Definition functorlifting_preservesunitstrongly {Fs : preserves_unit_strongly (fmonoidal_preservesunit Fm)} {ms : flmonoidal_lax} (pfstrong : fl_strongunit (flmonoidal_preserves_unit ms) Fs) : preserves_unit_strongly (functorlifting_preserves_unit (flmonoidal_preserves_unit ms)). Proof. use tpair. - exists (pr1 Fs). exact (pr1 pfstrong). - use tpair. + use total2_paths_b. * exact (pr12 Fs). * exact (pr22 pfstrong). + use total2_paths_b. * exact (pr22 Fs). * exact (pr12 pfstrong). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.