proposition: Lemma AddEquiv2Inj {A1 A2 : CategoryWithAdditiveStructure} (AE : AddEquiv A1 A2) {x y : A2} (f g : x --> y) (H : # (AddEquiv2 AE) f = # (AddEquiv2 AE) g) : f = g.
proof: Proof. apply (maponpaths (# (AddEquiv1 AE))) in H. use (pre_comp_with_z_iso_is_inj (AddEquivCounitIso AE x)). use (pathscomp0 (! AddEquivCounitComm AE _ _ f)). use (pathscomp0 _ (AddEquivCounitComm AE _ _ g)). exact (maponpaths (λ gg : _, gg · (AddEquivCounit AE) y) H). 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