Proposition hset_struct_smash_prod_lassociator_mor_alt_eq1 {X Y Z : category_of_hset_struct P} (z₁ z₂ : pr11 Z) : hset_struct_smash_prod_lassociator_mor_alt_fun (hset_struct_point (pr12 P) (pr2 (X ∧* Y))) z₁ = hset_struct_smash_prod_lassociator_mor_alt_fun (hset_struct_point (pr12 P) (pr2 (X ∧* Y))) z₂. Proof. etrans. { apply maponpaths_2. apply hset_struct_with_smash_closed_point_smash. } refine (!_). etrans. { apply maponpaths_2. apply hset_struct_with_smash_closed_point_smash. } use iscompsetquotpr. apply hinhpr. use inr ; cbn. unfold product_point_coordinate ; cbn. split. - use inl. apply idpath. - use inl. 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.