Definition type_products_struct_poset (I : UU) : hset_struct_type_prod struct_poset I. Proof. simple refine (_ ,, _). - exact (λ D fs, depfunction_poset _ fs). - repeat split ; cbn. + abstract (intros D PD i ; apply is_monotone_depfunction_poset_pr). + abstract (intros D PD W PW fs Hfs i ; apply is_monotone_depfunction_poset_pair ; exact Hfs). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits.