proposition: Lemma weq_z_iso (af bg : C / x) : z_iso af bg ≃ ∑ h : z_iso (pr1 af) (pr1 bg), pr2 af = h · pr2 bg.
proof: Proof. apply (weqcomp (weqtotal2asstor _ _)). apply invweq. apply (weqcomp (weqtotal2asstor _ _)). apply weqfibtototal; intro h; simpl. apply (weqcomp (weqdirprodcomm _ _)). apply weqfibtototal; intro p. apply weqimplimpl. - intro hp; apply z_iso_to_slice_precat_z_iso; assumption. - intro hp; apply (slice_precat_z_iso_to_z_iso _ _ _ hp). - apply isaprop_is_z_isomorphism. - apply (isaprop_is_z_isomorphism(C:= C / x)). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis