proposition: Proposition poset_to_underlying_binary_prod_map_eq (f : x --> y₁) (g : x --> y₂) : BinProductArrow C (underlying_BinProduct E' y₁ y₂ (pr2 (EP y₁ y₂))) f g = poset_to_underlying_binary_prod_map f g.
proof: Proof. use is_binary_prod_enriched_arrow_eq. - exact (pr2 (EP y₁ y₂)). - refine (_ @ !(poset_to_underlying_binary_prod_map_pr1 f g)). apply (BinProductPr1Commutes C _ _ (underlying_BinProduct E' y₁ y₂ (pr2 (EP y₁ y₂))) _ f g). - refine (_ @ !(poset_to_underlying_binary_prod_map_pr2 f g)). apply (BinProductPr2Commutes C _ _ (underlying_BinProduct E' y₁ y₂ (pr2 (EP y₁ y₂))) _ 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