proposition: Proposition self_enrichment_is_copower_eq_2 (w : V) : internal_uncurry v₁ v₂ w · is_copower_enriched_map (self_enrichment V) v₁ v₂ self_enrichment_copower_cocone w = identity _.
proof: Proof. use internal_funext ; cbn. intros a₁ h₁. rewrite tensor_comp_r_id_r. rewrite !assoc'. unfold is_copower_enriched_map ; cbn. rewrite internal_beta. use internal_funext ; cbn. intros a₂ h₂. rewrite !tensor_comp_r_id_r. rewrite !assoc'. unfold internal_comp. rewrite internal_beta. etrans. { apply maponpaths. rewrite !assoc. rewrite tensor_lassociator. rewrite !assoc'. apply maponpaths. rewrite !assoc. rewrite <- tensor_comp_id_l. unfold internal_pair. rewrite internal_beta. rewrite tensor_id_id. apply id_left. } rewrite !assoc. rewrite tensor_lassociator. rewrite !assoc'. etrans. { apply maponpaths. rewrite tensor_split. rewrite !assoc'. unfold internal_uncurry. rewrite internal_beta. rewrite !assoc. rewrite tensor_rassociator. rewrite !assoc'. apply idpath. } rewrite !assoc. rewrite mon_lassociator_rassociator. rewrite id_left. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedInitial UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedBinaryCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoequalizers UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCopowers UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers