Definition hset_struct_smash_uncurry_fun {P : hset_cartesian_struct} {Pt : pointed_hset_struct P} (SP : hset_struct_with_smash P Pt) {PX PY PZ : category_of_hset_struct P} (g : hset_struct_with_smash_setquot_ob SP PX PY --> PZ) (x : pr11 PX) : PY --> PZ. Proof. simple refine (_ ,, _). - exact (λ y, pr1 g (setquotpr _ (x ,, y))). - abstract (use (hset_struct_comp P _ (pr2 g)) ; apply hset_struct_with_smash_setquotpr_r). Defined.
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.