proposition: Lemma to_ListK (A : HSET) : ∏ y : List A, to_List A (to_list A y) = y.
proof: Proof. apply listIndProp. * intro l; apply setproperty. * now unfold to_list; rewrite foldr_nil. * unfold to_list, to_List; intros a l IH. rewrite foldr_cons; simpl. apply maponpaths, pathsinv0. eapply pathscomp0; [eapply pathsinv0, IH|]; simpl. now destruct foldr. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.Combinatorics.Lists UniMath.MoreFoundations.PartA 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.PrecategoryBinProduct