instPartialOrder 📖 | CompOp | 1014 mathmath: SSet.OneTruncation₂.nerveEquiv_apply, CategoryTheory.Triangulated.SpectralObject.Hom.comm, HomotopyCategory.spectralObjectMappingCone_δ'_app, CategoryTheory.Abelian.SpectralObject.δ_eq_zero_of_isIso₂, finsetImage_castLE_Iio, image_addNat_Ioo, CategoryTheory.Abelian.SpectralObject.H_map_twoδ₂Toδ₁_toCycles_assoc, SSet.stdSimplex.objMk_bijective, image_castLE_Ioo, card_Ioi, CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin_deg, CategoryTheory.Abelian.SpectralObject.exact₁', CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_zero, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.ComposableArrows.isoMk₁_hom_app, CategoryTheory.ComposableArrows.exact_iff_δlast, preimage_natAdd_Iio_natAdd, map_succEmb_Iio, CategoryTheory.ComposableArrows.sc'MapIso_inv, finsetImage_natAdd_Ioc, CategoryTheory.Abelian.SpectralObject.δToCycles_iCycles, SSet.stdSimplex.mem_nonDegenerate_iff_strictMono, SSet.stdSimplex.coe_triangle_down_toOrderHom, SimplexCategory.eq_const_of_zero, addNatOrderEmb_toEmbedding, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, image_castLE_Icc, CategoryTheory.Abelian.SpectralObject.leftHomologyDataShortComplex_H, Ioi_succ, CategoryTheory.nerve.σ_obj, preimage_val_Ici_val, strictMono_pred_comp, CategoryTheory.ShortComplex.mapToComposableArrows_app_0, CategoryTheory.ComposableArrows.IsComplex.zero'_assoc, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_π, CategoryTheory.Abelian.SpectralObject.EIsoH_hom_opcyclesIsoH_inv_assoc, isAddFreimanIso_Iio, CategoryTheory.Abelian.SpectralObject.liftOpcycles_fromOpcycles_assoc, Ico_add_one_eq_Ioo, map_castLEEmb_Ioc, finsetImage_castLE_Ioo, preimage_castAdd_Ico_castAdd, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerve_hom_app, CategoryTheory.ComposableArrows.isIso_iff₂, CategoryTheory.Abelian.SpectralObject.zero₂_assoc, map_revPerm_Ioc, image_val_Iic, map_castAddEmb_Ico, predAbove_left_monotone, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCycles_X₁, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_zero, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesEIso_hom_τ₁, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_distinguished, finsetImage_addNat_Ioi, attachFin_Iic, CategoryTheory.nerve.δ₂_zero, CategoryTheory.Abelian.SpectralObject.instMonoFromOpcycles, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, preimage_natAdd_Ioi_natAdd, CategoryTheory.instMonoMap'KernelCokernelCompSequenceOfNatNat, preimage_rev_Ico, CategoryTheory.ComposableArrows.homMk₅_app_five, CategoryTheory.Abelian.SpectralObject.sc₂_X₃, finsetImage_addNat_Ici, finsetImage_castSucc_Ioo, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcycles_X₂, image_succ_Iic, range_natAdd_eq_Ici, CategoryTheory.Abelian.SpectralObject.toCycles_πE_d, preimage_castSucc_Iic_castSucc, map_castLEEmb_Iic, card_Ici, prod_Ico_succ, orderHom_injective_iff, CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_zero, finsetImage_natAdd_Icc, CategoryTheory.Abelian.SpectralObject.δToCycles_πE, SimplexCategory.const_comp, SimplexCategory.toMk₁_apply_eq_zero_iff, map_addNatEmb_Ici, CategoryTheory.ComposableArrows.scMap_τ₁, CategoryTheory.Abelian.SpectralObject.shortComplex_X₂, strictAnti_vecEmpty, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_inv_app, finsetImage_val_Ioi, CategoryTheory.Abelian.SpectralObject.d_ιE_fromOpcycles, SimplexCategory.toTopHomeo_symm_naturality, CategoryTheory.Abelian.SpectralObject.toCycles_πE_d_assoc, Matrix.det_vandermonde, orderPred_succ, prod_Ioo_castLE, attachFin_Ioo_eq_Ioi, image_natAdd_Icc, find_mono_of_le, preimage_rev_Ici, CategoryTheory.Abelian.SpectralObject.mono_H_map_twoδ₁Toδ₀, CategoryTheory.Abelian.SpectralObject.δ_toCycles, finsetImage_val_Ioo, preimage_succ_Ioi_succ, CategoryTheory.Abelian.SpectralObject.δ_δ_assoc, CategoryTheory.Abelian.SpectralObject.opcyclesIso_hom_δFromOpcycles, image_natAdd_Ico, CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin_i₃, map_natAddEmb_Ici, CategoryTheory.ComposableArrows.homMk₃_app_three, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_i, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_EIsoH_inv, SSet.prodStdSimplex.orderHomOfSimplex_coe, CategoryTheory.ComposableArrows.homMk₄_app_four, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_H, strictMono_succAbove, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₀_le', AugmentedSimplexCategory.eqToHom_toOrderHom, sum_sum_eq_sum_triangle_add, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₃, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₁, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_one, Matrix.det_projVandermonde, SimplexCategory.toTopHomeo_naturality_apply, finsetImage_castAdd_Iio, CategoryTheory.Abelian.SpectralObject.