`{Univalence} (n : trunc_index) (k : nat) (A : pType) : pTr n (iterated_loops k A) <~>* iterated_loops k (pTr (trunc_index_inc' n k) A). Proof. revert A n. induction k. { intros A n; cbn. reflexivity. } intros A n. cbn; etransitivity. 1: apply ptr_loops. rapply (emap loops). apply IHk. Defined.
Require Import Basics Types WildCat Truncations