Proposition self_enrichment_pair_eq {a b : V} (φ ψ : a --> b ⊸ w) (p₁ : pair_fun_pr1 φ = pair_fun_pr1 ψ) (p₂ : pair_fun_pr2 φ = pair_fun_pr2 ψ) : φ = ψ. Proof. use internal_funext. intros c h. use (BinProductArrowsEq _ _ _ prod). - rewrite !pair_eq_pr1. rewrite p₁. apply idpath. - rewrite !pair_eq_pr2. rewrite p₂. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedTerminal. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedBinaryProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Import MonoidalNotations.