Definition fam_eq {X : UU} {Y₁ Y₂ : X → X → UU} (p : ∏ (x₁ x₂ : X), Y₁ x₁ x₂ ≃ Y₂ x₁ x₂) : Y₁ = Y₂. Proof. use funextsec ; intro x₁. use funextsec ; intro x₂. exact (invmap (univalence (Y₁ x₁ x₂) (Y₂ x₁ x₂)) (p x₁ x₂)). 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.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.