Proposition hset_struct_with_smash_point_smash {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) : hset_struct_point Pt (SP X Y PX PY) = setquotpr _ (hset_struct_point Pt PX ,, hset_struct_point Pt PY). Proof. exact (pr122 SP X Y PX PY). 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.