proposition: Proposition self_enrichment_equalizer_arr_eq {a b : V} (h : b --> a ⊸ v₁) (q : h · postcomp_arr (self_enrichment V) _ f = h · postcomp_arr (self_enrichment V) _ g) : h #⊗ identity a · internal_eval a v₁ · f = h #⊗ identity a · internal_eval a v₁ · g.
proof: Proof. rewrite !self_enrichment_postcomp in q. pose (maponpaths (λ z, z #⊗ identity _ · internal_eval _ _) q) as q'. cbn in q'. rewrite !tensor_comp_id_r in q'. rewrite !assoc' in q'. rewrite !internal_beta in q'. rewrite !assoc in q'. exact q'. 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