proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions