proposition: Lemma Nat_η {C: HSET} (h: pr1hSet C -> pr1hSet C) (x: pr1hSet C) (f: Nat → pr1hSet C) (p : f Z = x) (q: funcomp S f = funcomp f h): f = Nat_rec h x.
proof: Proof. apply funextfun. intro n. eapply pathscomp0. - apply maponpaths. apply pathsinv0. apply Nat_weak_eta. - unfold Nat_rec. induction n as [n0 H]. cbn in H; red in H. cbn. apply H; assumption. Defined.
imports: UniMath.Foundations.Init UniMath.Foundations.Preamble UniMath.Foundations.PartA UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Structures