Lemma BinProductOfArrows_compxid {a b c d : C} (f:C⟦ b, c ⟧) (g:C⟦ c, d ⟧) : BinProductOfArrows _ (CC c a) (CC b a) f (identity a) · BinProductOfArrows _ (CC _ _) (CC _ _) g (identity a) = BinProductOfArrows _ (CC _ _) (CC _ _) (f·g) (identity a). Proof. now rewrite BinProductOfArrows_comp, id_right. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.Combinatorics.StandardFiniteSets. Section BinProductFromIso. End BinProductFromIso. Section BinProductsFromProducts. End BinProductsFromProducts. Section ProductsFromBinProducts. End ProductsFromBinProducts.