proposition: Lemma Tinf_monoid_unit_right : monoid_laws_unit_right V Tinf_monoid_data.
proof: Proof. etrans. apply assoc. apply (pre_comp_with_z_iso_is_inj (is_inverse_in_precat_inv (monoidal_rightunitorisolaw V _))). apply pathsinv0. etrans. exact (pr2 (monoidal_rightunitorisolaw V _)). use colim_endo_is_identity. intro v. etrans. apply assoc. etrans. apply cancel_postcomposition. exact (pathsinv0 (monoidal_rightunitorinvnat V _ _ _)). etrans. apply assoc'. etrans. apply cancel_precomposition. { etrans. apply assoc. apply cancel_postcomposition. etrans. apply assoc. etrans. apply cancel_postcomposition. apply (whiskerscommutes V (bifunctor_equalwhiskers V)). etrans. apply assoc'. apply cancel_precomposition. exact (Tinf_monoid_mul_iso_precomp_with_colimIn v). } etrans. apply cancel_precomposition. etrans. apply assoc'. apply cancel_precomposition. { set (CC := free_monoid_coeq_sequence_rightwhisker_colim_on Tinf I_{ V}). apply (colimArrowCommutes CC Tinf _ v). } exact (Tinf_monoid_unit_right_pointwise v). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Chains.Chains UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.ModelCategories.Generated.GenericFreeMonoid UniMath.ModelCategories.Generated.MonoidalHelpers UniMath.ModelCategories.Helpers