proposition: Proposition poset_to_underlying_binary_prod_map_monotone {φ₁ φ₂ : x --> y₁} {ψ₁ ψ₂ : x --> y₂} (p : E x y₁ φ₁ φ₂) (q : E x y₂ ψ₁ ψ₂) : E _ _ (poset_to_underlying_binary_prod_map φ₁ ψ₁) (poset_to_underlying_binary_prod_map φ₂ ψ₂).
proof: Proof. exact (pr2 (@BinProductArrow _ _ _ (is_binary_prod_enriched_to_BinProduct E' _ _ (pr2 (EP y₁ y₂)) x) prod prod_pr1 prod_pr2) (φ₁ ,, ψ₁) (φ₂ ,, ψ₂) (p ,, q)). 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