proposition: Proposition continuation_adjunction_unit_enrichment : nat_trans_enrichment continuation_adjunction_unit (functor_id_enrichment (self_enrichment V)) (functor_comp_enrichment continuation_functor_enrichment continuation_functor_op_enrichment).
proof: Proof. use nat_trans_enrichment_via_comp. intros x y ; cbn. unfold continuation_adjunction_unit_data. rewrite self_enrichment_precomp. rewrite self_enrichment_postcomp. rewrite id_left. use internal_funext. intros a h. rewrite !tensor_comp_r_id_r. rewrite !assoc'. rewrite !internal_beta. refine (!_). rewrite tensor_split. rewrite !assoc'. rewrite internal_beta. refine (!_). etrans. { rewrite tensor_split. rewrite !assoc'. apply idpath. } apply maponpaths. etrans. { apply maponpaths. rewrite !assoc. rewrite <- tensor_split'. rewrite tensor_split. rewrite !assoc'. rewrite internal_beta. rewrite !assoc. rewrite tensor_sym_mon_braiding. apply idpath. } use internal_funext. intros a' h'. rewrite !tensor_comp_r_id_r. rewrite !assoc'. rewrite !internal_beta. etrans. { do 2 apply maponpaths. unfold internal_comp. rewrite !internal_beta. rewrite !assoc. rewrite tensor_lassociator. rewrite !assoc'. apply idpath. } rewrite !assoc. rewrite <- tensor_comp_mor. rewrite !tensor_sym_mon_braiding. rewrite id_right. rewrite tensor_comp_r_id_r. rewrite !assoc'. etrans. { apply maponpaths. rewrite !assoc. rewrite tensor_lassociator. rewrite !assoc'. apply maponpaths. rewrite !assoc. rewrite <- !tensor_comp_mor. rewrite !id_left, !id_right. rewrite internal_beta. rewrite tensor_split. rewrite !assoc'. rewrite internal_beta. cbn. rewrite tensor_comp_l_id_l. rewrite !assoc'. apply maponpaths. rewrite !assoc. rewrite tensor_sym_mon_braiding. rewrite !assoc'. unfold internal_comp. rewrite internal_beta. apply idpath. } rewrite !assoc. apply maponpaths_2. rewrite tensor_split. refine (!_). rewrite <- tensor_sym_mon_braiding. rewrite tensor_split. rewrite !assoc'. apply maponpaths. clear a h a' h'. refine (!_). rewrite !assoc. rewrite tensor_sym_mon_braiding. apply maponpaths_2. rewrite <- sym_mon_hexagon_lassociator. cbn. apply lassociator_hexagon_two. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.EnrichedCats.EnrichmentAdjunction UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched UniMath.CategoryTheory.EnrichedCats.Examples.OppositeEnriched UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedTerminal UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedBinaryProducts UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers UniMath.CategoryTheory.EnrichedCats.Limits.Examples.SelfEnrichedLimits UniMath.CategoryTheory.EnrichedCats.Limits.Examples.OppositeEnrichedLimits UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedInitial UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedBinaryCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCopowers UniMath.CategoryTheory.EnrichedCats.Colimits.Examples.SelfEnrichedColimits UniMath.CategoryTheory.EnrichedCats.Colimits.Examples.OppositeEnrichedColimits UniMath.Semantics.EnrichedEffectCalculus.EECModel