proposition: Lemma CohomologyFunctorHomotopy_eq1 {C1 C2 : Complex (AbelianToAdditive A)} (H : ComplexHomot _ C1 C2) (i : hz) : KernelArrow (Kernel (Diff C1 i)) · transportf (precategory_morphisms (C1 i)) (maponpaths C2 (hzrminusplus i 1)) (H i · Diff C2 (i - 1)) · Diff C2 i = ZeroArrow (to_Zero A) (Kernel (Diff C1 i)) (C2 (i + 1)).
proof: Proof. induction (hzrminusplus i 1). cbn. rewrite <- assoc. rewrite <- assoc. set (tmp := DSq _ C2 (i - 1)). cbn in tmp. rewrite tmp. clear tmp. rewrite ZeroArrow_comp_right. rewrite ZeroArrow_comp_right. apply idpath. Qed.
imports: UniMath.Foundations.UnivalenceAxiom UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups 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.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