Documentation Verification Report

AddMonoidHom

📁 Source: Mathlib/Algebra/CharZero/AddMonoidHom.lean

Statistics

Metric	Count
Definitions `AddMonoidHom`	1
Theorems `of_addMonoidHom`	1
Total	2

CharZero

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`of_addMonoidHom` 📖	mathematical	`DFunLike.coe` `AddMonoidHom` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoidWithOne.toAddMonoid` `AddCommMonoidWithOne.toAddMonoidWithOne` `AddMonoidHom.instFunLike` `AddMonoidWithOne.toOne`	`CharZero`	—	`map_natCast'` `AddMonoidHom.instAddMonoidHomClass`

(root)

Definitions

Name	Category	Theorems
`AddMonoidHom` 📖	CompData	1986 math math: `ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup`, `AddMonoid.Coprod.swap_surjective`, `QuotientAddGroup.kerLift_mk`, `ValueDistribution.logCounting_zero`, `SkewMonoidAlgebra.mapDomain_smul`, `AddCommGrpCat.forget₂AddGroup_preservesLimitsOfShape`, `AddUnits.map_mk`, `FreeAddMonoid.lift_symm_apply`, `RCLike.conj_re`, `Finsupp.sum_toMultiset`, `AddMonoidHom.coe_rangeRestrict`, `RCLike.sqrt_eq_ite`, `Finsupp.finite_of_degree_le`, `DFinsupp.liftAddHom_apply`, `AddMonoidHom.coe_ker`, `TensorAlgebra.ofDirectSum_of_tprod`, `AddCommGrpCat.coyoneda_obj_obj_coe`, `Finsupp.mulHom_ext'_iff`, `MvPowerSeries.WithPiTopology.tendsto_trunc_atTop`, `RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm`, `DirectSum.mulHom_of_of`, `Ideal.Filtration.submodule_closure_single`, `DirectSum.mker_map`, `AddGrpCat.forget_grp_preserves_epi`, `IsAddIndecomposable.image_baseOf_neg_comp_eq`, `AddEquiv.coprodComm_apply`, `RCLike.one_re`, `DFinsupp.toMultiset_sup`, `negAddMonoidHom_apply`, `ModuleCat.forget₂_reflectsLimitsOfSize`, `Ideal.Filtration.submodule_eq_span_le_iff_stable_ge`, `CategoryTheory.opHom_apply`, `MeasureTheory.VectorMeasure.coeFnAddMonoidHom_apply`, `AddMonoidHom.mgraph_eq_mrange_prod`, `RCLike.map_apply`, `LinearMap.toAddMonoidHom_coe`, `AddCommMonCat.coyoneda_obj_obj_coe`, `Finsupp.degree_eq_sum`, `RCLike.geometric_hahn_banach_point_open`, `AddMonoidHom.isOfFinAddOrder`, `MvPowerSeries.weightedOrder_monomial`, `MvPowerSeries.eq_iff_frequently_trunc'_eq`, `taylorWithin_succ`, `AddGrpCat.forget₂_map`, `ExteriorAlgebra.GradedAlgebra.liftι_eq`, `PresentedAddMonoid.ext_iff`, `AddMonoid.Coprod.swap_inj`, `DirectSum.Gmodule.smulAddMonoidHom_apply_of_of`, `AddMonoid.Coprod.toProd_apply_inr`, `AddCommGrpCat.biproductIsoPi_inv_comp_π_apply`, `AddCommGrpCat.comp_apply`, `PolynomialModule.comp_single`, `RingCat.FilteredColimits.instPreservesFilteredColimitsAddCommGrpCatForget₂RingHomCarrierAddMonoidHomCarrier`, `AddGrpCat.id_apply`, `RCLike.reCLM_apply`, `MvPowerSeries.trunc'_trunc'`, `RCLike.div_re_ofReal`, `FreeAddMonoid.lift_ofList`, `RCLike.separate_convex_open_set`, `MvPolynomial.degrees_monomial`, `FreeAddGroup.map.id'`, `AddEquiv.addMonoidHomCongrLeftEquiv_apply`, `AddMonoidAlgebra.liftNC_mul`, `FreeAddMonoid.count_apply`, `NumberField.Units.logEmbedding_fundSystem`, `addMonoidHomLequivNat_symm_apply`, `AddMonoidHom.coe_mk`, `Finset.singletonAddMonoidHom_apply`, `AddSubgroup.map_toAddSubmonoid`, `AddEquiv.toMultiplicative_apply_symm_apply`, `AddMonoidHom.toMultiplicative_add`, `Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall`, `AddMonoid.Coprod.mk_of_inr`, `ModuleCat.forget₂PreservesColimitsOfSize`, `AddMonoid.Coprod.snd_apply_inr`, `SkewMonoidAlgebra.erase_apply_toFinsupp`, `Finsupp.toMultiset_strictMono`, `AddMonCat.comp_apply`, `AddMonoidHom.restrictHom_apply`, `DirectSum.coe_toModule_eq_coe_toAddMonoid`, `MvPolynomial.weightedDegree_eq_zero_iff`, `MonoidHom.toAdditive_apply_apply`, `ZMod.LFunction_stdAddChar_eq_expZeta`, `FreeAddMonoid.lift_apply`, `AddSubgroup.closure_preimage_eq_top`, `CoalgHom.coe_addMonoidHom_injective`, `RCLike.re_add_im`, `InnerProductSpace.Core.inner_mul_inner_self_le`, `AddCommGrpCat.hom_add`, `qExpansionRingHom_apply`, `AddCommGrpCat.asHom_hom_apply`, `Ideal.isHomogeneous_iff_subset_iInter`, `AddSubmonoid.prod_le_iff`, `prevD_comp_left`, `DirectSum.mrange_map`, `Finsupp.singleAddHom_apply`, `Multiset.equivDFinsupp_symm_apply`, `addMonoidHomLequivInt_apply`, `AddCommGrpCat.FilteredColimits.forget_preservesFilteredColimits`, `ModuleCat.forget₂AddCommGroup_preservesLimitsOfSize`, `DFinsupp.liftAddHom_apply_single`, `WittVector.verschiebung_zmod`, `AlgHom.coe_addMonoidHom_injective`, `AddMonoidHom.map_zero`, `AddMonoidHom.toZModLinearMap_injective`, `AddMonoidHom.toMultiplicativeRight_apply_apply`, `FreeAbelianGroup.toFinsupp_toFreeAbelianGroup`, `AddMonoidHom.noncommPiCoprod_apply`, `Multiset.toDFinsupp_support`, `ModuleCat.mkOfSMul'_smul`, `ContinuousMultilinearMap.alternatization_apply_apply`, `Submodule.re_inner_starProjection_eq_normSq`, `NormedAddGroupHom.coe_toAddMonoidHom`, `AddMonCat.zeroHom_apply`, `AddUnits.embedProduct_injective`, `AddMonoidHom.toAddEquiv_symm_apply`, `AddSubgroup.coe_addSubgroupOf`, `LinearMap.IsPositive.re_inner_nonneg_right`, `DirectSum.of_smul`, `AddMonoidHom.coe_prodMap`, `LinearMap.IsSymmetric.im_inner_self_apply`, `DirectSum.fromAddMonoid_of_apply`, `AddGroupExtension.Section.exists_eq_inl_add`, `RCLike.sub_conj`, `PresentedAddMonoid.surjective_mk`, `RCLike.re_sqrt_ofReal`, `RCLike.pos_iff`, `AddMonoid.Coprod.fst_swap`, `CategoryTheory.ShortComplex.ShortExact.ab_surjective_g`, `MeasureTheory.Lp.indicatorConstLp_compMeasurePreserving`, `MeasureTheory.Lp.coeFn_const`, `CategoryTheory.Abelian.Ext.precomp_mk₀_injective_of_epi`, `instIsCancelAddAddMonoidHom`, `WittVector.eq_iterate_verschiebung`, `MvPowerSeries.trunc'_expand_trunc'`, `AddSubmonoidClass.coe_subtype`, `SkewMonoidAlgebra.coeff_erase_same`, `AddEquiv.coprodPUnit_symm_apply`, `AddMonoidHom.coe_prod`, `AddSubmonoid.prod_top`, `SemimoduleCat.instReflectsIsomorphismsAddCommMonCatForget₂LinearMapIdCarrierAddMonoidHomCarrier`, `AddChar.doubleDualEmb_injective`, `AddMonoidHom.prod_map_comap_prod'`, `AddMonoidHom.map_dfinsuppSumAddHom`, `AddMonoidHom.inl_strictMono`, `MulEquiv.toAdditive_apply_apply`, `NonUnitalRingHom.coe_addMonoidHom_injective`, `SkewMonoidAlgebra.mapDomain_one`, `AddEquiv.toMultiplicativeRight_apply_apply`, `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `FreeAddMonoid.count_of`, `Finsupp.weight_single_one_apply`, `CochainComplex.HomComplex.Cocycle.toCochainAddMonoidHom_apply`, `Ideal.isHomogeneous_iff_forall_subset`, `AddMonoid.Coprod.map_map`, `Finsupp.mapDomain_comapDomain_nat_add_one`, `AddMonCat.forget_reflects_isos`, `TensorAlgebra.toDirectSum_tensorPower_tprod`, `AddMonCat.forget_preservesLimitsOfSize`, `AddSubgroup.coe_comap`, `AddCommMonCat.coe_id`, `AddMonCat.hom_zero`, `CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply`, `OrderAddMonoidHom.toAddMonoidHom_injective`, `Finsupp.prod_toMultiset`, `AddMonoidHom.instAddMonoidHomClass`, `iSupIndep.dfinsuppSumAddHom_injective`, `Multiset.mapAddMonoidHom_apply`, `Finsupp.toMultiset_zero`, `MonoidAlgebra.liftNC_mul`, `AddSubgroup.coe_subtype`, `AddMonoid.Coprod.swap_bijective`, `AddCommMonCat.ofHom_apply`, `AddMonoidHom.toFun_eq_coe`, `RCLike.ofReal_re`, `Finsupp.le_weight_of_ne_zero'`, `DirectSum.toAddMonoid.unique`, `AddMonoidHom.coe_flip_mul`, `AddMonoidHom.coe_id`, `PiTensorProduct.lifts_smul`, `LinearMap.BilinMap.toQuadraticMapAddMonoidHom_apply`, `RCLike.re_add_im_ax`, `AddSubgroup.noncommPiCoprod_single`, `mulRight_bound`, `AddMonoidHom.toZeroHom_injective`, `AddSubmonoid.LocalizationMap.addEquivOfLocalizations_symm_apply`, `AddCommGrpCat.hom_zero`, `WittVector.verschiebung_coeff_succ`, `MvPowerSeries.ext_trunc'`, `RCLike.is_real_TFAE`, `AddMonoidHom.map_zsmul`, `AddGrpCat.forget_preservesLimits`, `QuotientAddGroup.mk'_eq_mk'`, `PresheafOfModules.sections_property`, `lp.coeFnAddMonoidHom_apply`, `CentroidHom.coe_toAddMonoidHom`, `RCLike.abs_im_div_norm_le_one`, `AddSubgroupClass.inclusion_self`, `norm_sub_mul_self`, `AddMonoidHom.mapMatrix_zero`, `Multiset.Icc_eq`, `RingCat.forget₂AddCommGroup_preservesLimits`, `multiplesAddHom_apply`, `PresheafOfModules.toSheafify_app_apply'`, `PiTensorProduct.projectiveSeminormAux_smul`, `Matrix.IsHermitian.eigenvalues_eq`, `AddChar.directSum_apply`, `AddMonoidHom.map_finsum`, `AddMonoidHom.fst_comp_inr`, `AddMonoidHom.coe_of_map_add_neg`, `Set.mem_center_iff_addMonoidHom`, `im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four`, `uliftMultiplesHom_symm_apply`, `AddMonoidHom.coe_smul'`, `MonoidHom.coe_toMultiplicative_range`, `AddCommMonCat.FilteredColimits.forget₂AddMonPreservesFilteredColimits`, `PresheafOfModules.Derivation.d_map`, `ConvexOn.univ_sSup_of_countable_affine_eq`, `AddMonoid.End.mulRight_apply_apply`, `DomMulAct.smul_addMonoidHom_apply`, `AddAction.stabilizer_vadd_eq_stabilizer_map_conj`, `SeparationQuotient.mkAddMonoidHom_apply`, `WeierstrassCurve.Affine.Point.toClass_zero`, `AddMonCat.ext_iff`, `RCLike.ofNat_re`, `AddCommGrpCat.isColimit_iff_bijective_desc`, `groupCohomology.mem_cocycles₁_of_addMonoidHom`, `QuotientAddGroup.coe_mk'`, `AddCon.mk'_surjective`, `AddMonoidHom.toRatLinearMap_injective`, `Set.conj_mem_fixingAddSubgroup`, `AddMonoidHom.restrict_eq_zero_iff`, `SkewMonoidAlgebra.coeff_erase_ne`, `FreeAbelianGroup.lift_add`, `Multiset.coe_sumAddMonoidHom`, `AddSubmonoid.iSup_map_single`, `RCLike.nonpos_iff`, `RCLike.smul_re`, `HahnSeries.single.addMonoidHom_apply_coeff`, `AddSubmonoid.pi_le_iff`, `ProbabilityTheory.Kernel.coeAddHom_apply`, `DirectSum.coeAddMonoidHom_eq_dfinsuppSum`, `AddMonoidHom.toZeroHom_coe`, `AddMonoid.Coprod.neg_def`, `AddCommMonCat.hom_forget₂_map`, `DirectSum.fromAddMonoid_of`, `SkewMonoidAlgebra.mapDomain_mul`, `DFinsupp.sumAddHom_single`, `TensorProduct.liftAux_tmul`, `MvPolynomial.supDegree_esymmAlgHomMonomial`, `ModuleCat.forget₂_addCommGrp_essSurj`, `MvPolynomial.le_weightedTotalDegree`, `Function.locallyFinsuppWithin.logCounting_nonneg`, `AddMonoidHom.coe_toMultiplicativeRight`, `AddUnits.coeHom_apply`, `DFinsupp.coeFnAddMonoidHom_apply`, `Finsupp.toMultiset_toFinsupp`, `RCLike.abs_re_le_norm`, `DirectSum.mk_smul`, `ZMod.completedLFunction_def_even`, `Behrend.map_mod`, `MvPolynomial.pow_idealOfVars`, `MvPolynomial.idealOfVars_eq_restrictSupportIdeal`, `AddCommGrpCat.neg_hom_apply`, `AddGroupExtension.Equiv.map_inl`, `RCLike.geometric_hahn_banach_closed_point`, `Filter.pureAddMonoidHom_apply`, `AEMeasurable.im`, `AddMonoidAlgebra.divOfHom_apply_apply`, `SkewMonoidAlgebra.mapDomain_single`, `DistribMulAction.toAddMonoidHom_apply`, `Finsupp.coeFnAddHom_apply`, `Behrend.map_succ`, `AddCommGrpCat.forget_preservesLimits`, `DirectSum.mk_injective`, `Behrend.map_le_of_mem_box`, `Polynomial.trunc_toLaurent`, `MvPolynomial.totalDegree_eq`, `WittVector.iterate_verschiebung_mul`, `AddMonoidHom.ker_eq_bot_iff`, `RCLike.norm_sq_eq_def_ax`, `AddMonoidHom.addSubgroupOf_range_eq_of_le`, `ModuleCat.forget₂AddCommGroup_reflectsLimitOfShape`, `AddAction.map_stabilizer_le`, `Homotopy.prevD_succ_cochainComplex`, `AddCommGrpCat.forget_preservesLimitsOfShape`, `DirectSum.decompose_of_mem`, `Finsupp.mapRange.addMonoidHom_apply`, `MvPolynomial.mem_pow_idealOfVars_iff`, `WittVector.verschiebung_nonzero`, `Multiset.toDFinsupp_apply`, `AddMonoidHom.fiberEquiv_symm_apply`, `RCLike.intCast_re`, `Matrix.addMonoidHomMulLeft_apply`, `DirectSum.coe_of_mul_apply_aux`, `AddMonoidHom.rangeRestrict_surjective`, `RCLike.im_eq_zero_iff_isSelfAdjoint`, `Seminorm.pullback_apply`, `AddMonoidHom.toNatLinearMap_injective`, `MvPowerSeries.trunc_C`, `FreeAddMonoid.mem_map`, `inner_mul_inner_self_le`, `commute_lmul_rmul`, `CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply`, `AddSubgroup.map_zero_eq_bot`, `MvPolynomial.degrees_def`, `ModN.basis_apply_eq_mkQ`, `HahnSeries.map_neg`, `RCLike.mul_im_ax`, `Function.locallyFinsuppWithin.logCounting_eval_zero`, `Polynomial.eval₂_ofFinsupp`, `AddCommGrpCat.coe_comp`, `InnerProductSpace.Core.norm_eq_sqrt_re_inner`, `DirectSum.Gmodule.of_smul_of`, `AdjoinRoot.evalEval_apply`, `MonoidAlgebra.coe_liftNCAlgHom`, `CuspForm.coeHom_apply`, `zmultiplesAddHom_symm_apply`, `Module.End.ringHomEndFinsupp_apply_apply`, `RCLike.abs_re_div_norm_le_one`, `AddMonoidHom.addSubmonoidComap_apply_coe`, `norm_sub_sq`, `ValueDistribution.logCounting_top`, `ContinuousAt.compMeasurePreservingLp`, `LinearMap.BilinForm.coeFnAddMonoidHom_apply`, `RCLike.I_re_ax`, `DirectSum.sum_univ_of`, `AddGrpCat.forget_grp_preserves_mono`, `DirectSum.lie_of_of_ne`, `AddCommGrpCat.forget₂_map`, `Finsupp.liftAddHom_comp_single`, `ModuleCat.HasColimit.colimitCocone_ι_app`, `Finsupp.card_toMultiset`, `RCLike.re_nonneg_of_nonneg`, `MonoidHom.toAdditive_symm_apply_apply`, `CentroidHom.centroid_eq_centralizer_mulLeftRight`, `ZMod.LFunction_def_odd`, `LinearMap.IsSymmetric.coe_re_inner_self_apply`, `SkewMonoidAlgebra.comapSMul_def`, `AddChar.coe_compAddMonoidHom`, `AddMonoidHom.id_apply`, `Sym.coe_equivNatSum_symm_apply`, `PolynomialModule.monomial_smul_single`, `Multiset.addHom_ext_iff`, `LinearMap.applyₗ'_apply_apply`, `multiplesAddHom_symm_apply`, `postcomp_extClass_surjective_of_projective_X₂`, `PresheafOfModules.Derivation.postcomp_d_apply`, `ContinuousMap.coeFnAddMonoidHom_apply`, `AddSubmonoid.closure_image_isAddIndecomposable_baseOf`, `AddMonoidHom.mulRight_apply`, `ModuleCat.forget₂_addCommGroup_full`, `DirectSum.gMulHom_apply_apply`, `PresheafOfModules.Derivation.d_one`, `CategoryTheory.Idempotents.Karoubi.inclusionHom_apply`, `DoubleCentralizer.norm_def`, `FreeAddGroup.lift_mk`, `Module.DirectLimit.quotMk_of`, `PresheafOfModules.sectionsMap_coe`, `re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two`, `AddMonoid.Coprod.mrange_lift`, `AddCommGrpCat.FilteredColimits.forget₂AddGroup_preservesFilteredColimits`, `AddMonCat.FilteredColimits.colimit_add_mk_eq`, `AddMonCat.forget_preservesLimitsOfShape`, `CategoryTheory.ShortComplex.abToCycles_apply_coe`, `CochainComplex.HomComplex.leftHomologyData_π_hom_apply`, `MvPowerSeries.weightedOrder_monomial_of_ne_zero`, `groupCohomology.H1IsoOfIsTrivial_inv_apply`, `AddGrpCat.FilteredColimits.colimit_add_mk_eq`, `DirectSum.lie_of`, `AddMonoidHom.rangeRestrict_injective_iff`, `AddCommMonCat.forget₂AddMonPreservesLimitsOfSize`, `re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two`, `FreeAbelianGroup.liftMonoid_coe_addMonoidHom`, `AddEquiv.withZeroCongr_apply`, `AddMonoidHom.coe_dfinsuppSumAddHom`, `Function.locallyFinsuppWithin.logCounting_eventually_le`, `PresheafOfModules.Derivation.d_mul`, `WittVector.verschiebung_injective`, `FreeAbelianGroup.map_of_apply`, `groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply`, `AddSubgroup.noncommPiCoprod_apply`, `DirectSum.support_of`, `AddEquiv.toMultiplicativeLeft_apply_symm_apply`, `Multiset.equivDFinsupp_apply`, `inner_re_zero_right`, `two_nsmul_lie_lmul_lmul_add_add_eq_zero`, `AddMonoid.Coprod.prod_mk_fst_snd`, `AddSubgroupClass.subtype_apply`, `AddMonCat.equivalence_inverse_map`, `Derivation.mapCoeffs_C`, `FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite`, `AddMonoidHom.map_finsum_plift`, `AddMonoidAlgebra.toDirectSum_single`, `AddMonoidHom.eval_apply_apply`, `qExpansion_of_mul`, `AddSubmonoid.subPairs_comap`, `AddMonoidHom.flip_apply`, `AddSubgroup.mem_map_of_mem`, `DFinsupp.toMultiset_single`, `CochainComplex.HomComplex.leftHomologyData_i_hom_apply`, `AddEquiv.symm_addMonoidHomCongrRight`, `MvPowerSeries.trunc'_trunc'_pow`, `ModuleCat.smul_naturality`, `Algebra.directSumGAlgebra_toFun_apply`, `AddEquiv.addMonoidHomCongrRightEquiv_refl`, `LinearMap.toAddMonoidHom'_apply`, `Module.Free.addMonoidHom`, `Finset.coe_coeAddMonoidHom`, `AddMonCat.equivalence_counitIso`, `PolynomialModule.single_smul`, `SkewMonoidAlgebra.addHom_ext_iff`, `LinearMap.compMultilinearMap_alternatization`, `CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply`, `Finsupp.toMultiset_apply`, `AddMonoidHom.addSubgroupMap_apply_coe`, `DirectSum.coeLinearMap_of`, `OrderAddMonoidHom.coe_addMonoidHom`, `AddMonoidHom.toAddHom_coe`, `AddMonoid.Coprod.clift_mk`, `MeasureTheory.VectorMeasure.restrictGm_apply`, `AddSubgroup.tendsto_zmultiples_subtype_cofinite`, `AddMonoidHom.comp_zero`, `ModuleCat.HasColimit.colimitCocone_pt_isModule`, `DirectSum.coe_of_mul_apply_add`, `DoubleCentralizer.nnnorm_def`, `RCLike.re_monotone`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left`, `AddMonCat.forget_map`, `AddMonoidAlgebra.decomposeAux_coe`, `AddGroupSeminorm.comp_zero`, `AddAut.conj_symm_apply`, `RCLike.im_ofReal_pow`, `AddEquiv.toMultiplicativeRight_apply_symm_apply`, `CategoryTheory.preadditiveYoneda_obj`, `SemimoduleCat.forget₂_obj_moduleCat_of`, `AddMonoidHom.instSMulCommClass`, `DirectSum.ofPow`, `AddMonoidHom.isClosed_range_coe`, `AddMonoidAlgebra.gradeBy.isInternal`, `MvPowerSeries.trunc_one`, `DirectSum.of_zero_smul`, `AddCommGrpCat.ext_iff`, `NumberField.Units.logEmbeddingQuot_apply`, `LowerSemicontinuousOn.isClosed_re_epigraph`, `AddCommMonCat.equivalence_functor_map`, `AddMonoidHom.map_mrange`, `CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply`, `LieRingModule.toEnd_apply_apply`, `LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional`, `Finsupp.weight_single`, `NumberField.Units.basisOfIsMaxRank_apply`, `Module.Invertible.rTensorEquiv_apply_apply`, `AddMonoidHom.toMultiplicativeRight_symm_apply_apply`, `MeasureTheory.Measure.coeAddHom_apply`, `DirectSum.coe_congr_addEquiv`, `AddMonoid.Coprod.inl_injective`, `AddMonoidHom.map_add_neg`, `inner_self_im`, `WithBot.coe_addHom`, `AddEquiv.map_dfinsuppSumAddHom`, `Set.singletonAddMonoidHom_apply`, `AddMonoidHom.zero_apply`, `nsmulAddMonoidHom_apply`, `groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply`, `AddCommGrpCat.forget_commGrp_preserves_epi`, `AddMonoidHom.map_finsum_mem'`, `FreeAbelianGroup.liftAddEquiv_symm_apply`, `AddCommMonCat.forget_preservesLimitsOfShape`, `AddCommGrpCat.coyonedaForget_inv_app_app`, `Finsupp.toFreeAbelianGroup_comp_singleAddHom`, `AddMonoidHom.coe_coe`, `AddEquiv.addMonoidHomCongrLeft_apply`, `AddCommGrpCat.free_map_coe`, `AddMonoidHom.compl₂_apply`, `AddMonoidHom.mulOp_