proposition: Lemma comonoid_disp_unit_laws : comonoid_laws M comonoid_disp_unit_data.
proof: Proof. refine (_ ,, _ ,, _). - unfold comonoid_laws_unit_left. cbn. rewrite (bifunctor_rightid M). rewrite id_right. apply monoidal_leftunitorisolaw. - unfold comonoid_laws_unit_right. cbn. rewrite (bifunctor_leftid M). rewrite id_right. rewrite mon_runitor_I_mon_lunitor_I. apply monoidal_leftunitorisolaw. - unfold comonoid_laws_assoc. cbn. rewrite ! assoc'. apply maponpaths. apply lunitorinv_preserves_leftwhiskering_with_unit. 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.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Examples.Fullsub UniMath.CategoryTheory.Monoidal.Examples.Sigma UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.Monoidal.Displayed.Symmetric UniMath.CategoryTheory.Monoidal.Comonoids.Category