Definition struct_pointed_poset_strict_with_smash_data : hset_struct_with_smash_data cartesian_struct_pointed_poset_strict pointed_struct_pointed_poset_strict. Proof. refine (_ ,, _). - exact pointed_PartialOrder_boolset. - intros X Y PX PY. use (pointed_quotient_poset (prod_pointed_PartialOrder PX PY) (smash_set PX PY) (smash_set_downward_closd PX PY)). exact (pointed_poset_strict_smash_eqrel_equiv PX PY). 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. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructuresSmashProduct.