proposition: Lemma isalghom_pr1foldr : is_algebra_mor _ Tree_alg Tree_alg (λ l, pr1 (foldr P'HSET P0' Pc' l)).
proof: Proof. apply BinCoproductArrow_eq_cor. - apply funextfun; intro x; destruct x. apply (maponpaths pr1 (foldr_leaf P'HSET P0' Pc')). - apply funextfun; intro x; destruct x as [a [l1 l2]]. apply (maponpaths pr1 (foldr_node P'HSET P0' Pc' a l1 l2)). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Inductives.Lists