proposition: Proposition poset_to_underlying_prod_map_eq (fs : ∏ (j : J), x --> ys j) : ProductArrow _ C (underlying_Product E' ys (pr2 (EP ys))) fs = poset_to_underlying_prod_map fs.
proof: Proof. use is_prod_enriched_arrow_eq. - exact (pr2 (EP ys)). - intro j. refine (_ @ !(poset_to_underlying_prod_map_pr fs j)). apply (ProductPrCommutes _ C _ (underlying_Product E' ys (pr2 (EP ys))) _ fs). 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