proposition: Lemma diag_is_symmetric (x : V) : diag x · cartesian_to_braiding_data Ccart x x = diag x.
proof: Proof. apply (BinProductArrowsEq _ _ _ (is_cartesian_BinProduct Ccart x x)). - rewrite assoc'. etrans. { apply maponpaths. apply (BinProductPr1Commutes _ _ _ (is_cartesian_BinProduct Ccart x x)). } etrans. { apply (BinProductPr2Commutes _ _ _ (is_cartesian_BinProduct Ccart x x)). } apply pathsinv0, (BinProductPr1Commutes _ _ _ (is_cartesian_BinProduct Ccart x x)). - rewrite assoc'. etrans. { apply maponpaths. apply (BinProductPr2Commutes _ _ _ (is_cartesian_BinProduct Ccart x x)). } etrans. { apply (BinProductPr1Commutes _ _ _ (is_cartesian_BinProduct Ccart x x)). } apply pathsinv0, (BinProductPr2Commutes _ _ _ (is_cartesian_BinProduct Ccart x x)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.catiso UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.DisplayedCats.CatIsoDisplayed UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.Monoidal.Comonoids.Category UniMath.CategoryTheory.Monoidal.Comonoids.Tensor UniMath.CategoryTheory.Monoidal.Comonoids.Monoidal UniMath.CategoryTheory.Monoidal.Comonoids.Symmetric