Proposition hset_struct_smash_prod_rassociator_mor_alt_eq3 {X Y Z : ∁} (x₁ x₂ : pr11 X) : hset_struct_smash_prod_rassociator_mor_alt_fun x₁ (hset_struct_point (pr12 P) (pr2 (Y ∧* Z))) = hset_struct_smash_prod_rassociator_mor_alt_fun x₂ (hset_struct_point (pr12 P) (pr2 (Y ∧* Z))). Proof. etrans. { apply maponpaths. apply hset_struct_with_smash_closed_point_smash. } refine (!_). etrans. { apply maponpaths. apply hset_struct_with_smash_closed_point_smash. } use iscompsetquotpr. apply hinhpr ; cbn. use inr. unfold product_point_coordinate ; cbn. split. - use inr. apply idpath. - use inr. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructuresSmashProduct. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal.