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. intros a f g aa ff gg. exact (pr1 (pr2 (pr1 (is_dispBinProduct_dispBinProduct P dP _ _ _ _ ff gg)))). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total.