apply_apply`, `CategoryTheory.ShortComplex.ShortExact.ab_injective_f`, `inner_re_zero_left`, `inner_self_ofReal_re`, `prevD_eq_toPrev_dTo`, `FreeAddGroup.lift_apply_of`, `commute_lmul_sq_rmul`, `DirectSum.one_def`, `AddOreLocalization.numerator_isAddUnit`, `RCLike.imLm_coe`, `AddMonCat.coe_comp`, `LocallyConstant.coeFnAddMonoidHom_apply`, `AddMonoidHom.fiberEquivKer_apply`, `RCLike.div_im`, `AddMonoid.Coprod.map_apply_inr`, `FreeAbelianGroup.liftAddGroupHom_apply`, `AddMonoidHom.mem_graph`, `MonoidAlgebra.singleAddHom_apply`, `AddMonoidHom.withTopMap_apply`, `AddCommGrpCat.coyonedaForget_hom_app_app_hom`, `ZMod.toAddCircle_inj`, `FreeAddGroup.map.comp`, `CategoryTheory.Iso.addCommGroupIsoToAddEquiv_symm_apply`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff'`, `Homotopy.dNext_zero_chainComplex`, `DirectSum.of_mul_of`, `ZMod.completedLFunction_def_odd`, `RCLike.im_to_real`, `AddGroupExtension.rightHom_inl`, `PiTensorProduct.liftAux.smul`, `GrpCat.toAddGrp_map`, `Fin.accumulate_invAccumulate`, `RCLike.ext_iff`, `Homotopy.prevD_chainComplex`, `AddGrpCat.forget₂AddMonPreservesLimitsOfSize`, `Finset.coe_singletonAddMonoidHom`, `AddGroupExtension.Section.exists_add_eq_inl_add_add`, `Real.Angle.coe_coeHom`, `MvPolynomial.coeff_homogeneousComponent`, `FreeAddMonoid.ofList_map`, `DFinsupp.eraseAddHom_apply`, `BoundedContinuousFunction.toContinuousMapAddMonoidHom_apply`, `AddMonoid.Coprod.snd_toProd`, `DirectSum.coe_mul_of_apply_of_not_le`, `LocallyConstant.constAddMonoidHom_apply`, `AddMonoidHom.coe_graph`, `lp.singleAddMonoidHom_apply`, `AddMonoidHom.sub_apply`, `RCLike.re_eq_norm_of_mul_conj`, `AddMonoidHom.coe_finset_sum`, `FreeAbelianGroup.equivFinsupp_symm_apply`, `AddGrpCat.FilteredColimits.forget_preservesFilteredColimits`, `CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles`, `MeasureTheory.Lp.coeFn_compMeasurePreserving`, `AddCommGrpCat.biprodIsoProd_inv_comp_snd_apply`, `AddCommMonCat.comp_apply`, `Behrend.map_injOn`, `AddEquiv.coprodAssoc_apply_inr`, `Derivation.mapCoeffs_monomial`, `AddCommMonCat.forget₂_full`, `AddMonoidHom.mem_eqLocusM`, `CategoryTheory.ShortComplex.exact_iff_of_hasForget`, `RCLike.conj_eq_iff_re`, `AddMonoidHom.map_nsmul`, `PolynomialModule.single_apply`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff`, `AddMonoidHom.noncommCoprod_unique`, `MultilinearMap.domCoprod_alternization_coe`, `Behrend.map_apply`, `DomMulAct.coe_smul_addMonoidHom`, `Function.locallyFinsuppWithin.logCounting_eventuallyLE`, `Finsupp.comp_liftAddHom`, `MvPolynomial.pow_idealOfVars_eq_span`, `prevD_nat`, `CategoryTheory.ShortComplex.ab_exact_iff_function_exact`, `AddMonCat.FilteredColimits.forget_preservesFilteredColimits`, `AddSubmonoid.mk_add_mk_neg_eq_zero`, `FreeAddMonoid.map_surjective`, `ConvexOn.sSup_of_countable_affine_eq`, `MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported`, `RCLike.ofNat_mul_re`, `AddChar.doubleDualEmb_apply`, `QuadraticMap.evalAddMonoidHom_apply`, `monoidEndToAdditive_apply_apply`, `AddMonoid.Coprod.swap_injective`, `AddSubmonoid.le_prod_iff`, `AddSubmonoid.closure_singleton_eq`, `AddSubmonoid.mrange_subtype`, `DFinsupp.sumAddHom_comm`, `InnerProductSpace.Core.inner_im_symm`, `AddEquiv.comp_left_injective`, `AddCommGrpCat.homAddEquiv_symm_apply_hom`, `AddSubgroup.addCommute_subtype_of_addCommute`, `AddMonoidHom.map_closure`, `AddMonoidHom.toMultiplicative_symm_apply_apply`, `AddSubmonoid.le_comap_single_pi`, `AddCommGrpCat.hom_sub`, `AddGrpCat.zero_apply`, `LinearMap.toAddMonoidHom_injective`, `Matrix.addMonoidHomMulRight_apply`, `AddMonoidHom.coe_toMultiplicativeLeft`, `GradedAlgebra.proj_recompose`, `RCLike.I_eq_zero_or_im_I_eq_one`, `MvPowerSeries.coeff_homogeneousComponent`, `MonoidHom.toAdditiveLeft_apply_apply`, `AddMonoid.Coprod.snd_surjective`, `LinearMap.tensorProductEnd_apply`, `Finsupp.degree_apply`, `DirectSum.algebraMap_apply`, `RCLike.le_iff_re_im`, `AddChar.coe_toAddMonoidHom`, `AddCommMonCat.instFullMonCatForget₂AddMonoidHomCarrierCarrier`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right`, `AddMonoidAlgebra.mapDomainBialgHom_apply`, `AddMonoidHom.addSubmonoidMap_surjective`, `MeasureTheory.indicatorConstLp_univ`, `Module.End.rTensorAlgHom_apply_apply`, `ModuleCat.forget₂AddCommGroup_preservesLimits`, `Fin.accumulate_rec`, `AddCommMonCat.forget_preservesLimits`, `AddSubmonoid.iSup_map_single_le`, `AddMonoidHom.inl_apply`, `Finsupp.toFreeAbelianGroup_single`, `AddGrpCat.forget_preservesLimitsOfShape`, `AddMonoidHom.associator_apply`, `TensorPower.galgebra_toFun_def`, `AddSubmonoid.LocalizationMap.isAddUnit_comp`, `AddCommGrpCat.Colimits.quotUliftToQuot_ι`, `DirectSum.lof_eq_of`, `Multiset.cardHom_apply`, `Polynomial.divX_hom_toFun`, `PresheafOfModules.presheaf_map_apply_coe`, `controlled_sum_of_mem_closure_range`, `MeasureTheory.Lp.norm_const_le`, `precomp_extClass_surjective_of_projective_X₂`, `AddMonoidHom.single_apply`, `AddCommGrpCat.hom_nsmul`, `LocallyConstant.comapAddMonoidHom_apply`, `DirectSum.map_injective`, `SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk`, `QuotientAddGroup.lift_mk'`, `FreeAddGroup.map.id`, `DirectSum.of_zero_mul`, `AddMonoidHom.compr₂_apply`, `Derivation.coeFnAddMonoidHom_apply`, `AddMonoidHom.smul_comp`, `PresheafOfModules.Derivation.congr_d`, `Finsupp.finite_of_nat_weight_le`, `commute_lmul_rmul_sq`, `AddMonoidHom.withBotMap_apply`, `RCLike.measurable_re`, `DirectSum.lmap_eq_map`, `real_inner_eq_re_inner`, `RCLike.add_conj`, `RCLike.ofReal_re_ax`, `InnerProductSpace.Core.inner_self_eq_norm_mul_norm`, `AddSubmonoid.map_inl`, `RCLike.im_eq_conj_sub`, `AddSubmonoid.map_coe_toAddMonoidHom`, `AddMonoidHom.neg_apply`, `WeierstrassCurve.Affine.Point.map_injective`, `RCLike.conj_im_ax`, `AddMonoidHom.finsuppSum_apply`, `AddSubmonoid.map_id`, `AddSubgroup.range_zmultiplesHom`, `CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom`, `ModuleCat.forget₂_obj`, `AddCommMonCat.FilteredColimits.forget_preservesFilteredColimits`, `AddMonoid.End.mulLeft_apply_apply`, `FreeAddGroup.closure_eq_range`, `zmultiplesHom_ker_eq`, `AddAction.stabilizerEquivStabilizer_symm_apply`, `Finsupp.le_degree`, `MvPolynomial.degree_degLexDegree`, `CategoryTheory.pullbackShiftFunctorZero'_hom_app`, `AddSubmonoid.sup_eq_range`, `Matrix.singleAddMonoidHom_apply`, `MultilinearMap.domCoprod_alternization_eq`, `AddMonCat.coe_id`, `AddMonoidHom.mapMatrix_sub`, `NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component`, `MonoidHom.coe_toAdditive_map`, `DirectSum.mk_apply_of_notMem`, `ContinuousWithinAt.compMeasurePreservingLp`, `AddCommMonCat.neg_hom_apply`, `MvPolynomial.DirectSum.coeAddMonoidHom_eq_support_sum`, `LinearOrderedField.inducedOrderRingHom_toFun`, `Finsupp.le_weight`, `mulRight_continuous`, `FreeAddGroup.ext_hom_iff`, `NonUnitalRingHom.op_symm_apply_apply`, `AddMonoid.Coprod.fst_toProd`, `MeasureTheory.Lp.constₗ_apply`, `RCLike.im_mul_ofReal`, `AddMonCat.FilteredColimits.M.map_mk`, `RCLike.geometric_hahn_banach_point_point`, `AddCommMonCat.forget₂Mon_preservesLimits`, `Fin.accumulate_apply`, `AddCommGrpCat.forget_commGrp_preserves_mono`, `CategoryTheory.whiskering_linearCoyoneda₂`, `DFinsupp.toMultiset_le_toMultiset`, `normedAddGroupHomCompletionHom_apply`, `QuotientAddGroup.ker_le_range_iff`, `AddEquiv.add_submonoid_map_symm_apply`, `AddMonoidHom.range_eq_top`, `LinearMap.map_dfinsuppSumAddHom`, `AddMonoidHom.ext_nat_iff`, `AddOreLocalization.numeratorHom_surjective_of_finite`, `FreeAddGroup.lift_of_eq_id`, `AddMonCat.neg_hom_apply`, `MeasureTheory.Lp.norm_const'`, `Function.locallyFinsuppWithin.toClosedBall_divisor`, `QuotientAddGroup.mk'_comp_subtype`, `SchwartzMap.coeHom_injective`, `AddGrpCat.ext_iff`, `AddCon.mrange_mk'`, `WithZero.lift_coe`, `Submodule.setLike.coe_galgebra_toFun`, `AddMonoidHom.mulLeft₃_apply`, `Finsupp.mem_toMultiset`, `LinearMap.extendTo𝕜'_apply_re`, `AddMonoidHom.snd_mono`, `AddSubmonoid.mem_bsupr_iff_exists_dfinsupp`, `AddMonoidHom.addSubgroupComap_apply_coe`, `CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply`, `RCLike.re_to_real`, `ZMod.lift_castAddHom`, `AddSubgroup.injective_noncommPiCoprod_of_iSupIndep`, `ContinuousAddMonoidHom.toAddMonoidHom_injective`, `prevD_eq`, `RCLike.neg_iff`, `RCLike.sqrt_eq_real_add_ite`, `AddMonoidHom.zero_comp`, `AddMonoid.Coprod.toProd_apply_inl`, `RCLike.inv_im`, `AddEquiv.coprodPUnit_apply`, `AddMonoidHom.restrict_mker`, `WithZero.mapAddHom_injective'`, `CategoryTheory.Preadditive.epi_iff_surjective`, `AddCommMonCat.ext_iff`, `PiTensorProduct.liftAux_tprodCoeff`, `FreeAddMonoid.toList_map`, `ZMod.lift_comp_coe`, `DirectSum.coeAlgHom_of`, `AddEquiv.addMonoidHomCongrLeftEquiv_refl`, `AddMonoidHom.range_eq_bot_iff`, `MulEquiv.AddMonoid.End_apply`, `MvPolynomial.monomial_mem_pow_idealOfVars_iff`, `InnerProductSpaceable.inner_.norm_sq`, `CategoryTheory.Preadditive.mono_iff_injective`, `ConvexOn.sSup_of_nat_affine_eq`, `AddMonoidHom.coe_of_map_sub`, `RCLike.one_im`, `AddGroupExtension.Splitting.rightHom_splitting`, `AddMonoid.Coprod.lift_apply_inl`, `HomogeneousIdeal.mem_irrelevant_iff`, `Ideal.homogeneousHull_eq_iSup`, `AddMonCat.forget_isCorepresentable`, `RCLike.natCast_re`, `AddSubmonoid.le_pi_iff`, `Int.coe_castAddHom`, `InnerProductSpace.Core.inner_self_nonneg`, `inner_re_symm`, `AddCon.comap_eq`, `CliffordAlgebra.GradedAlgebra.ι_apply`, `FreeAbelianGroup.map_id_apply`, `AddAut.conj_inv_apply`, `NonUnitalNonAssocCommSemiring.mem_center_iff`, `AddMonoid.Coprod.fst_comp_inr`, `Multiset.coe_countPAddMonoidHom`, `FiniteAddGrp.ofHom_apply`, `AddChar.coe_toAddMonoidHomEquiv`, `AddMonoidHom.mul_apply`, `RCLike.norm_le_re_iff_eq_norm`, `Multiset.toDFinsupp_replicate`, `Ideal.mul_homogeneous_element_mem_of_mem`, `AddEquiv.comp_right_injective`, `AddMonoidHom.mker_fst`, `Matrix.entryAddMonoidHom_apply`, `AddMonoid.Coprod.mk_surjective`, `AddMonoidHom.coe_snd`, `AddEquiv.toMultiplicativeLeft_symm_apply_symm_apply`, `CategoryTheory.Abelian.Ext.bilinearComp_apply_apply`, `DirectSum.lieAlgebraOf_apply`, `AddMonoid.Coprod.mk_of_neg_add`, `DirectSum.map_of`, `AddEquiv.coprodAssoc_symm_apply_inr_inr`, `AddMonoidHom.coe_toNatLinearMap`, `AddMonoidHom.map_inv₂`, `CategoryTheory.whiskering_preadditiveYoneda`, `QuotientAddGroup.sound`, `MvPowerSeries.le_weightedOrder_subst`, `Pi.constAddMonoidHom_apply`, `Subsemiring.isHomogeneous_iff_subset_iInter`, `Multiset.uIcc_eq`, `MvPowerSeries.trunc'_expand`, `multiplesHom_symm_apply`, `RCLike.ofReal_im`, `prevD_eq_zero`, `Finset.card_nsmul_quotient_add_nsmul_inter_addSubgroup_le`, `Finsupp.count_toMultiset`, `RCLike.abs_im_le_norm`, `DFinsupp.mker_mapRangeAddMonoidHom`, `AddMonoidHom.map_neg`, `AddMonoidHom.compHom_apply_apply`, `AddMonoidHom.toMultiplicative_id`, `AddSubmonoid.fromCommLeftNeg_apply`, `AddCommGrpCat.forget₂AddGroup_preservesLimits`, `AddMonoidHom.inr_mono`, `AddMonoid.Coprod.lift_apply_inr`, `AddChar.toAddMonoidHomEquiv_symm_zero`, `RCLike.nonneg_iff`, `FreeAbelianGroup.toFinsupp_of`, `LocallyConstant.toContinuousMapAddMonoidHom_apply`, `MvPolynomial.supDegree_esymm`, `AddMonoid.Coprod.codisjoint_mrange_inl_mrange_inr`, `ZMod.toAddCircle_natCast`, `SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_conj`, `SkewMonoidAlgebra.liftNC_one`, `RCLike.continuous_re`, `AddGrpCat.ofHom_injective`, `NumberField.mixedEmbedding.logMap_eq_logEmbedding`, `FreeAddGroup.map_eq_lift`, `AddCommMonCat.coe_comp`, `AddChar.doubleDualEmb_bijective`, `AddMonoidHom.op_symm_apply_apply`, `AddCon.coe_mk'`, `AddMonoid.Coprod.swap_eq_zero`, `AddCommGrpCat.Colimits.quotToQuotUlift_ι`, `SkewMonoidAlgebra.update_eq_erase_add_single`, `AddEquiv.toMultiplicativeRight_symm_apply_apply`, `AddMonoidHom.nsmul_apply`, `RCLike.zero_re`, `InnerProductSpace.Core.inner_re_symm`, `AddMonoidHom.coe_mgraph`, `ModuleCat.smulNatTrans_apply_app`, `AddSubmonoid.fg_iff_exists_fin_addMonoidHom`, `RCLike.smul_im`, `AddCommGroup.DirectLimit.of_f`, `DirectSum.coe_of_mul_apply_of_not_le`, `Localization.mkAddMonoidHom_apply`, `MvPowerSeries.trunc_map`, `Finsupp.weight_single_index`, `AddMonoid.Coprod.snd_apply_inl`, `QuadraticMap.coeFnAddMonoidHom_apply`, `WittVector.iterate_verschiebung_coeff_eq_zero`, `addMonoidEndRingEquivInt_apply`, `CategoryTheory.Functor.mapExtAddHom_apply`, `SkewMonoidAlgebra.mapDomain_id`, `AddMonoidHom.ENatMap_apply`, `RCLike.re_eq_add_conj`, `AddGrpCat.toGrp_map`, `AddGrpCat.hasLimit_iff_small_sections`, `DivisibleHull.coeAddMonoidHom_apply`, `AddCommMonCat.coyoneda_map_app`, `LieDerivation.coeFnAddMonoidHom_apply`, `commute_lmul_lmul_sq`, `AddCommGrpCat.zero_apply`, `AddSubgroup.comap_toAddSubmonoid`, `AddGrpCat.mono_iff_injective`, `Finsupp.degree_preimage_add`, `DirectSum.mk_apply_of_mem`, `AddCommGrpCat.id_apply`, `ContinuousLinearMap.reApplyInnerSelf_apply`, `AddAction.compHom_vadd_def`, `AddSubmonoid.iSup_eq_mrange_dfinsuppSumAddHom`, `Finsupp.liftAddHom_apply`, `WithZero.mapAddHom_coe`, `PresheafOfModules.unitHomEquiv_apply_coe`, `MvPowerSeries.coeff_trunc'`, `inner_self_eq_norm_mul_norm`, `Ideal.Filtration.submodule_span_single`, `AddSubgroupClass.inclusion_mk`, `AddSubmonoid.inclusion_inj`, `Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀`, `AddCommGrpCat.int_hom_ext_iff`, `AddMonoidAlgebra.mapDomainAlgHom_apply`, `Behrend.map_succ'`, `BoundedContinuousFunction.coeFnAddMonoidHom_apply`, `AddMonoidHom.coe_toMultiplicative'`, `AddSubgroup.apply_coe_mem_map`, `AddEquiv.coprodAssoc_apply_inl_inr`, `AddEquiv.coprodCongr_apply`, `WittVector.verschiebung_coeff_zero`, `AddCommGrpCat.Colimits.Quot.desc_toCocone_desc_app`, `DFinsupp.toMultiset_toDFinsupp`, `Finsupp.DegLex.lt_iff`, `AddCon.kerLift_range_eq`, `AddMonoidHom.mker_zero`, `AddMonoid.Coprod.swap_map`, `MvPowerSeries.coeff_weightedHomogeneousComponent`, `MvPowerSeries.order_le`, `AddSubmonoid.FG.map`, `AddEquiv.symm_addMonoidHomCongrLeftEquiv`, `LocallyConstant.evalAddMonoidHom_apply`, `AddOreLocalization.numeratorHom_apply`, `LinearMap.re_inner_adjoint_mul_self_nonneg`, `AddCommGrpCat.μ_forget_apply`, `MonoidAlgebra.liftNC_single`, `AddLocalization.addEquivOfQuotient_apply`, `MeasureTheory.Integrable.re_im_iff`, `AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjective`, `Finsupp.degLex_def`, `uliftMultiplesHom_apply_apply`, `two_nsmul_lie_lmul_lmul_add_eq_lie_lmul_lmul_add`, `Filter.Germ.coe_coeAddHom`, `ContinuousMap.compAddMonoidHom'_apply`, `AddEquiv.addMonoidHomCongrRightEquiv_symm_apply`, `AddMonoidHom.comp_sub`, `CategoryTheory.Functor.coe_mapAddHom`, `Module.Finite.addMonoidHom`, `AddChar.toAddMonoidHomEquiv_symm_apply`, `AddGrpCat.forget₂_map_ofHom`, `Filter.Tendsto.compMeasurePreservingLp`, `NormedAddGroupHom.toAddMonoidHom_injective`, `AddCommGrpCat.epi_iff_surjective`, `AddEquiv.toMultiplicative_apply_apply`, `WeierstrassCurve.Affine.Point.map_baseChange`, `DFinsupp.sumAddHom_piSingle`, `AddAction.IsBlock.of_addSubgroup_of_conjugate`, `PresheafOfModules.freeAdjunctionUnit_app`, `AddSubmonoid.mrange_inr'`, `Matrix.entryAddMonoidHom_toAddHom`, `MvPowerSeries.coeff_trunc`, `Measurable.im`, `AddMonoidHom.addSubgroupMap_surjective`, `mulLeft_continuous`, `RCLike.norm_im_le_norm`, `ModularForm.coeHom_apply`, `AddMonoidHom.compHom'_apply_apply`, `MonoidHom.coe_toAdditiveLeft`, `WittVector.iterate_verschiebung_iterate_frobenius`, `ConvexOn.convex_re_epigraph`, `AddMonoidHom.coe_comp_rangeRestrict`, `Int.tendsto_zmultiplesHom_cofinite`, `ValueDistribution.characteristic_sub_characteristic_inv`, `RCLike.sqrt_of_nonneg`, `FreeAbelianGroup.notMem_support_iff`, `CategoryTheory.Discrete.addMonoidalFunctor_obj`, `FreeAddGroup.freeAddGroupCongr_apply`, `AddMonoidAlgebra.GradesBy.decompose_single`, `AddMonoidHom.toAddEquiv_apply`, `AddCon.kerLift_mk`, `LinearMap.isPositive_iff_complex`, `inner_self_eq_norm_sq`, `RCLike.lipschitzWith_re`, `AddCommGrpCat.forget₂_addGrp_map_ofHom`, `Finsupp.toMultiset_add`, `Measurable.re`, `WittVector.verschiebung_mul_frobenius`, `AddMonoidHom.noncommPiCoprod_mrange`, `convexHullAddMonoidHom_apply`, `AddGroupExtension.Equiv.rightHom_comm`, `AddMonoidAlgebra.singleAddHom_apply`, `Matrix.diagonalAddMonoidHom_apply`, `FreeAddMonoid.lift_comp_of`, `Multiset.toFinsupp_symm_apply`, `AddMonoidAlgebra.coe_liftNCAlgHom`, `FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG`, `FreeAbelianGroup.equivFinsupp_apply`, `QuotientAddGroup.lift_mk`, `MeasureTheory.Lp.norm_const`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff`, `AddCommGrpCat.forget₂AddCommMon_preservesLimitsOfShape`, `MvPowerSeries.exists_coeff_ne_zero_and_order`, `DirectSum.coeAddMonoidHom_of`, `MeasureTheory.AEStronglyMeasurable.re`, `AddMonCat.id_apply`, `AddCon.ker_apply`, `CategoryTheory.unopHom_apply`, `RCLike.I_im`, `DFinsupp.toMultiset_inf`, `AddCommMonCat.instSmallElemForallObjCompMonCatForget₂AddMonoidHomCarrierCarrierForgetSections`, `CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply`, `PolynomialModule.equivPolynomial_single`, `MvPolynomial.homogeneousComponent_apply`, `AddMonoidHom.op_apply_apply`, `DirectSum.GAlgebra.map_mul`, `iSupIndep.linearEquiv_apply`, `Multiset.replicateAddMonoidHom_apply`, `AddSubmonoid.mrange_inl_sup_mrange_inr`, `AddEquiv.addMonoidHomCongrLeftEquiv_symm_apply`, `AddMonoidHom.ext_iff`, `AddUnits.coeHom_injective`, `PresheafOfModules.toPresheaf_map_app_apply`, `ContinuousLinearMap.IsPositive.re_inner_nonneg_left`, `AddMonoidHom.inl_mono`, `ZMod.LFunction_def_even`, `AddSubmonoid.subtype_injective`, `ZMod.lift_comp_castAddHom`, `AddCommGrpCat.mono_iff_injective`, `AddMonoidHom.mapMatrix_neg`, `AddMonoidHom.coe_toRatLinearMap`, `quotient_norm_mk_eq`, `PresheafOfModules.Derivation'.d_app`, `ModuleCat.HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier`, `AddMonCat.ofHom_apply`, `AddMonoidHom.coe_toMultiplicative`, `PolynomialModule.smul_single_apply`, `AddCommGrpCat.Colimits.Quot.