Proposition pointed_struct_pointed_hset_with_smash_laws_enrich : hset_struct_with_smash_closed_laws_enrich pointed_struct_pointed_hset_with_smash_adj. Proof. split. - intros X Y Z. induction X as [ X x ]. induction Y as [ Y y ]. induction Z as [ Z z ]. use subtypePath. { intro ; apply setproperty. } use funextsec. use setquotunivprop'. { intro ; apply setproperty. } intro xz. cbn in *. apply idpath. - intros X Y Z. induction X as [ X x ]. induction Y as [ Y y ]. induction Z as [ Z z ]. use subtypePath. { intro ; apply setproperty. } use funextsec. intro a. use subtypePath. { intro ; apply setproperty. } use funextsec. intro b. cbn in *. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. 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.