated_loops n.+1) f y. Proof. apply fmap_loops_pp. 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.