Definition section_from_diagonal (isPb : isPullback H) : (∑ x : C⟦b, c⟧, x · g = f) -> ∑ s' : C⟦b, d⟧, s' · h = identity _ . Proof. intro X. use tpair. - use (PullbackArrow (make_Pullback _ isPb) _ (identity _ ) (pr1 X)). abstract (rewrite id_left ; apply (! (pr2 X))). - abstract (apply (PullbackArrow_PullbackPr1 (make_Pullback H isPb))). Defined.
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.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Monics. Definition UnivProductFromPullback (c d a : C) (f : a --> c) (g : a --> d): exists (UnivProductFromPullback c d a f g). Definition BinProductsFromPullbacks : BinProducts C := BinProduct_Pullback.