proposition: Lemma dispBinProductPr1Commutes {c d : C} (P : BinProduct C c d) (cc : D c) (dd : D d) (dP : dispBinProduct c d P cc dd): ∏ (a : C) (f : a --> c) (g : a --> d) (aa : D a) (ff : aa -->[f] cc) (gg : aa -->[g] dd), dispBinProductArrow P dP ff gg ;; dispBinProductPr1 P dP = transportb _ (BinProductPr1Commutes _ _ _ P _ f g) ff.
proof: Proof. intros a f g aa ff gg. exact (pr1 (pr2 (pr1 (is_dispBinProduct_dispBinProduct P dP _ _ _ _ ff gg)))). 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