proposition: Proposition sym_mon_braiding_linvunitor (x : V) : mon_linvunitor x · sym_mon_braiding (I_{V}) x = mon_rinvunitor x.
proof: Proof. refine (!(id_right _) @ _ @ id_left _). rewrite <- mon_runitor_rinvunitor. rewrite !assoc. apply maponpaths_2. rewrite !assoc'. rewrite sym_mon_braiding_runitor. apply mon_linvunitor_lunitor. 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