Definition path_cat_with_enrichment_alt_data_help {V : monoidal_cat} {ob : UU} {arr : ob -> ob -> V} {E₁ E₂ : cat_with_enrichment_alt_data_help ob arr} (f : ∏ (x y : ob), pr1 E₁ x y → pr1 E₂ x y) (Hf : ∏ (x y : ob), isweq (f x y)) (p₁ : ∏ (x : ob), f _ _ (pr12 E₁ x) = pr12 E₂ x) (p₂ : ∏ (x y z : ob) (g₁ : pr1 E₁ x y) (g₂ : pr1 E₁ y z), f _ _ (pr122 E₁ _ _ _ g₁ g₂) = pr122 E₂ _ _ _ (f _ _ g₁) (f _ _ g₂)) (p₃ : ∏ (x y : ob) (g : pr1 E₁ x y), (pr1 (pr222 E₁)) _ _ g = (pr1 (pr222 E₂)) _ _ (f _ _ g)) (p₄ : ∏ (x y : ob) (g : I_{V} --> arr x y), f _ _ (pr2 (pr222 E₁) _ _ g) = pr2 (pr222 E₂) _ _ g) : E₁ = E₂.
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.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.Enriched. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.UnderlyingCategory. Import MonoidalNotations.