proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedTerminal UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedBinaryProducts UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedProducts UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products