proposition: Lemma ComplexHomotComm3 {C1 C2 C3 C4 C5 C6 : ob ComplexHomot_Additive} {f1 : C1 --> C2} {f2 : C2 --> C3} {f3 : C3 --> C6} {g1 : C1 --> C4} {g2 : C4 --> C5} {g3 : C5 --> C6} (f1' : hfiber (# ComplexHomotFunctor) f1) (f2' : hfiber (# ComplexHomotFunctor) f2) (f3' : hfiber (# ComplexHomotFunctor) f3) (g1' : hfiber (# ComplexHomotFunctor) g1) (g2' : hfiber (# ComplexHomotFunctor) g2) (g3' : hfiber (# ComplexHomotFunctor) g3) (H : f1 · f2 · f3 = g1 · g2 · g3 ) : # ComplexHomotFunctor ((hfiberpr1 _ _ f1') · (hfiberpr1 _ _ f2') · (hfiberpr1 _ _ f3')) = # ComplexHomotFunctor ((hfiberpr1 _ _ g1') · (hfiberpr1 _ _ g2') · (hfiberpr1 _ _ g3')).
proof: Proof. rewrite functor_comp. rewrite functor_comp. rewrite functor_comp. rewrite functor_comp. rewrite (hfiberpr2 _ _ f1'). rewrite (hfiberpr2 _ _ f2'). rewrite (hfiberpr2 _ _ f3'). rewrite (hfiberpr2 _ _ g1'). rewrite (hfiberpr2 _ _ g2'). rewrite (hfiberpr2 _ _ g3'). exact H. Qed.
imports: UniMath.Foundations.UnivalenceAxiom UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.Tactics UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.NumberSystems.Integers UniMath.CategoryTheory.Core.Categories 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.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