proposition: Proposition sym_mon_braiding_id : sym_mon_braiding I_{V} I_{V} = identity (I_{V} ⊗ I_{V}).
proof: Proof. refine (_ @ mon_runitor_rinvunitor _). rewrite <- sym_mon_braiding_lunitor. rewrite !assoc'. rewrite mon_lunitor_I_mon_runitor_I. rewrite mon_runitor_rinvunitor. rewrite id_right. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories