Definition SpecialGenMendlerIterationWithActegoryAndStrength : ∃! h : v ⊗_{Act} μF --> y, charprop_SpecialGenMendlerIterationWithActegoryAndStrength h. Proof. simple refine (iscontrretract _ _ _ (SpecialGenMendlerIterationWithActegory (Const_plus_H c0) HF y (Const_plus_H y) (BinCoproductArrow (CP _ _) (identity y) ρ) IL HL θ')). - intros [h Hyp]. exists h. apply charpropequivsingleeq. apply instanceequivsingle. exact Hyp. - intros [h Hyp]. exists h. apply charpropequivsingleeq in Hyp. apply instanceequivsingle in Hyp. exact Hyp. - intros [h Hyp]. use total2_paths_f. + apply idpath. + apply isaprop_charprop_SpecialGenMendlerIterationWithActegoryAndStrength. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.Chains.Chains. Require Import UniMath.CategoryTheory.Chains.Adamek. Require Import UniMath.CategoryTheory.Chains.OmegaCocontFunctors. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Actegories.CoproductsInActegories. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.SubstitutionSystems.GenMendlerIteration_alt. Require Import UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems. Import BifunctorNotations. Import ActegoryNotations.