δToCycles_cyclesIso_inv_assoc, preimage_castSucc_Ico_castSucc, CategoryTheory.Abelian.SpectralObject.cyclesMap_id, CategoryTheory.Abelian.SpectralObject.cyclesIso_hom_i, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_zero, preimage_val_Ioc_val, finsetImage_castSucc_Ioc, SSet.prodStdSimplex.objEquiv_apply_fst, SSet.stdSimplex.map_id, CategoryTheory.Abelian.SpectralObject.pOpcycles_δFromOpcycles, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_one, CategoryTheory.ComposableArrows.whiskerLeft_obj, sum_Icc_castAdd, List.SortedGT.strictAnti, sum_Ico_castSucc, image_addNat_Ici, CategoryTheory.Triangulated.TStructure.ω₁δ_naturality_assoc, preimage_natAdd_Icc_natAdd, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_iso_inv, preimage_succ_Icc_succ, preimage_succ_Iic_succ, image_natAdd_Ici, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_two, castSuccOrderEmb_toEmbedding, sum_Iic_cast, CategoryTheory.Abelian.SpectralObject.δ_δ, CategoryTheory.Abelian.SpectralObject.cyclesMap_i, orderPred_zero, Equiv.Perm.sign_eq_prod_prod_Ioi, CategoryTheory.Abelian.SpectralObject.cyclesIso_hom_i_assoc, map_addNatEmb_Ioi, Equiv.Perm.prod_Ioi_comp_eq_sign_mul_prod, CategoryTheory.ShortComplex.mapToComposableArrows_app_1, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₂, Tuple.monotone_proj, finsetImage_castAdd_Iic, finsetImage_succ_Iio, CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac_assoc, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, CategoryTheory.Abelian.SpectralObject.HasSpectralSequence.isZero_H_obj_mk₁_i₀_le, Module.Basis.flag_mono, SimplexCategory.mkOfSucc_homToOrderHom_one, map_castAddEmb_Ici, map_finCongr_Ioo, CategoryTheory.Triangulated.TStructure.spectralObject_ω₁, CategoryTheory.Abelian.SpectralObject.toCycles_descCycles, natAddOrderEmb_toEmbedding, CategoryTheory.Abelian.SpectralObject.fromOpcycles_H_map_twoδ₁Toδ₀, CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin_i₀, SimplexCategory.Hom.mk_toOrderHom_apply, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, CategoryTheory.ComposableArrows.homMk₂_app_two, finsetImage_castLE_Ico, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₃_le', CategoryTheory.Abelian.SpectralObject.comp_hom, SSet.prodStdSimplex.strictMono_orderHomOfSimplex_iff, monotone_vecEmpty, CategoryTheory.Abelian.SpectralObject.EToCycles_i_assoc, CategoryTheory.Localization.essSurj_mapComposableArrows_of_hasRightCalculusOfFractions, SSet.stdSimplex.face_eq_ofSimplex, preimage_addNat_Iic_addNat, prod_Ioo_castAdd, Monotone.vecCons, prod_Icc_div, finsetImage_succ_Ico, image_natAdd_Ioo, SSet.prodStdSimplex.objEquiv_δ_apply, CategoryTheory.ComposableArrows.homMk₅_app_zero, CategoryTheory.ComposableArrows.precomp_obj, Tuple.sort_eq_refl_iff_monotone, CategoryTheory.ComposableArrows.Precomp.map_zero_succ_succ, CategoryTheory.Abelian.SpectralObject.epi_H_map_twoδ₁Toδ₀', sum_Ioo_succ, CategoryTheory.Triangulated.TStructure.ω₁_map, CategoryTheory.Abelian.SpectralObject.toCycles_cyclesMap, strictMono_vecEmpty, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_two, prod_Iic_div, sum_Iic_castAdd, preimage_castAdd_Ici_castAdd, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_iso_hom, CategoryTheory.Abelian.SpectralObject.IsFirstQuadrant.isZero₂, CategoryTheory.Abelian.SpectralObject.comp_hom_assoc, preimage_cast_Ici, CategoryTheory.Abelian.SpectralObject.πE_ιE, image_castLE_Iio, CategoryTheory.Abelian.SpectralObject.fromOpcycles_H_map_twoδ₁Toδ₀_assoc, attachFin_Icc, map_finCongr_Iic, SSet.prodStdSimplex.objEquiv_naturality, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, preimage_cast_Iic, CategoryTheory.ComposableArrows.isoMkSucc_hom, map_revPerm_Ico, CategoryTheory.Abelian.SpectralObject.p_opcyclesIso_inv, image_castSucc_Ioc, finsetImage_castAdd_Ico, CategoryTheory.Abelian.SpectralObject.πE_EIsoH_hom_assoc, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE_X₃, extDeriv_apply_vectorField, CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom, HomologicalComplex.HomologySequence.instEpiMap'ComposableArrows₃OfNatNat, CategoryTheory.ComposableArrows.isoMk₅_inv, attachFin_Ico_eq_Ici, CategoryTheory.ComposableArrows.homMkSucc_app_zero, CategoryTheory.Abelian.SpectralObject.isIso_H_map_twoδ₁Toδ₀, CategoryTheory.ComposableArrows.exact_iff_δ₀, card_Ico, finsetImage_cast_Ioi, SimplexCategory.toTop_map, image_castAdd_Ioo, CategoryTheory.Abelian.SpectralObject.isIso_fromOpcycles, CategoryTheory.Abelian.SpectralObject.zero₃, CategoryTheory.ComposableArrows.homMk₄_app_three, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, Ioo_add_one_eq_Ioc, CategoryTheory.Abelian.SpectralObject.rightHomologyDataShortComplex_ι, sum_Ioi_cast, map_castLEEmb_Ico, strictMono_castPred_comp, sum_Ico_succ, preimage_val_Ioi_val, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_g, isAddFreimanIso_Iic, preimage_succ_Ioc_succ, image_succ_Ico, finsetImage_cast_Iio, finsetImage_val_Iio, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_g, SimplexCategory.II.map'_map', CategoryTheory.Abelian.SpectralObject.toCycles_cyclesMap_assoc, CategoryTheory.Abelian.SpectralObject.exact₂', Ico_add_one_eq_Icc, CategoryTheory.ComposableArrows.homMk₄_app_zero, SimplexCategory.toTop₀_map, preimage_succ_Iio_succ, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₁, PartialOrder.mem_nerve_nonDegenerate_iff_injective, SSet.prodStdSimplex.objEquiv_apply_snd, CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_zero, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_p, finsetImage_cast_Icc, CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_map, SimplexCategory.congr_toOrderHom_apply, CategoryTheory.Abelian.SpectralObject.p_opcyclesToE, CategoryTheory.Triangulated.SpectralObject.triangle_obj₂, CategoryTheory.Abelian.SpectralObject.rightHomologyDataShortComplex_H, finsetImage_castAdd_Ici, image_castSucc_Icc, finsetImage_cast_Ici, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv_hom_id, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', sum_Ioo_castLE, preimage_natAdd_Ioo_natAdd, image_val_Ici, sum_Ioc_castAdd, prod_Ici_cast, addRothNumber_eq_rothNumberNat, CategoryTheory.ComposableArrows.map'_comp, CategoryTheory.ComposableArrows.IsComplex.zero_assoc, preimage_castLE_Ioo_castLE, CategoryTheory.Abelian.SpectralObject.ιE_δFromOpcycles_assoc, StrictMono.vecCons, CategoryTheory.Abelian.SpectralObject.isIso_toCycles, preimage_castLE_Ioi_castLE, CategoryTheory.ComposableArrows.isoMk₄_hom, Equiv.Perm.sign_eq_prod_prod_Iio, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₃, Polynomial.card_support_eq, map_revPerm_Ici, SSet.horn_obj, CategoryTheory.Abelian.SpectralObject.shortComplexMap_id, CategoryTheory.Abelian.SpectralObject.liftE_ιE_fromOpcycles, CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor_map, sum_Ioo_cast, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, prod_Ioc_castLE, image_val_Ioc, finsetImage_castSucc_Ico, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₀_le, finsetImage_addNat_Ioc, map_castLEEmb_Ioo, sum_Icc_cast, preimage_rev_Icc, image_succ_Ici, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesEIso_hom_τ₃, CategoryTheory.Abelian.SpectralObject.isZero₁_of_isFirstQuadrant, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac_assoc, CategoryTheory.ComposableArrows.δ₀Functor_obj_map, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcycles_X₂, SSet.stdSimplex.face_obj, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, CategoryTheory.Abelian.SpectralObject.kernelSequenceCyclesE_g, sum_Ici_cast, map_revPerm_Icc, sum_Iic_castLE, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_one, CategoryTheory.ComposableArrows.isoMkSucc_inv, image_succ_Ioc, CategoryTheory.Abelian.SpectralObject.fromOpcyles_δ_assoc, preimage_castAdd_Ioo_castAdd, prod_Ioc_castSucc, SSet.Truncated.spine_map_vertex, SimplexCategory.id_toOrderHom, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCycles_X₂, CategoryTheory.Abelian.SpectralObject.sc₂_g, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv_hom_id_assoc, List.SortedGT.strictAnti_get, CochainComplex.mappingConeCompTriangle_mor₃_naturality, List.sortedGT_iff_strictAnti_get, prod_Ioo_cast, classifyingSpaceUniversalCover_map, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerve_inv_app, CategoryTheory.Abelian.SpectralObject.toCycles_Ψ_assoc, CategoryTheory.Abelian.SpectralObject.isZero₁_of_isThirdQuadrant, finsetImage_rev_Iic, List.SortedLE.monotone_get, CategoryTheory.Abelian.SpectralObject.H_map_twoδ₂Toδ₁_toCycles, sum_Ioc_castLE, sum_Iio_castLE, preimage_val_Iic_val, preimage_castAdd_Ioi_castAdd, finsetImage_val_Ioc, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, map_revPerm_Ioi, Iio_last_eq_map, CategoryTheory.Abelian.SpectralObject.δToCycles_πE_assoc, map_addNatEmb_Ico, preimage_val_Ico_val, preimage_cast_Ioi, CategoryTheory.Abelian.SpectralObject.sc₁_X₁, List.SortedLE.monotone, CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_obj, Matrix.IsHermitian.eigenvalues₀_antitone, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, List.sorted_gt_ofFn_iff, map_castLEEmb_Icc, AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply, prod_Iio_castSucc, CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin_i₂, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_hom_app, val_strictMono, preimage_addNat_Ioi_addNat, preimage_addNat_Iio_addNat, image_castAdd_Iic, SimplexCategory.toMk₁_of_le_castSucc, CategoryTheory.ComposableArrows.sc'MapIso_hom, preimage_natAdd_Ioc_natAdd, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCycles_f, SSet.stdSimplex.coe_edge_down_toOrderHom, map_valEmbedding_Ici, CategoryTheory.ComposableArrows.opEquivalence_inverse_obj, SimplexCategory.toTopHomeo_symm_naturality_apply, CategoryTheory.Abelian.SpectralObject.zero₂, SimplexCategory.eqToHom_toOrderHom, HomotopyCategory.composableArrowsFunctor_obj, prod_Icc_castLE, CategoryTheory.Triangulated.TStructure.spectralObjectFunctor_map_hom, preimage_castAdd_Iio_castAdd, map_succEmb_Ioi, CategoryTheory.ComposableArrows.scMapIso_inv, image_val_Iio, finsetImage_rev_Ioc, map_finCongr_Ici, preimage_succ_Ico_succ, LTSeries.strictMono, List.Sorted.get_mono, CategoryTheory.Abelian.SpectralObject.toCycles_πE_descE_assoc, card_Icc, SSet.OneTruncation₂.nerveEquiv_symm_apply_map, CategoryTheory.ComposableArrows.mk₁_obj, CategoryTheory.ComposableArrows.map'_inv_eq_inv_map', image_castAdd_Ici, SSet.stdSimplex.isoNerve_hom_app_apply, CategoryTheory.ComposableArrows.homMk₅_app_two, predAbove_right_monotone, CategoryTheory.ComposableArrows.whiskerLeft_map, CategoryTheory.ComposableArrows.Exact.isIso_map', CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_EIsoH_inv_assoc, finsetImage_rev_Ioi, prod_Iic_castSucc, preimage_castLE_Ioc_castLE, PartialOrder.mem_range_nerve_σ_iff, finsetImage_succ_Iic, strictMono_addNat, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_inv_π_assoc, preimage_rev_Ioi, antitone_vecCons, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_hom_π_assoc, CategoryTheory.Abelian.SpectralObject.opcyclesMap_fromOpcycles, CategoryTheory.Abelian.SpectralObject.shortComplexMap_comp_assoc, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_X₂, CategoryTheory.Abelian.SpectralObject.instEpiToCycles, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.ComposableArrows.mapFunctorArrows_app, SimplexCategory.II.castSucc_mem_finset_iff, CategoryTheory.ShortComplex.mapToComposableArrows_comp, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesE_X₁, prod_Ioi_cast, preimage_succ_Ioo_succ, CategoryTheory.Functor.mapComposableArrows_obj_map, CategoryTheory.Abelian.SpectralObject.Ψ_fromOpcycles_assoc, finsetImage_castAdd_Ioi, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_ι, CategoryTheory.Abelian.SpectralObject.exact₃', prod_Iio_castAdd, SimplexCategory.mono_iff_injective, CategoryTheory.Abelian.SpectralObject.p_fromOpcycles_assoc, CategoryTheory.Abelian.SpectralObject.πE_EIsoH_hom, finsetImage_natAdd_Ico, clamp_monotone, sum_Ico_cast, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, CategoryTheory.ComposableArrows.isoMk₂_inv, castLEOrderEmb_toEmbedding, CategoryTheory.Abelian.SpectralObject.isZero₂_of_isFirstQuadrant, orderPred_apply, image_castSucc_Ici, finsetImage_val_Ico, CategoryTheory.Abelian.SpectralObject.IsFirstQuadrant.isZero₁, prod_Ico_cast, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_obj, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_ω₁, CategoryTheory.Triangulated.TStructure.ω₁_obj, CategoryTheory.Abelian.SpectralObject.liftOpcycles_fromOpcycles, map_succEmb_Ici, SimplexCategory.II.map'_eq_last_iff, CategoryTheory.Abelian.SpectralObject.IsThirdQuadrant.isZero₂, find_congr, preimage_rev_Ioc, map_natAddEmb_Icc, prod_Ioi_succ, CategoryTheory.Triangulated.SpectralObject.triangle_mor₂, CategoryTheory.Abelian.SpectralObject.cokernelIsoCycles_hom_fac_assoc, finsetImage_cast_Ioo, image_natAdd_Ioc, card_Iio, CategoryTheory.ShortComplex.mapToComposableArrows_app_2, CategoryTheory.Abelian.SpectralObject.iCycles_δ, CategoryTheory.ComposableArrows.naturality', finsetImage_val_Ici, preimage_natAdd_Ico_natAdd, SimplexCategory.rev_map_apply, strictMono_succ, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesEIso_inv_τ₁, image_castSucc_Ioi, cast_strictMono, CategoryTheory.Abelian.SpectralObject.Hom.comm, strictMono_iff_lt_succ, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_f, CategoryTheory.instEpiMap'KernelCokernelCompSequenceOfNatNat, card_Ioo, map_valEmbedding_Icc, CategoryTheory.ComposableArrows.sc'Map_τ₁, map_castSuccEmb_Ici, CategoryTheory.ComposableArrows.isoMk_inv, image_castAdd_Icc, SimplexCategory.mkOfSucc_homToOrderHom_zero, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_hom_π, attachFin_Ico, CategoryTheory.Abelian.SpectralObject.kernelSequenceCycles_X₂, prod_Iic_cast, SimplexCategory.II.map'_succAboveOrderEmb, image_castAdd_Ioc, SimplexCategory.instReflectsIsomorphismsForgetOrderHomFinHAddNatLenOfNat, List.sortedLT_iff_strictMono_get, finsetImage_addNat_Ico, extDerivWithin_apply_vectorField, CategoryTheory.Limits.FormalCoproduct.cechFunctor_map_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, map_natAddEmb_Ico, CategoryTheory.Abelian.SpectralObject.p_opcyclesMap_assoc, CategoryTheory.Abelian.SpectralObject.d_ιE_fromOpcycles_assoc, CategoryTheory.ComposableArrows.mk₀_obj, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, Tuple.comp_sort_eq_comp_iff_monotone, SimplexCategory.toTopHomeo_naturality, CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_one, image_addNat_Icc, CategoryTheory.Triangulated.SpectralObject.id_hom, CategoryTheory.ComposableArrows.homMkSucc_app_succ, preimage_castLE_Iic_castLE, preimage_addNat_Icc_addNat, CategoryTheory.Abelian.SpectralObject.sc₂_X₁, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_inv_hom_id_assoc, image_addNat_Ioi, SSet.stdSimplex.monotone_apply, List.SortedGE.antitone, CategoryTheory.ComposableArrows.mk₁_map, preimage_castLE_Icc_castLE, Finset.prod_fin_Icc_eq_prod_nat_Icc, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_two, castAddOrderEmb_toEmbedding, SimplexCategory.II.map'_eq_castSucc_iff, PartialOrder.mem_nerve_nonDegenerate_iff_strictMono, CategoryTheory.ComposableArrows.isComplex₂_iff, SSet.prodStdSimplex.objEquiv_map_apply, predAboveOrderHom_coe, List.sorted_le_ofFn_iff, CategoryTheory.Abelian.SpectralObject.zero₁, image_succ_Ioi, CategoryTheory.Limits.FormalCoproduct.instHasLimitWidePullbackShapeToTypeSimplexCategoryOrderHomFinHAddNatLenOfNatWideCospanObjInclFromIsTerminalIncl, CategoryTheory.Abelian.SpectralObject.δ_naturality_assoc, CategoryTheory.ComposableArrows.δlastFunctor_obj_obj, monotone_pred_comp, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CompositionSeries.strictMono, CategoryTheory.Limits.FormalCoproduct.cech_map, SSet.horn.edge₃_coe_down, orderSucc_last, CategoryTheory.Abelian.SpectralObject.δ_naturality, CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom_assoc, map_castAddEmb_Ioc, CategoryTheory.Abelian.SpectralObject.sc₃_X₁, List.sortedLT_finRange, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_naturality_app_assoc, SSet.stdSimplex.const_down_toOrderHom, finsetImage_succ_Ioo, CategoryTheory.ComposableArrows.scMapIso_hom, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_obj, attachFin_Ioo, List.Sorted.get_strictMono, prod_Ioo_castSucc, map_revPerm_Ioo, CategoryTheory.Abelian.SpectralObject.leftHomologyDataShortComplex_π, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_three, CategoryTheory.Triangulated.SpectralObject.distinguished', preimage_castAdd_Icc_castAdd, Algebra.discr_powerBasis_eq_prod, CategoryTheory.Triangulated.SpectralObject.triangle_mor₁, CategoryTheory.ComposableArrows.isoMk₃_hom, Tuple.eq_sort_iff, finsetImage_castSucc_Ioi, List.sortedGT_ofFn_iff, CategoryTheory.Abelian.SpectralObject.p_opcyclesIso_inv_assoc, List.SortedLT.strictMono_get, StrictAnti.vecCons, CategoryTheory.ComposableArrows.whiskerLeftFunctor_map_app, CategoryTheory.Abelian.SpectralObject.shortComplexMap_τ₂, map_valEmbedding_Ioi, finsetImage_natAdd_Ioi, CategoryTheory.ComposableArrows.scMap_τ₃, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_zero, CategoryTheory.ComposableArrows.δlastFunctor_map_app, SimplexCategoryGenRel.simplicialEvalσ_of_isAdmissible, finsetImage_val_Icc, image_val_Ioi, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_K, CategoryTheory.Abelian.SpectralObject.δ_pOpcycles_assoc, map_castLEEmb_Iio, preimage_cast_Iio, image_castAdd_Ioi, CategoryTheory.Abelian.SpectralObject.id_hom, orderSucc_apply, succAboveOrderEmb_toEmbedding, HomotopyCategory.composableArrowsFunctor_map, SimplexCategory.II.monotone_map', CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, prod_Ico_castSucc, strictMono_castSucc, CategoryTheory.ComposableArrows.sc'Map_τ₃, CategoryTheory.nerve.δ_obj, map_succEmb_Ioo, preimage_castSucc_Iio_castSucc, sum_Iic_sub, map_valEmbedding_Ioo, CategoryTheory.Abelian.SpectralObject.shortComplexMap_τ₃, sum_Iio_castAdd, CategoryTheory.Abelian.SpectralObject.map_comp, preimage_rev_Iio, CategoryTheory.Abelian.SpectralObject.sc₂_X₂, orderPred_eq, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_inv_π, monotone_castPred_comp, CategoryTheory.ComposableArrows.homMk₄_app_one, map_castSuccEmb_Icc, CategoryTheory.Abelian.SpectralObject.cokernelIsoCycles_hom_fac, SSet.stdSimplex.δ_objMk₁_of_le, SSet.spine_map_vertex, sum_Ioo_castAdd, CategoryTheory.Abelian.SpectralObject.δToCycles_cyclesIso_inv, SSet.prodStdSimplex.le_orderHomOfSimplex, image_castSucc_Ico, CategoryTheory.ComposableArrows.homMk₅_app_three, CategoryTheory.Abelian.SpectralObject.p_descOpcycles, sum_Iio_cast, preimage_addNat_Ici_addNat, Finset.sum_fin_Icc_eq_sum_nat_Icc, Iio_castSucc, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcyclesE_X₁, CategoryTheory.Abelian.SpectralObject.πE_ιE_assoc, map_castAddEmb_Iio, SimplexCategory.toMk₁_apply, CategoryTheory.ComposableArrows.homMk₃_app_two, image_castSucc_Ioo, Ioc_sub_one_eq_Icc, Iio_add_one_eq_Iic, sum_Iio_castSucc, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcycles_g, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac_assoc, card_Iic, prod_Icc_succ, image_castLE_Ico, SimplexCategory.II.map'_predAbove, preimage_natAdd_Iic_natAdd, SimplexCategory.II.mem_finset_iff, image_castLE_Iic, CategoryTheory.ComposableArrows.instIsIsoOfNatNatTwoδ₁Toδ₀, finsetImage_castSucc_Iic, attachFin_Iio, range_castAdd, CategoryTheory.ShortComplex.toComposableArrows_map, sort_univ, CategoryTheory.Abelian.SpectralObject.Hom.comm_assoc, CategoryTheory.Abelian.SpectralObject.opcyclesIsoKernel_hom_fac, CategoryTheory.ComposableArrows.isoMk₅_hom, finsetImage_castSucc_Icc, sum_Icc_succ, map_natAddEmb_Ioi, map_valEmbedding_Ico, map_castSuccEmb_Iio, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_two, SSet.stdSimplex.objEquiv_toOrderHom_apply, CategoryTheory.Abelian.SpectralObject.sc₁_X₃, CategoryTheory.Abelian.SpectralObject.δ_toCycles_assoc, map_revPerm_Iio, addRothNumber_le_rothNumberNat, SimplexCategory.const_apply, AugmentedSimplexCategory.inl'_eval, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_two, Icc_sub_one_eq_Ico, map_succEmb_Ico, prod_Iic_castLE, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_one, preimage_val_Icc_val, CategoryTheory.Triangulated.SpectralObject.comp_hom, finsetImage_succ_Icc, preimage_rev_Iic, preimage_rev_Ioo, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_inv_hom_id, CategoryTheory.ComposableArrows.homMk₂_app_zero, CategoryTheory.ComposableArrows.isoMk_hom, CategoryTheory.ComposableArrows.scMap_τ₂, CategoryTheory.Abelian.SpectralObject.p_descOpcycles_assoc, prod_Ioc_castAdd, finsetImage_rev_Iio, CategoryTheory.ComposableArrows.isIso_iff₀, CategoryTheory.Abelian.SpectralObject.p_fromOpcycles, CategoryTheory.Abelian.SpectralObject.Ψ_fromOpcycles, CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin_i₁, CategoryTheory.Abelian.SpectralObject.p_opcyclesMap, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ', CategoryTheory.Abelian.SpectralObject.opcyclesIso_hom_δFromOpcycles_assoc, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_of_isIso, finsetImage_addNat_Icc, List.sorted_lt_ofFn_iff, map_castSuccEmb_Iic, map_finCongr_Ioi, sum_Icc_castLE, map_addNatEmb_Ioc, map_succEmb_Ioc, CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor_obj, CategoryTheory.Abelian.SpectralObject.instEpiPOpcycles, preimage_castSucc_Ici_castSucc, CategoryTheory.Triangulated.TStructure.ω₁δ_app, CategoryTheory.ComposableArrows.isoMk₂_hom, CategoryTheory.Abelian.SpectralObject.opcyclesIsoKernel_hom_fac_assoc, finsetImage_rev_Icc, HomologicalComplex.HomologySequence.instMonoMap'ComposableArrows₃OfNatNat, image_natAdd_Ioi, CategoryTheory.Abelian.SpectralObject.ιE_δFromOpcycles, Tuple.eq_sort_iff', SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquiv, Iic_sub_one_eq_Iio, CategoryTheory.ComposableArrows.isoMk₃_inv, Ici_add_one_eq_Ioi, SSet.prodStdSimplex.nonDegenerate_max_dim_iff, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_H, SSet.stdSimplex.objMk_apply, CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_one, CategoryTheory.Abelian.SpectralObject.δToCycles_iCycles_assoc, prod_Ioi_zero, SimplexCategory.δ_comp_toMk₁_of_le, sum_Ioc_succ, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_one, image_castLE_Ioc, HomotopyCategory.spectralObjectMappingCone_ω₁, sum_Ico_castAdd, CategoryTheory.ComposableArrows.opEquivalence_inverse_map, prod_Icc_castSucc, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac, SimplexCategory.toType_apply, sum_Ioc_cast, CategoryTheory.Abelian.SpectralObject.shortComplexMap_τ₁, List.SortedLT.strictMono, preimage_addNat_Ioo_addNat, CategoryTheory.Functor.mapComposableArrows_obj_obj, image_castAdd_Ico, prod_Ici_succ, CategoryTheory.Arrow.cechNerve_map, strictMono_castAdd, CategoryTheory.ShortComplex.toComposableArrows_obj, CategoryTheory.Abelian.SpectralObject.opcyclesMap_id, SimplexCategory.concreteCategoryHom_id, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', prod_Iio_cast, CategoryTheory.Abelian.SpectralObject.liftCycles_i, preimage_castSucc_Icc_castSucc, prod_Ico_castLE, sum_Iic_castSucc, CategoryTheory.ComposableArrows.homMk₃_app_one, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_inv_id_assoc, CategoryTheory.Abelian.SpectralObject.EToCycles_i, CategoryTheory.Abelian.SpectralObject.zero₃_assoc, CategoryTheory.Abelian.SpectralObject.mono_H_map_twoδ₁Toδ₀', prod_Icc_castAdd, List.sorted_ge_ofFn_iff, CategoryTheory.ComposableArrows.δ₀Functor_obj_obj, castSuccFunctor_obj, preimage_castSucc_Ioo_castSucc, image_succ_Icc, Ioo_sub_one_eq_Ico, preimage_castLE_Ici_castLE, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₃_le, CategoryTheory.Arrow.cechConerve_map, CategoryTheory.ComposableArrows.map'_self, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', SSet.OneTruncation₂.nerveEquiv_symm_apply_obj, range_natAdd_eq_Ioi, antitone_iff_succ_le, CategoryTheory.Abelian.SpectralObject.shortComplex_X₁, preimage_castAdd_Ioc_castAdd, preimage_natAdd_Ici_natAdd, finsetImage_val_Iic, finsetImage_succ_Ici, CategoryTheory.Abelian.SpectralObject.isIso_H_map_twoδ₁Toδ₀', finsetImage_castLE_Iic, SimplexCategory.toMk₁_of_castSucc_lt, CategoryTheory.ComposableArrows.homMk₅_app_one, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcycles_X₁, strictMono_vecCons, SimplexCategory.comp_toOrderHom, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom_inv_id, preimage_castAdd_Iic_castAdd, OrderedFinpartition.parts_strictMono, Algebra.discr_powerBasis_eq_prod'', SimplexCategory.II.map'_id, image_val_Ico, preimage_castLE_Ico_castLE, CategoryTheory.Abelian.SpectralObject.sc₃_X₃, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_Q, preimage_cast_Ioo, CategoryTheory.ComposableArrows.isoMk₁_inv_app, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_one, CategoryTheory.Abelian.SpectralObject.shortComplex_X₃, SSet.prodStdSimplex.strictMono_orderHomOfSimplex, CategoryTheory.nerve.ext_of_isThin_iff, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_zero, Ioc_sub_one_eq_Ioo, List.sortedGE_iff_antitone_get, CategoryTheory.Abelian.SpectralObject.sc₃_X₂, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_naturality_app, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_two, finsetImage_addNat_Ioo, List.SortedGE.antitone_get, castSuccFunctor_map, card_Ioc, SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquiv, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₂, preimage_castSucc_Ioc_castSucc, CategoryTheory.Abelian.SpectralObject.kernelSequenceCycles_X₃, rev_strictAnti, finsetImage_castSucc_Ici, prod_Iio_castLE, CategoryTheory.Triangulated.SpectralObject.triangle_obj₃, finsetImage_rev_Ico, preimage_val_Ioo_val, CategoryTheory.ComposableArrows.isoMk₄_inv, CategoryTheory.ComposableArrows.mk₀_map, sum_Icc_sub, SSet.horn.primitiveEdge_coe_down, CategoryTheory.ComposableArrows.homMk₄_app_two, Algebra.discr_powerBasis_eq_prod', CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_two, CategoryTheory.Triangulated.SpectralObject.comp_hom_assoc, map_castSuccEmb_Ioi, finsetImage_castSucc_Iio, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, map_succEmb_Icc, HomologicalComplex.HomologySequence.composableArrows₃Functor_map, OrderedFinpartition.emb_strictMono, sum_Icc_castSucc, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, CategoryTheory.Abelian.SpectralObject.p_opcyclesToE_assoc, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₂, Ioi_sub_one_eq_Ici, finsetImage_cast_Iic, CategoryTheory.Abelian.SpectralObject.δ_pOpcycles, map_finCongr_Iio, orderSucc_castSucc, strictMono_castLE, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_three, finsetImage_castAdd_Icc, Antitone.vecCons, map_castSuccEmb_Ico, map_addNatEmb_Icc, map_castSuccEmb_Ioo, CategoryTheory.ComposableArrows.homMk_app, preimage_castSucc_Ioi_castSucc, CategoryTheory.Abelian.SpectralObject.EIsoH_hom_opcyclesIsoH_inv, CategoryTheory.Abelian.SpectralObject.δ_eq_zero_of_isIso₁, finsetImage_castLE_Ioc, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_X₁, CategoryTheory.ComposableArrows.Precomp.map_comp, image_succ_Iio, prod_Ioc_succ, CategoryTheory.Triangulated.SpectralObject.triangle_obj₁, CategoryTheory.Abelian.SpectralObject.toCycles_Ψ, finsetImage_natAdd_Ioo, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesEIso_inv_τ₃, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_X₂, CategoryTheory.ComposableArrows.homMk₂_app_one, CategoryTheory.ComposableArrows.δ₀Functor_map_app, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom_inv_id_assoc, RootPairing.Base.exists_eq_sum_and_forall_sum_mem_of_isPos, List.sortedLE_ofFn_iff, preimage_cast_Ico, CategoryTheory.ComposableArrows.homMk₅_app_four, rev_anti, HomologicalComplex.HomologySequence.composableArrows₃Functor_obj, CategoryTheory.ComposableArrows.sc'Map_τ₂, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_exists, CategoryTheory.ComposableArrows.isoMk₀_hom_app, preimage_addNat_Ico_addNat, CategoryTheory.ComposableArrows.functorArrows_map, CategoryTheory.Abelian.SpectralObject.liftCycles_i_assoc, CategoryTheory.nerveMap_app, image_addNat_Ioc, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_f, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_one, List.sortedLT_ofFn_iff, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, prod_Icc_cast, map_castAddEmb_Iic, finsetImage_cast_Ioc, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_inv_id, CategoryTheory.Abelian.SpectralObject.sc₁_X₂, map_valEmbedding_Iio, strictAnti_iff_succ_lt, sum_Ico_castLE, prod_Iic_castAdd, strictAnti_vecCons, Ioi_zero_eq_map, map_finCongr_Ioc, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, CategoryTheory.Abelian.SpectralObject.shortComplexMap_comp, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isColimit, AugmentedSimplexCategory.inr'_eval, map_natAddEmb_Ioo, image_succ_Ioo, sum_Ioi_zero, CategoryTheory.Abelian.SpectralObject.sc₂_f, Icc_add_one_eq_Ioc, Equiv.Perm.monotone_iff, image_castSucc_Iic, CategoryTheory.Abelian.SpectralObject.isZero₂_of_isThirdQuadrant, map_addNatEmb_Ioo, CategoryTheory.ComposableArrows.naturality'_assoc, finsetImage_cast_Ico, preimage_addNat_Ioc_addNat, CategoryTheory.Abelian.SpectralObject.toCycles_πE_descE, CategoryTheory.Abelian.SpectralObject.EIsoH_hom_naturality, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₃, CategoryTheory.ComposableArrows.instIsIsoOfNatNatTwoδ₂Toδ₁, finsetImage_castAdd_Ioo, image_addNat_Ico, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_X₃, CategoryTheory.Triangulated.TStructure.