proposition: Lemma is_symmetric_isPullback : isPullback H -> isPullback (!H).
proof: Proof. intro isPb. use make_isPullback. intros e x y Hxy. set (Pb := make_Pullback _ isPb). use tpair. - use tpair. + use (PullbackArrow Pb). * assumption. * assumption. * abstract (apply (!Hxy)). + abstract (split; [apply (PullbackArrow_PullbackPr2 Pb) | apply (PullbackArrow_PullbackPr1 Pb)]). - abstract (intro t; apply subtypePath; [intro; apply isapropdirprod; apply C | destruct t as [t Ht]; cbn; apply PullbackArrowUnique; [apply (pr2 Ht) | apply (pr1 Ht)]]). 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