fact: Definition disp_isProduct {d : I → C} (dd : ∏ (i : I), D (d i)) (p : Product I C d) (pp : D p) (ππ : ∏ (i : I), pp -->[ ProductPr _ _ p i ] dd i) : UU := ∏ (w : C) (ww : D w) (f : ∏ (i : I), w --> d i) (ff : ∏ (i : I), ww -->[ f i ] dd i), ∃! (hh : ww -->[ ProductArrow _ _ p f ] pp), ∏ (i : I), transportf (λ z, _ -->[ z ] _) (ProductPrCommutes _ _ _ p _ f i) (hh ;; ππ i) = ff i.
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