proposition: Lemma cartesian_associator (x y z : V) : mon_lassociator x y z = BinProductArrow V (is_cartesian_BinProduct Ccart _ _) (semi_cart_tensor_pr1 Ccart _ _ · semi_cart_tensor_pr1 Ccart _ _) (semi_cart_tensor_pr2 Ccart _ _ ⊗^{M}_{r} z).
proof: Proof. use (BinProductArrowUnique _ _ _ (is_cartesian_BinProduct Ccart _ _)). - apply (mon_lassociator_pr1 Ccart). - refine (mon_lassociator_pr2 Ccart x y z @ _). unfold monoidal_cat_tensor_mor. now apply (when_bifunctor_becomes_rightwhiskering M). 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