proposition: Proposition hset_struct_smash_prod_lassociator_mor_alt_eq3 {X Y Z : category_of_hset_struct P} (xy₁ xy₂ : pr11 (X ∧* Y)) : hset_struct_smash_prod_lassociator_mor_alt_fun xy₁ (hset_struct_point (pr12 P) (pr2 Z)) = hset_struct_smash_prod_lassociator_mor_alt_fun xy₂ (hset_struct_point (pr12 P) (pr2 Z)).
proof: Proof. revert xy₁. use setquotunivprop'. { intro. apply setproperty. } intros xy₁. induction xy₁ as [ x₁ y₁ ]. revert xy₂. use setquotunivprop'. { intro. apply setproperty. } intros xy₂. induction xy₂ as [ x₂ y₂ ]. use iscompsetquotpr. apply hinhpr ; cbn. use inr. unfold product_point_coordinate ; cbn. split ; use inr ; refine (_ @ !(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. - use iscompsetquotpr. apply hinhpr ; cbn. use inr. unfold product_point_coordinate ; cbn. split. + use inr. apply idpath. + use inr. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits UniMath.CategoryTheory.DisplayedCats.Structures.StructuresSmashProduct UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal