Proposition symmetric_lax_monoidal_sym_mon_braiding {V₁ V₂ : sym_monoidal_cat} (F : symmetric_lax_monoidal_functor V₁ V₂) (x y : V₁) : sym_mon_braiding V₂ (F x) (F y) · mon_functor_tensor F y x = mon_functor_tensor F x y · #F (sym_mon_braiding V₁ x y). Proof. exact (pr2 F x y). 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.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations.