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. 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.
Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.BinDirectSums. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Abelian. Require Import UniMath.CategoryTheory.AbelianToAdditive. Require Import UniMath.CategoryTheory.AdditiveFunctors. Require Import UniMath.HomologicalAlgebra.Complexes. Require Import UniMath.HomologicalAlgebra.KA. Require Import UniMath.HomologicalAlgebra.TranslationFunctors.