proposition: Proposition isPullback_to_isBinproduct_cod_fib_unique : isaprop (∑ (fg : wh --> gp), fg · π₁ = φq × fg · π₂ = ψr).
proof: Proof. use invproofirrelevance. intros ζ₁ ζ₂. use subtypePath. { intro. apply isapropdirprod ; apply homset_property. } use eq_mor_cod_fib. use (MorphismsIntoPullbackEqual (isPullback_Pullback P)). - pose (s := maponpaths dom_mor (pr12 ζ₁ @ !(pr12 ζ₂))). rewrite !comp_in_cod_fib in s. exact s. - pose (s := maponpaths dom_mor (pr22 ζ₁ @ !(pr22 ζ₂))). rewrite !comp_in_cod_fib in s. exact s. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.PullbackConstructions UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.FiberwiseTerminal UniMath.CategoryTheory.DisplayedCats.FiberwiseProducts UniMath.CategoryTheory.DisplayedCats.FiberwiseEqualizers UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint