proposition: Proposition enriched_from_arr_smash_lemma (x y : C) : pr1 (enriched_from_arr E (hset_struct_point P (make_smash_struct_enrichment_data x y))) true = hset_struct_point P (pr2 (E ⦃ x, y ⦄)).
proof: Proof. assert (mor_hset_struct P (pr2 (monoidal_unit (smash_product_monoidal_cat P))) (pr2 (E ⦃ x, y ⦄)) (pointed_hset_struct_map_from_unit P (pr2 (E ⦃ x, y ⦄)) (hset_struct_point P (pr2 (E ⦃ x, y ⦄))))) as H. { apply hset_struct_with_smash_map_from_unit. } refine (_ @ maponpaths (λ z, pr1 z true) (enriched_from_to_arr E (_ ,, H))). apply maponpaths_2. apply maponpaths. unfold make_smash_struct_enrichment_data. unfold transportf_struct_weq. rewrite transportf_hset_struct_point. cbn ; unfold enriched_smash_hom_to_mor. apply maponpaths. use eq_mor_hset_struct. intro ; cbn. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits UniMath.CategoryTheory.DisplayedCats.Structures.StructuresSmashProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Examples.SmashProductMonoidal UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor