Proposition hset_struct_with_smash_closed_funspace_point {P : hset_cartesian_struct} {Pt : pointed_hset_struct P} {SP : hset_struct_with_smash P Pt} (PC : hset_struct_with_smash_closed_pointed SP) {X Y : hSet} (PX : P X) (PY : P Y) (x : X) : pr1 (hset_struct_point Pt (pr1 PC X Y PX PY)) x = hset_struct_point Pt PY. Proof. exact (pr2 PC 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.