proposition: Lemma pullbackiso {A B D:C} {f : A --> D} {g : B --> D} (pb : Pullback f g) (pb' : Pullback f g) : ∑ (t : z_iso (PullbackObject pb) (PullbackObject pb')), t · PullbackPr1 pb' = PullbackPr1 pb × t · PullbackPr2 pb' = PullbackPr2 pb.
proof: Proof. use tpair. - use z_iso_from_Pullback_to_Pullback. - split. + use PullbackArrow_PullbackPr1. + use PullbackArrow_PullbackPr2. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Monics