Definition make_is_power_enriched (a : power_cone) (p_map : ∏ (w : C), v ⊸ (E ⦃ w, x ⦄) --> E ⦃ w, a ⦄) (H₁ : ∏ (w : C), is_power_enriched_map a w · p_map w = identity _) (H₂ : ∏ (w : C), p_map w · is_power_enriched_map a w = identity _) : is_power_enriched a. Proof. intro w. use make_is_z_isomorphism. - exact (p_map w). - split. + exact (H₁ w). + exact (H₂ w). Defined.
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.