proposition: Lemma AddEquivCounitUnit {A1 A2 : CategoryWithAdditiveStructure} (AE : AddEquiv A1 A2) (x : A1) : inv_from_z_iso (AddEquivCounitIso AE (AddEquiv1 AE x)) = # (AddEquiv1 AE) (AddEquivUnitIso AE x).
proof: Proof. use (post_comp_with_z_iso_is_inj (AddEquivCounitIso AE (AddEquiv1 AE x))). apply pathsinv0. rewrite (is_inverse_in_precat2 (AddEquivCounitIso AE ((AddEquiv1 AE) x))). exact (AddEquivLeftTriangle AE x). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.BinDirectSums