proposition: Lemma RotMorphismIsoEq2'_eq {C1 C2 : Complex A} (f : Morphism C1 C2) (i : hz) : let DS1 := to_BinDirectSums A (C1 (i + 1)) (C2 i) in let DS2 := to_BinDirectSums A (C2 (i + 1)) DS1 in to_binop DS2 DS2 (to_binop DS2 DS2 (to_Pr2 DS2 · to_Pr2 DS1 · to_inv (Diff C2 i · to_In1 DS2)) (to_Pr2 DS2 · to_Pr2 DS1 · (to_In2 DS1 · to_In2 DS2))) (to_binop DS2 DS2 (to_Pr1 DS2 · to_In1 DS2) (to_binop DS2 DS2 (to_Pr2 DS2 · to_Pr1 DS1 · f (i + 1) · to_In1 DS2) (to_Pr2 DS2 · to_Pr2 DS1 · Diff C2 i · to_In1 DS2))) = to_binop DS2 DS2 (identity DS2) (to_inv (to_Pr2 DS2 · to_Pr1 DS1 · to_binop (C1 (i + 1)) DS2 (to_inv (f (i + 1)) · to_In1 DS2) (to_In1 DS1 · to_In2 DS2))).
proof: Proof. intros DS1 DS2. use (pathscomp0 (RotMorphismEq2' f i)). fold DS1 DS2. rewrite (to_BinOpId DS2). apply maponpaths. apply maponpaths. rewrite to_premor_linear'. rewrite assoc. rewrite assoc. apply idpath. Qed.
imports: UniMath.Foundations.UnivalenceAxiom UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.NumberSystems.Integers UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinDirectSums UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Abelian UniMath.CategoryTheory.AbelianToAdditive UniMath.CategoryTheory.AdditiveFunctors UniMath.HomologicalAlgebra.Complexes UniMath.HomologicalAlgebra.KA UniMath.HomologicalAlgebra.TranslationFunctors