Definition isPullback_to_isBinProduct_cod_fib {x : C} {fy₁ fy₂ gp : C/x} (π₁ : gp --> fy₁) (π₂ : gp --> fy₂) (H : isPullback (fib_isPullback π₁ π₂)) : isBinProduct _ fy₁ fy₂ gp π₁ π₂. Proof. intros wh φq ψr. use iscontraprop1. - apply (isPullback_to_isBinproduct_cod_fib_unique H). - simple refine (_ ,, _ ,, _). + exact (isPullback_to_isBinproduct_cod_fib_mor H φq ψr). + apply isPullback_to_isBinproduct_cod_fib_pr1. + apply isPullback_to_isBinproduct_cod_fib_pr2. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.PullbackConstructions. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseEqualizers. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint. Section FromEqCodFib. End FromEqCodFib. Section FromUMP. End FromUMP.