ι_desc`, `DFinsupp.mrange_mapRangeAddMonoidHom`, `DirectSum.of_injective`, `ModuleCat.FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits`, `AddEquiv.coprodAssoc_symm_apply_inl`, `CharacterModule.homEquiv_symm_apply_apply_apply`, `Matrix.diagAddMonoidHom_apply`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left`, `AddEquiv.punitCoprod_symm_apply`, `dNext_comp_left`, `groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe`, `AddMonoidHom.addSubmonoidMap_apply_coe`, `Summable.toCompl_tsum`, `instIsRightCancelAddAddMonoidHom`, `AddCommGrpCat.Colimits.Quot.map_ι`, `WittVector.ghostComponent_verschiebung`, `RCLike.ofNat_mul_im`, `AddSubgroup.mem_comap`, `QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk`, `PiTensorProduct.liftAux_tprod`, `AddMonoid.Coprod.inr_injective`, `Nat.coe_castAddMonoidHom`, `AddMonoidHom.map_mul₂`, `zsmulAddGroupHom_apply`, `AlgEquiv.algHomUnitsEquiv_apply_symm_apply`, `AddCommMonCat.hom_neg_apply`, `LinearEquiv.map_dfinsuppSumAddHom`, `AddCommGrpCat.kernelIsoKer_inv_comp_ι`, `RCLike.isCauSeq_im`, `InnerProductSpace.norm_sq_eq_re_inner`, `CentroidHom.coe_toAddMonoidHom_injective`, `AddGrpCat.forget_reflects_isos`, `ModuleCat.forget₂_obj_moduleCat_of`, `ContMDiffSection.coeAddHom_apply`, `AddMonoidHom.snd_comp_inl`, `AdicCompletion.sum_of`, `WithZero.lift_zero`, `AddMonoidHom.coe_toHomAddUnits`, `AddGrpCat.μ_forget_apply`, `AddCommGrpCat.forget₂AddGroup_preservesLimit`, `MonoidHom.toAdditiveRight_symm_apply_apply`, `Matrix.blockDiagonal'AddMonoidHom_apply`, `AddMonoidHom.toMultiplicativeLeft_symm_apply_apply`, `AddSubmonoid.bsupr_eq_mrange_dfinsuppSumAddHom`, `DirectSum.mulHom_apply`, `DirectSum.coe_mul_of_apply_of_mem_zero`, `DirectSum.of_eq_same`, `RCLike.hasSum_re`, `DomMulAct.instSMulCommClassAddMonoidHom`, `FreeAbelianGroup.lift_comp_apply`, `AddMonoidHom.map_zmultiples`, `AddCommGrpCat.injective_of_mono`, `CategoryTheory.ShortComplex.ShortExact.injective_f`, `AddMonoidHom.coe_smul`, `AddMonoidHom.restrict_apply`, `MeasureTheory.OuterMeasure.coeFnAddMonoidHom_apply`, `ModuleCat.instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax`, `AddGroupSeminorm.comp_add_le`, `AddCommGrpCat.instFullAddGrpCatForget₂AddMonoidHomCarrierCarrier`, `AddMonoid.Coprod.fst_apply_inl`, `monoidEndToAdditive_symm_apply_apply`, `AddSubmonoid.mem_closure_image_pos_iff`, `AddEquiv.toMultiplicativeRight_symm_apply_symm_apply`, `AddMonoidHom.dfinsuppSum_apply`, `AddMonoidHom.mapMatrix_apply`, `AddMonoid.fg_range`, `DirectSum.sigmaCurry_apply`, `MultilinearMap.alternatization_apply`, `QuotientAddGroup.norm_lift_apply_le`, `DirectSum.coeRingHom_of`, `Isometry.inl`, `locallyFinsuppWithin.logCounting_divisor`, `AddMonoid.Coprod.map_mk_ofList`, `WeierstrassCurve.Affine.Point.map_map`, `Homotopy.dNext_succ_chainComplex`, `AddMonoid.Coprod.mk_eq_mk`, `AddSubmonoid.LocalizationMap.toAddMonoidHom_injective`, `AddMonoid.Coprod.toProd_surjective`, `AddChar.coe_doubleDualEquiv`, `Subsemiring.isHomogeneous_iff_forall_subset`, `AddCon.mk'_ker`, `WittVector.map_verschiebung`, `AddMonoidHom.restrict_mrange`, `WittVector.verschiebung_frobenius`, `AddMonoidHom.instIsCentralScalar`, `PresheafOfModules.Elements.fromFreeYoneda_app_apply`, `AddMonoidHom.preimage_vadd_setₛₗ`, `AddMonoidAlgebra.liftNC_smul`, `AddCommGroup.DirectLimit.congr_apply_of`, `SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eq`, `AddMonoidHom.mker_prod_map`, `ModuleCat.HasColimit.coconePointSMul_apply`, `Complex.coe_imAddGroupHom`, `RCLike.mul_im_I_ax`, `Algebra.GrothendieckAddGroup.of_injective`, `CategoryTheory.ShortComplex.ab_exact_iff`, `AddGroupSeminorm.comp_apply`, `AddMonoidAlgebra.liftNC_single`, `AddUnits.embedProduct_apply`, `TensorProduct.SMul.aux_of`, `AddEquiv.addMonoidHomCongrLeft_trans`, `PrimeMultiset.coe_coePNatMonoidHom`, `MeasureTheory.VectorMeasure.mapGm_apply`, `AddCommGrpCat.coe_id`, `PreInnerProductSpace.Core.re_inner_nonneg`, `AddCommGrpCat.forget₂AddGroup_preservesLimitsOfSize`, `ModuleCat.instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier`, `AddEquiv.toMultiplicative_symm_apply_apply`, `CochainComplex.HomComplex.CohomologyClass.toHom_bijective`, `AddCommMonCat.coe_forget₂_obj`, `WithZero.map_injective`, `MulEquiv.toAdditive_symm_apply_apply`, `ZMod.lift_coe`, `LinearMap.mul''_apply`, `AddEquiv.addMonoidHomCongrRight_trans`, `Function.Exact.iff_of_ladder_addEquiv`, `FreeAddMonoid.lift_eval_of`, `RCLike.re_mul_ofReal`, `AddSubmonoid.mrange_inr`, `AlternatingMap.coe_alternatization`, `DirectSum.coe_mul_of_apply_aux`, `PiTensorProduct.mapLMultilinear_apply_apply`, `AddSubmonoid.mk_neg_add_mk_eq_zero`, `AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj`, `FreeAddGroup.sum_mk`, `FreeAddMonoid.mrange_lift`, `BoxIntegral.BoxAdditiveMap.map_apply`, `SkewMonoidAlgebra.liftNC_mul`, `Matrix.blockDiag'AddMonoidHom_apply`, `AddUnits.coe_map_neg`, `AddSubmonoid.surjOn_iff_le_map`, `CategoryTheory.ShortComplex.ShortExact.surjective_g`, `AddEquiv.addSubmonoidMap_symm_apply`, `AddMonCat.forget_preservesLimits`, `AddMonoid.Coprod.fst_apply_inr`, `Finsupp.toFreeAbelianGroup_toFinsupp`, `RCLike.im_tsum`, `AddMonoid.Coprod.swap_swap`, `smulAddHom_apply`, `AddMonoidAlgebra.gradeBy.gradedMonoid`, `AddSubmonoid.one_eq_mrange`, `AddSubmonoid.top_prod`, `CategoryTheory.ShortComplex.zero_apply`, `AddMonoidHom.map_list_sum`, `DirectSum.lie_of_same`, `CategoryTheory.NatTrans.appHom_apply`, `groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply`, `RCLike.norm_re_le_norm`, `AddAction.toPermHom_apply_symm_apply`, `AddGroupExtension.inl_injective`, `AddMonoidHom.apply_nat`, `AddEquiv.toAddMonoidHom_injective`, `AddGroupExtension.Section.rightHom_comp_section`, `re_inner_self_pos`, `AddAut.conj_apply`, `NumberField.mixedEmbedding.logMap_unit_smul`, `AddMonoidHom.zsmul_apply`, `MvPowerSeries.weightedOrder_eq_nat`, `QuotientAddGroup.quotientBot_apply`, `MvPowerSeries.totalDegree_trunc'`, `CochainComplex.HomComplex.CohomologyClass.mkAddMonoidHom_apply`, `TensorAlgebra.GradedAlgebra.ι_apply`, `WittVector.ghostComponent_zero_verschiebung`, `Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const`, `RCLike.geometric_hahn_banach_open`, `AddMonoidHom.toAddHom_injective`, `WithZero.map_injective'`, `AddEquiv.addMonoidHomCongrLeft_refl`, `SkewMonoidAlgebra.sum_mapDomain_index`, `AddUnits.coe_map`, `uliftZMultiplesHom_apply_apply`, `DFinsupp.toMultiset_injective`, `FreeAddMonoid.lift_restrict`, `DMatrix.map_add`, `Finset.le_card_quotient_add_sq_inter_addSubgroup`, `LocallyFiniteOrder.orderAddMonoidHom_apply`, `SkewMonoidAlgebra.toFinsupp_mapDomain`, `MonoidHom.coe_toAdditive_range`, `MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree`, `ContinuousMultilinearMap.alternatization_apply_toContinuousMultilinearMap`, `DFinsupp.mapRange.addMonoidHom_apply`, `Multiset.toFinsupp_toMultiset`, `SkewMonoidAlgebra.update_zero_eq_erase`, `AddSubmonoid.mrange_fst`, `AddLocalization.mkHom_apply`, `InnerProductSpace.Core.inner_mul_symm_re_eq_norm`, `AddSubmonoid.mrange_snd`, `FreeAbelianGroup.mul_def`, `ContMDiffMap.coeFnAddMonoidHom_apply`, `Matrix.traceAddMonoidHom_apply`, `AddLocalization.mkHom_surjective`, `DirectSum.toAddMonoidAlgebra_of`, `CategoryTheory.Discrete.addMonoidalFunctor_δ`, `Finset.coeAddMonoidHom_apply`, `AddMonoidHom.smul_apply`, `CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply`, `AddMonoid.Coprod.swap_inl`, `RCLike.re_le_re`, `AddMonoidAlgebra.grade.decompose_single`, `RCLike.reLm_coe`, `MonoidHom.toAdditive_id`, `AddMonoidHom.sub_mem_ker_iff`, `AddMonoidHom.neg_comp`, `AddMonoidHom.toMultiplicative_apply_apply`, `RCLike.natCast_im`, `AddGroupExtension.Section.rightHom_section`, `AddMonoidHom.map_finsum_Prop`, `AddSubmonoid.LocalizationMap.toAddMonoidHom_apply`, `AddGroupExtension.Section.exists_add_eq_add_add_inl`, `WeierstrassCurve.Affine.Point.toClass_some`, `MeasureTheory.MemLp.re`, `ModuleCat.mkOfSMul_smul`, `AddMonoidHom.fiberEquiv_apply`, `AddGrpCat.instSmallElemForallObjCompMonCatForget₂AddMonoidHomCarrierCarrierForgetSections`, `RCLike.ratCast_re`, `MeasureTheory.AEStronglyMeasurable.im`, `RCLike.ofReal_eq_re_of_isSelfAdjoint`, `DFinsupp.comp_liftAddHom`, `AddCommGrpCat.instReflectsIsomorphismsAddGrpCatForget₂AddMonoidHomCarrierCarrier`, `Matrix.IsHermitian.coe_re_apply_self`, `PresheafOfModules.sectionsMk_coe`, `MeasureTheory.Integrable.re`, `Finsupp.degree_preimage_nsmul`, `AddGroup.fg_iff_exists_freeAddGroup_hom_surjective`, `integral_coe_re_add_coe_im`, `NonUnitalRingHom.op_apply_apply`, `ZMod.toAddCircle_intCast`, `RCLike.lt_iff_re_im`, `MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder`, `ConvexOn.univ_sSup_affine_eq`, `AddMonoid.Coprod.snd_swap`, `HahnSeries.map_sub`, `AddCommGroup.DirectLimit.congr_symm_apply_of`, `AddCircle.continuous_mk'`, `AddMonoidHom.fiberEquivKer_symm_apply`, `DistribSMul.toAddMonoidHom_apply`, `FreeAddGroup.map.mk`, `norm_add_sq`, `DomMulAct.instSMulCommClassAddMonoidHom_1`, `RCLike.norm_sq_re_conj_add`, `PresheafOfModules.Derivation.d_app`, `AddGrpCat.neg_hom_apply`, `AddChar.compAddMonoidHom_apply`, `ZMod.toAddCircle_apply`, `Finsupp.sum_hom_add_index`, `AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf`, `norm_add_mul_self`, `MultilinearMap.domCoprod_alternization`, `FreeAddGroup.range_lift_le`, `AddEquiv.addMonoidHomCongrRightEquiv_apply`, `RCLike.conj_im`, `AddSubmonoid.mrange_inl`, `WeierstrassCurve.Affine.Point.toClass_injective`, `AddUnits.range_embedProduct`, `AddCommMonCat.coyonedaForget_inv_app_app`, `AddGrpCat.hom_neg_apply`, `MvPowerSeries.weightedOrder_le`, `AddMonoidHom.associator_eq_zero_iff_associative`, `WittVector.iterate_verschiebung_mul_coeff`, `InnerProductSpace.Core.inner_self_ofReal_re`, `RCLike.hasSum_iff`, `RCLike.measurable_im`, `MeasureTheory.AEEqFun.toGermAddMonoidHom_apply`, `AddMonoid.Coprod.lift_apply_mk`, `LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional`, `AddSubgroup.inclusion_inj`, `SubAddAction.fixingAddSubgroupEquivFixingAddSubgroup_coe_apply`, `AddMonoidHom.fst_mono`, `ModuleCat.reflectsColimitsOfShape`, `RCLike.re_eq_ofReal_of_isSelfAdjoint`, `AddMonoidHom.coe_mul`, `AddMonoid.Coprod.mrange_mk`, `FreeAddGroup.lift_symm_apply`, `LinearMap.snd_prodOfFinsuppNat`, `Finsupp.toFinset_toMultiset`, `DomAddAct.vadd_Lp_const`, `Finsupp.degree_single`, `ModuleCat.forget₂AddCommGroup_reflectsLimitOfSize`, `AddGrpCat.forget_preservesLimitsOfSize`, `Finsupp.applyAddHom_apply`, `addMonoidHomOfForallMemZMultiples_apply_gen`, `DirectSum.of_zero_pow`, `AddMonoidHom.ext_int_iff`, `AddMonoid.Coprod.mrange_inl_sup_mrange_inr`, `Matrix.PosSemidef.re_dotProduct_nonneg`, `QuotientAddGroup.map_mk'`, `DirectSum.coeFnAddMonoidHom_apply`, `PresheafOfModules.Derivation'.app_apply`, `Filter.coe_pureAddMonoidHom`, `AddMonoid.Coprod.mclosure_range_inl_union_inr`, `Module.End.baseChangeHom_apply_apply`, `MvPolynomial.weightedDecomposition.decompose'_eq`, `SchwartzMap.coe_coeHom`, `AddCommGrpCat.biprodIsoProd_inv_comp_desc_apply`, `AddSubmonoid.LocalizationMap.lift_id`, `AddEquiv.toMultiplicative_symm_apply_symm_apply`, `ProjectiveSpectrum.basicOpen_eq_union_of_projection`, `Finsupp.le_weight_of_ne_zero`, `MonoidHom.coe_toAdditive`, `CochainComplex.HomComplex.CohomologyClass.descAddMonoidHom_cohomologyClass`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_component`, `DirectSum.of_natCast`, `Algebra.Extension.tensorCotangentInvFun_smul_mk`, `AddSubgroupClass.coe_inclusion`, `AddMonoidHom.mem_mgraph`, `AddCommGrpCat.ofHom_apply`, `DirectSum.coe_mul_of_apply_add`, `RCLike.re_le_norm`, `Multiset.toFinsupp_eq_iff`, `ContinuousLinearMap.isPositive_iff_complex`, `AddMonoid.Coprod.mker_swap`, `Polynomial.eval₂AddMonoidHom_apply`, `AddCommGrpCat.biprodIsoProd_inv_comp_fst_apply`, `DirectSum.map_apply`, `Pi.evalAddMonoidHom_apply`, `Finsupp.mapDomain.addMonoidHom_apply`, `AddMonoidHom.coe_toMultiplicative_map`, `RCLike.ofNat_im`, `DistribMulActionHom.coe_fn_coe`, `CategoryTheory.Discrete.addMonoidalFunctor_μ`, `NumberField.Units.logEmbeddingQuot_injective`, `DirectSum.coe_of_mul_apply_of_le`, `DirectSum.support_of_subset`, `QuotientAddGroup.con_ker_eq_addConKer`, `DirectSum.coe_mul_of_apply_of_le`, `AddMonoidHom.map_div₂`, `DirectSum.coe_of_mul_apply_of_mem_zero`, `ZMod.lift_injective`, `MvPolynomial.homogeneousSubmodule_eq_finsupp_supported`, `zmultiplesHom_apply`, `NonUnitalNonAssocSemiring.mem_center_iff`, `FreeAbelianGroup.liftMonoid_coe`, `Subgroup.toAddSubgroup_comap`, `CategoryTheory.Functor.mapAddHom_apply`, `AddMonoidHom.coe_mulRight`, `RCLike.norm_sq_eq_def`, `AddCon.kerLift_injective`, `AddMonoidHom.vaddZeroHom_apply`, `AddMonCat.hom_neg_apply`, `Matrix.IsHermitian.coe_re_diag`, `AddMonoidHom.coe_comp`, `ContinuousMultilinearMap.alternatization_apply_toAlternatingMap`, `Surreal.dyadicMap_apply`, `Finsupp.liftAddHom_singleAddHom`, `MeasureTheory.Lp.constL_apply`, `DirectSum.of_apply`, `addMonoidHomLequivNat_apply`, `AddCommMonCat.instIsRightAdjointForgetAddMonoidHomCarrier`, `RCLike.ratCast_im`, `DirectSum.of_intCast`, `Function.locallyFinsuppWithin.restrictMonoidHom_apply`, `Finsupp.toMultiset_sum`, `AddSubmonoidClass.subtype_injective`, `dNext_eq_dFrom_fromNext`, `DirectSum.GAlgebra.smul_def`, `AddMonoidHom.map_addCyclic`, `MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc'`, `RCLike.I_mul_re`, `Multiset.toDFinsupp_injective`, `AddSubgroup.subtype_injective`, `AddGrpCat.comp_apply`, `AddSubmonoid.inclusion_injective`, `RCLike.conj_eq_iff_im`, `DirectSum.mul_eq_sum_support_ghas_mul`, `AddCon.map_apply`, `FreeAddMonoid.map_symm_apply_map_eq`, `Finsupp.range_single_one`, `SemiRingCat.forget₂AddCommMon_preservesLimits`, `Function.locallyFinsuppWithin.logCounting_mono`, `AddChar.toAddMonoidHom_apply`, `Function.ExtendByZero.hom_apply`, `AddMonoidHom.map_sub`, `SkewMonoidAlgebra.liftNC_single`, `AddSubgroup.coe_map`, `WittVector.verschiebung_shift`, `SubAddAction.of_fixingAddSubgroupEmpty_mapScalars_surjective`, `DFinsupp.sumAddHom_apply`, `RCLike.conj_re_ax`, `addMonoidHomLequivInt_symm_apply`, `Homotopy.prevD_zero_cochainComplex`, `MvPowerSeries.WithPiTopology.tendsto_trunc'_atTop`, `AddAction.stabilizerEquivStabilizer_apply`, `AddMonoidHom.surjective_of_card_ker_le_div`, `AddMonoidHom.coprod_apply`, `ZMod.toAddCircle_injective`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `PrimeMultiset.coe_coeNatMonoidHom`, `DFinsupp.liftAddHom_singleAddHom`, `CochainComplex.HomComplex.Cochain.shiftAddHom_apply`, `CategoryTheory.ShortComplex.ab_zero_apply`, `Function.Exact.iff_addMonoidHom_rangeRestrict`, `AddGrpCat.FilteredColimits.forget₂AddMon_preservesFilteredColimits`, `CategoryTheory.Discrete.addMonoidalFunctor_ε`, `Algebra.GrothendieckAddGroup.lift_apply`, `MultilinearMap.alternatization_coe`, `AddGroupSeminorm.coe_comp`, `CategoryTheory.Abelian.Ext.postcomp_mk₀_injective_of_mono`, `MulEquiv.toAdditive_symm_apply_symm_apply`, `AddMonoidHom.mrangeRestrict_mker`, `inner_mul_symm_re_eq_norm`, `AddCommGrpCat.HasLimit.lift_hom_apply`, `Submodule.re_inner_starProjection_nonneg`, `MeasureTheory.MemLp.im`, `AddMonoidAlgebra.liftNC_one`, `Multiset.toDFinsupp_le_toDFinsupp`, `DirectSum.liftRingHom_symm_apply_coe`, `Multiset.toDFinsupp_toMultiset`, `ModuleCat.HasColimit.colimitCocone_pt_carrier`, `ModuleCat.forget₂_addCommGrp_additive`, `MonoidAlgebra.liftNC_smul`, `AddMonoidHom.closure_preimage_le`, `RCLike.realRingEquiv_apply`, `AddMonoid.Coprod.fst_surjective`, `Homotopy.comm`, `WeierstrassCurve.Affine.Point.map_some`, `Multiset.toDFinsupp_singleton`, `MulEquiv.toAdditive_apply_symm_apply`, `RingCat.forget₂AddCommGroup_preservesLimitsOfSize`, `RCLike.mul_im`, `SkewMonoidAlgebra.erase_single`, `AddMonoid.Coprod.map_apply_inl`, `AddCommMonCat.forget₂_map_ofHom`, `DirectSum.coe_mul_of_apply`, `MvPowerSeries.order_monomial`, `AddMonoidHom.addCommute_inl_inr`, `RCLike.im_sq_le_normSq`, `DirectSum.mul_eq_dfinsuppSum`, `AddMonoidHom.coe_single`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_weight`, `QuotientAddGroup.map_mk`, `Finsupp.liftAddHom_apply_single`, `dNext_eq`, `addMonoidHomOfMemClosureRangeCoe_apply`, `AddSubmonoid.map_inr`, `AddMonoidHom.mk'_apply`, `AddGrpCat.epi_iff_surjective`, `summable_iff_cauchySeq_finset_and_tsum_mem`, `AddCommGrpCat.forget₂_commMonCat_map_ofHom`, `AddEquiv.addMonoidHomCongrRightEquiv_trans`, `LinearMap.tensorProduct_apply`, `AddCommGrpCat.forget₂AddCommMon_preservesLimitsOfSize`, `WithZero.lift_unique`, `AddMonoid.Coprod.mrange_swap`, `NonUnitalRingHom.coe_toAddMonoidHom`, `Behrend.map_zero`, `RCLike.re_ofReal_pow`, `HahnSeries.map_add`, `re_inner_self_nonpos`, `RCLike.norm_sq_re_add_conj`, `LinearMap.IsSymmetric.im_inner_apply_self`, `Finsupp.embDomain.addMonoidHom_apply`, `FreeAddMonoid.comp_lift`, `Isometry.inr`, `NormedAddGroupHom.coeAddHom_apply`, `DirectSum.of_eq_of_gradedMonoid_eq`, `AddCommMonCat.forget_isCorepresentable`, `RCLike.im_to_complex`, `Multiset.coe_countAddMonoidHom`, `InnerProductSpace.Core.cauchy_schwarz_aux'`, `AddCommGrpCat.coyoneda_map_app`, `AddChar.doubleDualEquiv_symm_doubleDualEmb_apply`, `AddMonoidHom.coeFn_apply`, `WittVector.verschiebung_frobenius_comm`, `CategoryTheory.Discrete.addMonoidalFunctor_η`, `AddEquiv.symm_addMonoidHomCongrRightEquiv`, `TensorProduct.liftAux.smul`, `Function.locallyFinsuppWithin.logCounting_le`, `Finsupp.weight_sub_single_add`, `AddAction.toPermHom_apply_apply`, `AddMonoidHom.range_le_ker_iff`, `DFinsupp.sumAddHom_zero`, `RCLike.re_eq_complex_re`, `AddSubmonoid.mrange_inl'`, `DirectSum.ofList_dProd`, `Module.End.lTensorAlgHom_apply_apply`, `DirectSum.GAlgebra.commutes`, `RCLike.norm_to_complex`, `AddCommGrpCat.forget_map`, `FreeAbelianGroup.lift_comp`, `AddMonoidHom.coe_ofMapMidpoint`, `FreeAddMonoid.lift_of_comp_eq_map`, `Nonneg.coeAddMonoidHom_apply`, `RCLike.re_sq_le_normSq`, `AddSubmonoid.mem_iSup_iff_exists_dfinsupp`, `AddMonoidHom.sub_comp`, `QuotientAddGroup.map_map`, `MvPolynomial.degrees_monomial_eq`, `QuotientAddGroup.lift_quot_mk`, `WittVector.iterate_verschiebung_mul_left`, `CategoryTheory.pullbackShiftFunctorZero'_inv_app`, `AddCommGroup.DirectLimit.map_id`, `instSubsingletonAddMonoidHom`, `TwoSidedIdeal.coeAddMonoidHom_apply`