proposition: Lemma Iteration_I_H_aux2 (av : V) (aη : I_{Mon_V} --> av) (aτ : H av --> av) (aα := av,, BinCoproductArrow (CP I_{ Mon_V} (H av)) aη aτ) (h : t --> av) : τ · h = # H h · aτ → η · h = aη → pr21 t_Initial -->[ h] pr2 aα.
proof: Proof. intros Hyp1 Hyp2. cbn. etrans. { apply cancel_postcomposition. apply BinCoproductArrowEta. } etrans. { apply postcompWithBinCoproductArrow. } etrans. 2: { apply pathsinv0, precompWithBinCoproductArrow. } apply maponpaths_12. + cbn. rewrite id_left. exact Hyp2. + cbn. exact Hyp1. 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.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.FunctorCoalgebras UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.Adamek UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.CompletelyIterativeAlgebras UniMath.CategoryTheory.Chains.OmegaCocontFunctors UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.CoproductsInActegories UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems UniMath.SubstitutionSystems.ActionScenarioForGenMendlerIteration_alt UniMath.SubstitutionSystems.SigmaMonoids