proposition: Lemma BinProductArrow_as_diag (x y z : V) (f : V⟦x,y⟧) (g : V⟦x,z⟧) : diag x · f #⊗ g = BinProductArrow V (is_cartesian_BinProduct Ccart y z) f g.
proof: Proof. etrans. { apply maponpaths. apply (cartesian_tensor_mor Ccart). } etrans. { apply (postcompWithBinProductArrow _ (is_cartesian_BinProduct Ccart y z) (is_cartesian_BinProduct Ccart x x)). } now do 2 rewrite id_left. 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