Proposition hset_struct_with_smash_setquotpr_r {P : hset_cartesian_struct} {Pt : pointed_hset_struct P} (SP : hset_struct_with_smash P Pt) {X Y : hSet} (PX : P X) (PY : P Y) (x : X) : mor_hset_struct P PY (SP X Y PX PY) (λ y, setquotpr (smash_eqrel P Pt PX PY) (x ,, y)). Proof. exact (pr12 (pr22 (pr222 SP) X Y PX PY) x). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits.