proposition: Proposition poset_to_underlying_binary_prod_map_pr2 (f : x --> y₁) (g : x --> y₂) : poset_to_underlying_binary_prod_map f g · enriched_prod_cone_pr2 E' y₁ y₂ (pr1 (EP y₁ y₂)) = g.
proof: Proof. exact (eqtohomot (maponpaths pr1 (BinProductPr2Commutes category_of_posets _ _ (is_binary_prod_enriched_to_BinProduct E' _ _ (pr2 (EP y₁ y₂)) x) _ prod_pr1 prod_pr2)) (f ,, g)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Examples.CategoryOfPosets UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Examples.PosetEnriched UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedTerminal UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedBinaryProducts UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedProducts UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Examples.PosetsMonoidal UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Equalizers