proposition: Lemma Sum_weak_eta (x: Sum) : Sum_rec (C := Sum_as_set) Sum_inl Sum_inr x = x.
proof: Proof. induction x as [c H]. use total2_paths_f. - cbn. unfold pre_sum in c. apply funextsec; intro X. apply funextfun; intro f. apply funextfun; intro g. cbn in H; red in H. apply (H Sum_as_set X (fun x => pr1 x X f g)). - cbn. cbn in H; red in H. do 5 (apply funextsec; intro). apply setproperty. 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