, `AddMonoidHom.map_multiset_sum`, `AddMonoid.Coprod.mrange_eq`, `AddMonoidHom.comap_mker`, `AddMonoidHom.associator_eq_zero`, `AddSubmonoid.LocalizationMap.map_id`, `FreeAbelianGroup.lift_add_apply`, `AddChar.toAddMonoidHomEquiv_zero`, `RCLike.mul_re`, `ModuleCat.forget₂_reflectsLimits`, `AddCommGrpCat.kernelIsoKer_hom_comp_subtype`, `UniformSpace.Completion.continuous_toCompl`, `FreeAddMonoid.map_of`, `ContDiffMapSupportedIn.coe_coeHom`, `ContinuousMap.addEquivBoundedOfCompact_symm_apply`, `Matrix.blockDiagAddMonoidHom_apply`, `MeasureTheory.Lp.toLp_compMeasurePreserving`, `ModuleCat.forget₂PreservesColimitsOfShape`, `WittVector.iterate_verschiebung_coeff`, `AddAction.coe_toPermHom`, `FreeAddGroup.lift_eq_sum_map`, `AddMonoidHom.coe_dfinsuppSum`, `AddMonoidHom.ker_eq_top_iff`, `AddCommMonCat.equivalence_counitIso`, `AddMonoidHom.ker_toAddSubmonoid`, `Seminorm.coeFnAddMonoidHom_apply`, `RCLike.re_le_neg_norm_iff_eq_neg_norm`, `DirectSum.Decomposition.left_inv`, `RCLike.to_complex_nonneg_iff`, `DirectSum.GAlgebra.map_one`, `Module.toAddMonoidEnd_apply_apply`, `AddMonoid.Coprod.closure_range_inl_union_inr`, `QuotientAddGroup.kerLift_mk'`, `AddCommMonCat.forget_preservesLimitsOfSize`, `ModuleCat.forget₂AddCommGroup_reflectsLimit`, `AddGrpCat.coe_comp`, `MvPolynomial.coeffAddMonoidHom_apply`, `AddGroupExtension.Equiv.inl_comm`, `Finsupp.liftAddHom_symm_apply_apply`, `AddMonoidHom.range_zero`, `NumberField.Units.logEmbeddingEquiv_apply`, `AddEquiv.addMonoidHomCongrLeftEquiv_trans`, `AddEquiv.toMultiplicativeLeft_symm_apply_apply`, `RCLike.im_ofReal_mul`, `FreeAbelianGroup.lift_ext_iff`, `AddMonoidHom.add_apply`, `inner_self_re_eq_norm`, `prevD_comp_right`, `Circle.expHom_apply`, `LaurentPolynomial.leftInverse_trunc_toLaurent`, `DirectSum.Decomposition.right_inv`, `AddEquiv.coprodAssoc_apply_inl_inl`, `FreeAddMonoid.map_apply_map_symm_eq`, `QuotientAddGroup.quotientQuotientEquivQuotientAux_mk`, `PresheafOfModules.freeAdjunction_unit_app`, `RCLike.I_re`, `CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff`, `DirectSum.decompose_coe`, `Multiset.toDFinsupp_inter`, `AddGroupExtension.Section.rightInverse_rightHom`, `AddSubmonoid.LocalizationMap.lift_localizationMap_mk'`, `RCLike.im_eq_complex_im`, `instIsLeftCancelAddAddMonoidHom`, `AddSubgroup.surjOn_iff_le_map`, `AddMonoidHom.toMultiplicativeLeft_apply_apply`, `AddSubmonoid.comap_id`, `DirectSum.sigmaUncurry_apply`, `AddMonoidAlgebra.decomposeAux_single`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `AddCon.comapQuotientEquivOfSurj_symm_mk'`, `RCLike.ofReal_im_ax`, `Behrend.map_eq_iff`, `zmultiplesHom_symm_apply`, `AddGroupExtension.Equiv.rightHom_map`, `AddChar.doubleDualEmb_inj`, `Finsupp.DegLex.le_iff`, `QuotientAddGroup.mk'_surjective`, `AddMonoidHom.mapMatrix_add`, `Finsupp.liftAddHom_symm_apply`, `CategoryTheory.Functor.mapExtAddHom_coe`, `InnerProductSpace.Core.inner_self_im`, `addAddMonoidHom_apply`, `AddMonoidHom.mulOp_symm_apply_apply`, `AddCommMonCat.id_apply`, `AddMonoidHom.coe_mulLeft`, `AddMonoid.Coprod.con_ker_mk`, `groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom`, `MeasureTheory.Lp.compMeasurePreserving_continuous`, `DirectSum.list_prod_ofFn_of_eq_dProd`, `Finsupp.degree_eq_zero_iff`, `AddMonoidHom.coe_toIntLinearMap`, `Finsupp.toMultiset_single`, `AddMonoidHom.transfer_def`, `ModuleCat.forget₂AddCommGroup_preservesLimit`, `AddCommMonCat.coyoneda_obj_map`, `AddMonCat.equivalence_functor_map`, `Behrend.threeAPFree_image_sphere`, `WittVector.verschiebung_coeff_add_one`, `WeierstrassCurve.Affine.Point.toClass_eq_zero`, `LinearMap.evalAddMonoidHom_apply`, `AEMeasurable.re`, `AddMonoidHom.mrange_id`, `QuotientAddGroup.kerLift_injective`, `FreeAddMonoid.countP_apply`, `AddChar.doubleDualEmb_eq_zero`, `MonoidHom.coe_toAdditiveRight`, `FreeAbelianGroup.lift_neg_apply`, `AddSubgroup.mem_map`, `MonoidAlgebra.lift_def`, `ZMod.toAddCircle_eq_zero`, `Multiset.toDFinsupp_lt_toDFinsupp`, `AddSubmonoid.comap_comap`, `DFinsupp.liftAddHom_comp_single`, `AddMonoidHom.eq_iff`, `AddMonoidHom.eq_iff_eq_on_generator`, `Homotopy.dNext_cochainComplex`, `DFinsupp.sumAddHom_add`, `CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply`, `Multiset.toDFinsupp_union`, `AddEquiv.coprodCongr_symm_apply`, `Finsupp.sum_smul_index_addMonoidHom`, `AddMonoidHom.exact_iff`, `AddSubmonoid.subtype_apply`, `AddSubmonoidClass.subtype_apply`, `AddMonoidHom.dfinsuppSumAddHom_apply`, `Finsupp.comapDomain.addMonoidHom_apply`, `FreeAbelianGroup.lift_apply_of`, `MvPowerSeries.order_eq_nat`, `DirectSum.coe_of_apply`, `RCLike.re_ofReal_mul`, `norm_add_pow_two`, `zmultiplesAddHom_apply`, `AddMonoidHom.coe_toZModLinearMap`, `DomMulAct.smul_Lp_const`, `AddEquiv.coprodComm_symm_apply`, `FreeAbelianGroup.liftAddEquiv_apply_apply`, `AddMonoidAlgebra.decomposeAux_eq_decompose`, `QuotientAddGroup.exists_norm_add_lt`, `norm_eq_sqrt_re_inner`, `RCLike.iInter_halfSpaces_eq`, `inner_self_nonneg`, `RCLike.continuous_im`, `LaurentPolynomial.trunc_C_mul_T`, `AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde`, `MonoidHom.toAdditiveLeft_symm_apply_apply`, `WittVector.aeval_verschiebungPoly`, `LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues`, `dNext_comp_right`, `RCLike.normSq_add`, `RCLike.div_re`, `WittVector.verschiebung_isPoly`, `setIntegral_re_add_im`, `AddChar.compAddMonoidHom_injective_right`, `RCLike.geometric_hahn_banach_compact_closed`, `addMonoidEndRingEquivInt_symm_apply`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_degree`, `MvPolynomial.coeff_weightedHomogeneousComponent`, `AddMonoidHom.mker_inr`, `FreeAddGroup.lift_of_apply`, `AddChar.doubleDualEmb_doubleDualEquiv_symm_apply`, `SemiRingCat.forget₂AddCommMon_preservesLimitsOfSize`, `DFinsupp.singleAddHom_apply`, `CategoryTheory.whiskering_linearYoneda₂`, `DirectSum.coe_congrAddEquiv`, `Finsupp.degree_mono`, `AddCommMonCat.coyonedaForget_hom_app_app_hom`, `RCLike.geometric_hahn_banach_point_closed`, `DirectSum.liftRingHom_apply`, `summable_iff_summable_compl_and_tsum_mem`, `CliffordAlgebra.GradedAlgebra.lift_ι_eq`, `RingHom.map_dfinsuppSumAddHom`, `TensorPower.toTensorAlgebra_galgebra_toFun`, `WithZero.map_map`, `AddCommMonCat.equivalence_inverse_map`, `re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four`, `AddMonoidAlgebra.lift_def`, `TensorAlgebra.toDirectSum_ι`, `FreeAddMonoid.hom_map_lift`, `DirectSum.lmap_of`, `PresheafOfModules.sections_ext_iff`, `Finsupp.eraseAddHom_apply`, `AddCommGrpCat.hom_neg_apply`, `MonoidHom.coe_toAdditive''`, `AddSubgroup.inclusion_injective`, `Finsupp.toMultiset_sup`, `AddSubmonoid.coe_subtype`, `AddMonoid.Coprod.swap_inr`, `DFinsupp.toMultiset_inj`, `AddMonoidHom.noncommPiCoprod_single`, `norm_sub_pow_two`, `Set.coe_singletonAddMonoidHom`, `Matrix.blockDiagonalAddMonoidHom_apply`, `MvPowerSeries.trunc'_one`, `RCLike.conj_eq_re_sub_im`, `InnerProductSpace.Core.re_inner_smul_ofReal_smul_self`, `SubAddAction.fixingAddSubgroup_map_conj_eq`, `AddGrpCat.forget_isCorepresentable`, `AddChar.toAddMonoidHomEquiv_apply`, `MvPowerSeries.trunc_C_mul`, `SkewMonoidAlgebra.single_add_erase`, `AddCommGroup.DirectLimit.map_apply_of`, `UniformSpace.Completion.isDenseInducing_toCompl`, `PresheafOfModules.germ_ringCat_smul`, `FreeAddGroup.map.of`, `AddMonoidHom.comp_apply`, `AddMonoidHom.finset_sum_apply`, `AddMonoid.Coprod.snd_comp_inl`, `integral_re`, `AddMonoidHom.comp_neg`, `AddMonoidHom.mapDMatrix_apply`, `ModuleCat.HasColimit.reflectsColimit`, `AddMonoid.Coprod.lift_swap`, `AddMonoidHom.map_add`, `AlgebraicGeometry.Scheme.Modules.Hom.app_smul`, `RCLike.normSq_apply`, `AddMonoidHom.toIntLinearMap_injective`, `DFinsupp.toMultiset_lt_toMultiset`, `FreeAddMonoid.map_map`, `Finset.imageAddMonoidHom_apply`, `Finsupp.DegLex.monotone_degree`, `AddMonoidHom.coe_ofClosureMEqTopLeft`, `AddGroupExtension.rightHom_comp_inl`, `AddCommGrpCat.hom_add_apply`, `addMonoidEndToMultiplicative_apply_apply`, `AddSubgroup.quotientAddSubgroupOfEmbeddingOfLE_apply_mk`, `AddMonoidHom.compLeft_apply`, `ConvexOn.exists_affine_le_of_lt`, `AddSubgroupClass.subtype_injective`, `AddCommGrpCat.ofHom_injective`, `AddMonoidHom.inr_strictMono`, `AddUnits.continuous_embedProduct`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right`, `AddMonoidHom.smulLeft_apply`, `FreeAddMonoid.countP_of`, `AddSubgroupClass.inclusion_right`, `AddEquiv.coprodAssoc_symm_apply_inr_inl`, `Multiplicative.monoidHom_ext_iff`, `AddMonoidHom.instIsScalarTower`, `SheafOfModules.pushforwardSections_coe`, `WeierstrassCurve.Affine.Point.map_zero`, `DFinsupp.lsum_apply_apply`, `FreeAbelianGroup.lift_neg`, `PresheafOfModules.fromFreeYonedaCoproduct_app_mk`, `NumberField.Units.regulator_eq_det'`, `PresheafOfModules.Sheafify.map_smul`, `AddEquiv.addMonoidHomCongrRight_refl`, `MvPowerSeries.trunc'_map`, `AddMonoidHom.coe_ofClosureMEqTopRight`, `re_inner_le_norm`, `SlashInvariantForm.coeHom_injective`, `OrderAddMonoidHom.coe_mk`, `DirectSum.of_zero_one`, `PresheafOfModules.germ_smul`, `MonoidAlgebra.liftNC_one`, `ValueDistribution.logCounting_coe`, `DirectSum.decompose_symm_of`, `Pi.addMonoidHom_apply`, `CharacterModule.homEquiv_apply_apply`, `ExteriorAlgebra.GradedAlgebra.