proposition: Lemma Tinf_monoid_mul_iso_precomp_with_colimIn (v : vertex nat_graph) : colimIn free_monoid_coeq_sequence_colim_unit v ⊗^{V}_{r} Tinf · z_iso_inv Tinf_monoid_mul_iso = coconeIn (colimCocone (free_monoid_coeq_sequence_rightwhisker_colim_on Tinf I_{V})) v.
proof: Proof. cbn. match goal with |- _ · colimArrow ?CC_ _ _ = _ => set (CC := CC_) end. etrans; [|exact (colimArrowCommutes CC _ _ v)]. apply cancel_postcomposition. apply pathsinv0. etrans. apply cancel_precomposition. apply (bifunctor_leftid 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