Lemma flmonoidal_equality (fl1 fl2 : flmonoidal_lax) : (∏ x y : C', pr11 fl1 x y = pr11 fl2 x y) -> (pr21 fl1 = pr21 fl2) -> fl1 = fl2. Proof. intros pT pU. use total2_paths_f. 2: apply isaprop_flmonoidal_laxlaws. use total2_paths_f. - do 2 (apply funextsec ; intro). apply pT. - cbn. rewrite transportf_const. exact pU. Qed.
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.