Proposition equalizer_from_pb_prod_map_eq : h · f · Δ = h · φ. Proof. unfold Δ, diagonalMap', φ. use BinProductArrowsEq. - rewrite !assoc'. rewrite !BinProductPr1Commutes. rewrite id_right. apply idpath. - rewrite !assoc'. rewrite !BinProductPr2Commutes. rewrite id_right. exact p. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Section EqualizersFromPullbackProducts. End EqualizersFromPullbackProducts. - exact (BinProductsFromPullbacks PB T).