ω₁δ_naturality, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcyclesE_f, finsetImage_natAdd_Ici, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, finsetImage_rev_Ioo, SimplexCategory.toMk₁_apply_eq_one_iff, sum_Ioc_castSucc, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv, CategoryTheory.ComposableArrows.functorArrows_obj, orderSucc_eq, CategoryTheory.ComposableArrows.homMk₂_app_two', succFunctor_obj, CategoryTheory.Abelian.SpectralObject.cyclesMap_i_assoc, finsetImage_succ_Ioc, CategoryTheory.Limits.FormalCoproduct.cech_obj, preimage_castLE_Iio_castLE, map_castAddEmb_Icc, List.sortedLE_iff_monotone_get, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_zero, preimage_cast_Icc, SSet.stdSimplex.objEquiv_symm_apply, CategoryTheory.Abelian.SpectralObject.liftE_ιE_fromOpcycles_assoc, CategoryTheory.ComposableArrows.Mk₁.map_comp, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, CategoryTheory.Abelian.SpectralObject.sc₃_f, CategoryTheory.Abelian.SpectralObject.iCycles_δ_assoc, map_castAddEmb_Ioo, Equiv.Perm.prod_Iio_comp_eq_sign_mul_prod, preimage_succ_Ici_succ, CategoryTheory.Abelian.SpectralObject.zero₁_assoc, finsetImage_castAdd_Ioc, DivisorChain.exists_chain_of_prime_pow, CategoryTheory.ShortComplex.mapToComposableArrows_id, CategoryTheory.ComposableArrows.precomp_map, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_three, sum_Ioo_castSucc, CategoryTheory.ComposableArrows.IsComplex.zero, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac, CategoryTheory.Abelian.SpectralObject.instHasSpectralSequenceFinHAddNatOfNatProdIntCoreE₂CohomologicalFin, CategoryTheory.Abelian.SpectralObject.kernelSequenceCyclesE_X₃, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, antitone_vecEmpty, map_natAddEmb_Ioc, monotone_vecCons, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₁, Module.Basis.flag_strictMono, CategoryTheory.Abelian.SpectralObject.opcyclesMap_fromOpcycles_assoc, map_castSuccEmb_Ioc, CategoryTheory.Abelian.SpectralObject.pOpcycles_δFromOpcycles_assoc, CategoryTheory.Abelian.SpectralObject.instMonoICycles, prod_prod_eq_prod_triangle_mul, CategoryTheory.ComposableArrows.homMk₀_app, SimplexCategory.epi_iff_surjective, map_revPerm_Iic, CategoryTheory.Abelian.SpectralObject.fromOpcyles_δ, sum_Ioi_succ, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_three, CategoryTheory.Abelian.SpectralObject.epi_H_map_twoδ₁Toδ₀, CategoryTheory.Abelian.SpectralObject.toCycles_descCycles_assoc, List.sortedGE_ofFn_iff, image_val_Icc, CategoryTheory.Abelian.SpectralObject.IsThirdQuadrant.isZero₁, map_finCongr_Icc, CategoryTheory.Abelian.SpectralObject.map_comp_assoc, CategoryTheory.Abelian.SpectralObject.isZero_H_map_mk₁_of_isIso, succFunctor_map, map_succEmb_Iic, finsetImage_rev_Ici, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_zero, preimage_cast_Ioc, prod_Ioc_cast, preimage_val_Iio_val, CategoryTheory.ComposableArrows.homMk₁_app, CategoryTheory.Abelian.SpectralObject.HasSpectralSequence.isZero_H_obj_mk₁_i₃_le, CategoryTheory.Functor.instIsWellOrderContinuousFin, map_finCongr_Ico, finsetImage_succ_Ioi, CategoryTheory.Localization.essSurj_mapComposableArrows, CategoryTheory.ComposableArrows.isIso_iff₁, CategoryTheory.nerve.δ₂_two, sum_Ici_succ, CategoryTheory.Abelian.SpectralObject.sc₁_g, map_valEmbedding_Iic, LinearMap.IsSymmetric.eigenvalues_antitone, CategoryTheory.ComposableArrows.IsComplex.zero', image_castAdd_Iio, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcycles_X₃, image_castSucc_Iio, Tuple.monotone_sort, map_valEmbedding_Ioc, monotone_iff_le_succ, prod_Ioo_succ, attachFin_Ioc, CategoryTheory.Abelian.SpectralObject.toCycles_i, CategoryTheory.Abelian.SpectralObject.toCycles_i_assoc, LTSeries.monotone, map_castAddEmb_Ioi, SSet.stdSimplex.isoNerve_inv_app_apply, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac_assoc, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₃, CategoryTheory.Abelian.SpectralObject.map_id, strictMono_natAdd, CategoryTheory.ComposableArrows.δlastFunctor_obj_map, CategoryTheory.ComposableArrows.homMk₃_app_zero, finsetImage_castLE_Icc, image_val_Ioo, prod_Ico_castAdd, CategoryTheory.ComposableArrows.Precomp.map_one_one, CategoryTheory.Triangulated.TStructure.spectralObject_δ, CategoryTheory.Functor.mapComposableArrows_map_app
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