proposition: Lemma commutative_comonoid_to_comonoid_of_comonoids_laws (m : commutative_comonoid V) : comonoid_laws (symmetric_cat_commutative_comonoids V) (commutative_comonoid_to_comonoid_of_comonoids_data m).
proof: Proof. repeat split ; (use subtypePath ; [intro ; apply is_locally_propositional_commutative_comonoid | apply (pr12 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.Limits.BinProducts UniMath.CategoryTheory.DisplayedCats.Core 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.Displayed.Symmetric UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.Monoidal.Examples.MonoidalDialgebras UniMath.CategoryTheory.Monoidal.Comonoids.Category UniMath.CategoryTheory.Monoidal.Comonoids.Tensor UniMath.CategoryTheory.Monoidal.Comonoids.Monoidal UniMath.CategoryTheory.Monoidal.Comonoids.Symmetric UniMath.CategoryTheory.Monoidal.Comonoids.MonoidalCartesianBuilder