fact: Definition is_dispBinProduct (c d : C) (P : BinProduct C c d) (cc : D c) (dd : D d) (pp : D (BinProductObject _ P)) (pp1 : pp -->[BinProductPr1 _ P] cc) (pp2 : pp -->[BinProductPr2 _ P] dd) : UU := ∏ (a : C) (f : a --> c) (g : a --> d) (aa : D a) (ff : aa -->[f] cc) (gg : aa -->[g] dd), ∃! (fgfg : aa -->[BinProductArrow _ P f g] pp), (fgfg ;; pp1 = transportb _ (BinProductPr1Commutes _ _ _ P _ f g) ff) × (fgfg ;; pp2 = transportb _ (BinProductPr2Commutes _ _ _ P _ f g) gg).
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