proposition: Proposition tensor_sym_mon_braiding {x₁ x₂ y₁ y₂ : V} (f : x₁ --> x₂) (g : y₁ --> y₂) : f #⊗ g · sym_mon_braiding x₂ y₂ = sym_mon_braiding x₁ y₁ · g #⊗ f.
proof: Proof. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. rewrite !assoc'. etrans. { apply maponpaths. refine (!_). apply (pr1 (pr122 V) x₂ y₁ y₂ g). } rewrite !assoc. etrans. { apply maponpaths_2. refine (!_). apply (pr2 (pr122 V) x₁ x₂ y₁ f). } rewrite !assoc'. apply maponpaths. refine (!_). use (bifunctor_equalwhiskers V). 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