proposition: Lemma dispBinProductArrowUnique {c d : C} (P : BinProduct C c d) (cc : D c) (dd : D d) (dP : dispBinProduct c d P cc dd) {x : C} (xx : D x) (f : x --> c) (g : x --> d) (ff : xx -->[f] cc) (gg : xx -->[g] dd) (kk : xx -->[BinProductArrow _ P f g] dispBinProductObject P dP) : kk ;; dispBinProductPr1 P dP = transportb _ (BinProductPr1Commutes _ _ _ P _ f g) ff -> kk ;; dispBinProductPr2 P dP = transportb _ (BinProductPr2Commutes _ _ _ P _ f g) gg -> kk = dispBinProductArrow P dP ff gg.
proof: Proof. intros H1 H2. apply path_to_ctr; split; assumption. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total