proposition: Lemma monnattrans_to_monoidal_section_strongunit : smonoidal_strongunit V dialgebra_disp_monoidal (smonoidal_preserves_unit V dialgebra_disp_monoidal monnattrans_to_monoidal_section_data).
proof: Proof. use tpair. - cbn. unfold dialgebra_disp_unit. do 2 rewrite functor_id. rewrite id_left, id_right. cbn in ismnt_unit. rewrite <- ismnt_unit. rewrite assoc. apply pathsinv0. etrans. { apply cancel_postcomposition. apply (z_iso_after_z_iso_inv (_,,fmonoidal_preservesunitstrongly Fm)). } apply id_left. - split; apply base_disp_cells_isaprop. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Displayed.MonoidalSections UniMath.CategoryTheory.Monoidal.Displayed.Symmetric UniMath.CategoryTheory.Monoidal.Displayed.MonoidalFunctorLifting UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Monoidal.Structure.Symmetric