proposition: Proposition poset_to_underlying_binary_coprod_map_eq (f : x₁ --> y) (g : x₂ --> y) : BinCoproductArrow (underlying_BinCoproduct E' x₁ x₂ (pr2 (EP x₁ x₂))) f g = poset_to_underlying_binary_coprod_map f g.
proof: Proof. use is_binary_coprod_enriched_arrow_eq. - exact (pr2 (EP x₁ x₂)). - refine (_ @ !(poset_to_underlying_binary_coprod_map_in1 f g)). apply (BinCoproductIn1Commutes C _ _ (underlying_BinCoproduct E' x₁ x₂ (pr2 (EP x₁ x₂))) _ f g). - refine (_ @ !(poset_to_underlying_binary_coprod_map_in2 f g)). apply (BinCoproductIn2Commutes C _ _ (underlying_BinCoproduct E' x₁ x₂ (pr2 (EP x₁ x₂))) _ 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.Colimits.EnrichedInitial UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedBinaryCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoequalizers UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCopowers 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 UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Coequalizers