proposition: Lemma Product_classical_η (p: Product) : Pair (Proj1 p) (Proj2 p) = p.
proof: Proof. apply pathsinv0. eapply pathscomp0. - apply pathsinv0. apply Product_weak_η. - set (Product_η_inst := Product_η (C := Product_as_set) (fun x => Pair (Proj1 x) (Proj2 x))). cbn in Product_η_inst. apply toforallpaths in Product_η_inst. apply Product_η_inst. 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