Proposition mor_to_power_commutes {w : V} {b : C} (f : w --> v ⊸ (E ⦃ b, x ⦄)) : mor_to_power f · is_power_enriched_map a b = f. Proof. unfold mor_to_power. rewrite !assoc'. refine (_ @ id_right _). apply maponpaths. apply z_iso_after_z_iso_inv. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Import MonoidalNotations.