Proposition poset_enrichment_binary_prod_arr_eq {w x y : C} {f g : w --> poset_enrichment_obj_binary_prod x y} (p : f · poset_enrichment_obj_pr1 x y = g · poset_enrichment_obj_pr1 x y) (q : f · poset_enrichment_obj_pr2 x y = g · poset_enrichment_obj_pr2 x y) : f = g. Proof. use (BinProductArrowsEq _ _ _ (pr1 EBC x y)). - exact p. - exact q. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.CategoryOfPosets. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.PosetEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedTerminal. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedBinaryProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.PosetsMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Equalizers. Import MonoidalNotations.