proposition: Lemma is_z_iso_from_BinCoproduct_to_BinCoproduct (CC CC' : BinCoproductCocone a b) : is_z_isomorphism (from_BinCoproduct_to_BinCoproduct CC CC').
proof: Proof. exists (from_BinCoproduct_to_BinCoproduct CC' CC). split; simpl. - apply pathsinv0. apply BinCoproduct_endo_is_identity. + rewrite assoc. unfold from_BinCoproduct_to_BinCoproduct. rewrite BinCoproductIn1Commutes. rewrite BinCoproductIn1Commutes. apply idpath. + rewrite assoc. unfold from_BinCoproduct_to_BinCoproduct. rewrite BinCoproductIn2Commutes. rewrite BinCoproductIn2Commutes. apply idpath. - apply pathsinv0. apply BinCoproduct_endo_is_identity. + rewrite assoc; unfold from_BinCoproduct_to_BinCoproduct. repeat rewrite BinCoproductIn1Commutes; apply idpath. + rewrite assoc; unfold from_BinCoproduct_to_BinCoproduct. repeat rewrite BinCoproductIn2Commutes; apply idpath. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.EqDiag UniMath.CategoryTheory.Limits.BinCoproducts