proposition: Proposition cartesian_to_braiding_data_pr1 (x y : M) : cartesian_to_braiding_data x y · semi_cart_tensor_pr1 (pr1 M_cart) y x = semi_cart_tensor_pr2 M_cart x y.
proof: Proof. apply (BinProductPr1Commutes _ _ _ (is_cartesian_BinProduct M_cart y x)). 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.Adjunctions.Core UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts