proposition: Lemma binprod_to_pullback_inv (P : some_binprod (C / Z)) : pullback_to_binprod (binprod_to_pullback P) = P.
proof: Proof. induction P as [[A f] [[B g] P]]. unfold pullback_to_binprod , binprod_to_pullback. simpl. repeat (apply (total2_paths2_f (idpath _)); rewrite idpath_transportf). exact (slice_binprod_to_pullback_inv P). Qed.
imports: UniMath.MoreFoundations.Tactics UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.slicecat UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Pullbacks