proposition: Lemma Product_weak_η (x: Product) : Product_rec (C := Product_as_set) Pair x = x.
proof: Proof. induction x as [P H]. use total2_paths_f. - cbn. unfold pre_prod in P. apply funextsec; intro X. apply funextfun; intro f. cbn in H; red in H. exact (H Product_as_set X (fun x => pr1 x X f) Pair). - cbn. cbn in H. red in H. do 4 (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