proposition: Lemma Tinf_monoid_unit_left : monoid_laws_unit_left V Tinf_monoid_data.
proof: Proof. etrans. apply assoc. apply (pre_comp_with_z_iso_is_inj (is_inverse_in_precat_inv (monoidal_leftunitorisolaw V _))). apply pathsinv0. etrans. exact (pr2 (monoidal_leftunitorisolaw V _)). use colim_endo_is_identity. intro v. etrans. do 2 apply cancel_precomposition. apply cancel_postcomposition. exact (Tinf_monoid_mul_iso_precomp_with_colimIn 0). etrans. do 2 apply cancel_precomposition. { set (CC := free_monoid_coeq_sequence_rightwhisker_colim_on Tinf I_{ V}). apply (colimArrowCommutes CC Tinf _ 0). } etrans. apply cancel_precomposition. apply (pr2 (monoidal_leftunitorisolaw V _)). apply id_right. 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