ι_apply`, `AddGrpCat.instFullMonCatForget₂AddMonoidHomCarrierCarrier`, `AddSubgroup.normedMk.apply`, `RCLike.mul_re_ax`, `dNext_nat`, `LinearMap.im_inner_adjoint_mul_self_eq_zero`, `ValueDistribution.log_counting_zero_sub_logCounting_top`, `UniformSpace.Completion.toCompl_apply`, `AddSubmonoid.closure_eq_mrange`, `TestFunction.coeFnAddMonoidHom_apply`, `AddMonoidHom.map_one₂`, `FreeAbelianGroup.liftMonoid_symm_coe`, `PresheafOfModules.toSheafify_app_apply`, `DirectSum.gsmulHom_apply_apply`, `CategoryTheory.CommShift₂Setup.z_zero₂`, `Ideal.toIdeal_homogeneousHull_eq_iSup`, `integral_re_add_im`, `DirectSum.sum_support_of`, `AddCommGrpCat.instIsRightAdjointForgetAddMonoidHomCarrier`, `AddMonoidHom.completion_zero`, `AddSubgroup.subtype_apply`, `AddAut.neg_conj_apply`, `MonoidHom.coe_toMultiplicative`, `AddCommGrpCat.forget_isCorepresentable`, `FreeAddGroup.sum.of`, `RCLike.norm_le_im_iff_eq_I_mul_norm`, `LocallyFiniteOrder.orderAddMonoidEquiv_apply`, `RCLike.re_to_complex`, `SkewMonoidAlgebra.lift_def`, `CoalgHom.coe_toAddMonoidHom`, `DirectSum.toAddMonoid_injective`, `AddMonoidHom.map_mul_iff`, `qExpansion_of_pow`, `AddMonoidHom.coe_toMultiplicative''`, `AddMonoidHom.coe_range`, `AffineAddMonoid.embedding_injective`, `DFinsupp.liftAddHom_symm_apply`, `AddEquiv.addMonoidHomCongrRight_apply`, `RCLike.hasSum_im`, `ZMod.LFunction_dft`, `Algebra.GrothendieckAddGroup.lift_symm_apply`, `AddMonoidHom.mrangeRestrict_surjective`, `Matrix.mulVec.addMonoidHomLeft_apply`, `AddUnits.isClosedEmbedding_embedProduct`, `PresheafOfModules.freeAdjunction_homEquiv`, `DirectSum.toAddMonoid_of`, `DirectSum.of_zero_ofNat`, `dNext_eq_zero`, `RCLike.isCauSeq_re`, `SkewMonoidAlgebra.equivMapDomain_eq_mapDomain`, `ModuleCat.forget₂AddCommGroupIsEquivalence`, `HahnSeries.coeff.addMonoidHom_apply`, `RCLike.I_im'`, `Finsupp.nsmul_single_one_image`, `AddMonoidHom.inr_apply`, `Finsupp.DegLex.lt_def`, `Additive.addMonoidHom_ext_iff`, `AddMonoidHom.mker_inl`, `AddEquiv.coe_toAddMonoidHom`, `AddMonoidHom.mem_ker`, `Seminorm.coeFnAddMonoidHom_injective`, `MvPowerSeries.order_monomial_of_ne_zero`, `DoubleCentralizer.toProdHom_apply`, `CochainComplex.HomComplex.CohomologyClass.toHom_mk`, `QuotientAddGroup.rangeKerLift_injective`, `RingHom.coe_addMonoidHom_injective`, `addOrderOf_map_dvd`, `WittVector.frobenius_verschiebung`, `Finsupp.toMultiset_sum_single`, `AddMonoidHom.ker_zero`, `CategoryTheory.preadditiveCoyoneda_obj`, `NumberField.Units.regOfFamily_eq_det'`, `AddSubgroup.toSubgroup_comap`, `Continuous.compMeasurePreservingLp`, `MeasureTheory.Lp.const_val`, `DFinsupp.filterAddMonoidHom_apply`, `ConvexOn.sSup_affine_eq`, `KaehlerDifferential.quotKerTotalEquiv_apply`, `AddMonoid.Coprod.mk_of_inl`, `MeasureTheory.FiniteMeasure.toMeasureAddMonoidHom_apply`, `DirectSum.map_eq_iff`, `ContinuousOn.compMeasurePreservingLp`, `ContDiffMapSupportedIn.coeHom_injective`, `AddMonoidHom.map_finsum_mem`, `AddCommMonCat.forget_map`, `AddMonoidHom.ext_iff₂`, `LinearMap.IsSymmetric.coe_re_inner_apply_self`, `multiplesHom_apply`, `Finsupp.weight_eq_zero_iff_eq_zero`, `Function.locallyFinsuppWithin.logCounting_even`, `Surreal.dyadicMap_apply_pow`, `Finsupp.toMultiset_map`, `AddMonoidHom.mem_range`, `WithTop.coe_addHom`, `MonoidHom.toAdditiveRight_apply_apply`, `iSupIndep_iff_dfinsuppSumAddHom_injective`, `RCLike.geometric_hahn_banach_closed_compact`, `AddSubmonoid.mem_map_equiv`, `AddCommGrpCat.hom_neg`, `DMatrix.map_sub`, `CategoryTheory.CommShift₂Setup.z_zero₁`, `addMonoidHomOfTendsto_apply`, `RCLike.intCast_im`, `PresheafOfModules.freeObjDesc_app`, `AddMonoidHom.comp_add`, `DirectSum.coe_of_mul_apply`, `groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc`, `AddCommMonCat.forget_reflects_isos`, `AddMonoidHom.flipHom_apply`, `AddMonoidHom.apply_int`, `inner_im_symm`, `RCLike.re_extendTo𝕜'ₗ`, `WithZero.mapAddHom_injective`, `Finsupp.toMultiset_inf`, `CategoryTheory.CommShift₂Setup.hε`, `AddMonoidHom.prod_apply`, `Submodule.map_toAddSubmonoid`, `WeierstrassCurve.Affine.Point.toClass_apply`, `MeasureTheory.memLp_re_im_iff`, `CommGrpCat.toAddCommGrp_map`, `AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat`, `AddMonoidHom.mulRight₃_apply`, `AddUnits.isEmbedding_embedProduct`, `RCLike.normSq_sub`, `CategoryTheory.ShortComplex.exact_iff_exact_map_forget₂`, `Finsupp.weight_apply`, `AddCommGrpCat.homAddEquiv_apply`, `RCLike.re_tsum`, `ContinuousLinearMap.IsPositive.re_inner_nonneg_right`, `Finsupp.degree_def`, `Finsupp.sum_mapDomain_index_addMonoidHom`, `AddSubmonoid.LocalizationMap.lift_left_inverse`, `LeftInvariantDerivation.coeFnAddMonoidHom_apply`, `AlgHom.coe_toAddMonoidHom`, `SemimoduleCat.forget₂_obj`, `FreeAbelianGroup.map_comp_apply`, `SkewMonoidAlgebra.mapDomain_apply`, `MvPolynomial.weightedHomogeneousComponent_apply`, `Finsupp.coe_orderIsoMultiset`, `MeasureTheory.Lp.isometry_compMeasurePreserving`, `ContinuousMapZero.coeFnAddMonoidHom_apply`, `QuotientAddGroup.rangeKerLift_surjective`, `QuotientAddGroup.quotientQuotientEquivQuotientAux_mk_mk`, `AddUnits.isInducing_embedProduct`, `LocallyConstant.mapAddMonoidHom_apply`, `PolynomialModule.map_single`, `MonoidHom.coe_toAdditive'`, `MonoidHom.coe_toAdditive_ker`, `RCLike.imCLM_apply`, `AddMonoidHom.map_finsum_of_preimage_zero`, `DirectSum.Gmodule.smul_def`, `GradedRing.proj_apply`, `SemimoduleCat.forget₂_map`, `AddMonoidHom.coe_mrangeRestrict`, `ConvexOn.univ_sSup_of_nat_affine_eq`, `AddGroupExtension.rightHom_surjective`, `AddGrpCat.ofHom_apply`, `CategoryTheory.ShortComplex.ShortExact.ab_exact_iff_function_exact`, `QuotientAddGroup.mk'_apply`, `AddMonoidHom.mapMatrix_smul`, `CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier`, `RCLike.geometric_hahn_banach_open_open`, `HomologicalComplex.Hom.fAddMonoidHom_apply`, `RCLike.lipschitzWith_im`, `Complex.coe_reAddGroupHom`, `SkewMonoidAlgebra.singleAddHom_apply`, `WithZero.mapAddHom_mapAddHom`, `AddMonoidHom.coe_fst`, `mulLeft_bound`, `commute_rmul_rmul_sq`, `FreeAddMonoid.hom_eq_iff`, `AddMonoidHom.add_comp`, `AddMonoidHom.coe_finsuppSum`, `Multiset.toDFinsupp_inj`, `val_addUnitsCenterToCenterAddUnits_apply_coe`, `OrthogonalFamily.projection_directSum_coeAddHom`, `CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply`, `ContinuousAlternatingMap.toMultilinearAddHom_apply`, `MeasureTheory.Lp.compMeasurePreserving_val`, `addMonoidEndToMultiplicative_symm_apply_apply`, `AddEquiv.toMultiplicativeLeft_apply_apply`, `addUnitsCenterToCenterAddUnits_injective`, `GradedRing.proj_recompose`, `MeasureTheory.Lp.norm_compMeasurePreserving`, `MultilinearMap.alternatization_def`, `integral_im`, `AddSubmonoid.map_map`, `DomMulAct.mk_smul_addMonoidHom_apply`, `SkewMonoidAlgebra.liftNC_smul`, `AddMonoidAlgebra.mapDomainRingHom_apply`, `AddEquiv.punitCoprod_apply`, `FreeAddGroup.range_lift_eq_closure`, `RCLike.im_le_norm`, `AddSubgroup.coe_inclusion`, `AddCommGrpCat.toCommGrp_map`, `CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply`, `Matrix.IsHermitian.im_star_dotProduct_mulVec_self`, `Finsupp.toMultiset_eq_iff`, `AddMonoidHom.mrange_comp`, `Fin.accumulate_injective`, `SkewMonoidAlgebra.coeff_erase_apply`, `AddMonoidHom.mker_snd`, `DirectSum.map_surjective`, `CochainComplex.HomComplex_d_hom_apply`, `AlgebraicGeometry.Scheme.Modules.map_smul`, `Fin.accumulate_last`, `CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply`, `MvPowerSeries.trunc'_C`, `Multiset.coe_mapAddMonoidHom`, `RCLike.inv_re`, `AddSubgroupClass.coe_subtype`, `PiTensorProduct.mapLMultilinear_toFun_apply`, `DFinsupp.subtypeDomainAddMonoidHom_apply`, `AddCommGrpCat.hasLimit_iff_small_sections`, `Matrix.PosDef.re_dotProduct_pos`, `MvPolynomial.decomposition.decompose'_eq`, `Behrend.map_monotone`, `MonoidHom.coe_toMultiplicative_ker`, `AddEquiv.symm_addMonoidHomCongrLeft`, `hasSum_iff_hasSum_compl`, `MultilinearMap.coeAddMonoidHom_apply`, `AddCommGrpCat.hom_zsmul`, `SemiRingCat.forget₂_addCommMonCat_map`, `isLinearSet_iff_exists_fin_addMonoidHom`, `MvPowerSeries.trunc'_C_mul`, `IsAddIndecomposable.baseOf_subset_pos`, `AddChar.coe_toAddMonoidHomEquiv_symm`, `AddCommGrpCat.forget_preservesLimitsOfSize`, `Function.locallyFinsuppWithin.toClosedBall_eval_within`, `coe_negAddMonoidHom`, `SkewMonoidAlgebra.support_erase`, `AddGroupExtension.Splitting.rightInverse_rightHom`, `CategoryTheory.CommShift₂Setup.int_z`, `CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles`, `MeasureTheory.Integrable.im`, `TensorProduct.liftAux.smulₛₗ`, `Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply`, `LinearMap.IsPositive.re_inner_nonneg_left`, `MeasureTheory.MemLp.toLp_const`, `AddGroupExtension.Section.exists_eq_add_inl`, `AddSubmonoid.LocalizationMap.addEquivOfLocalizations_apply`, `RCLike.zero_im`, `SheafOfModules.unitHomEquiv_apply_coe`, `PolynomialModule.eval_single`, `RCLike.im_eq_zero`, `AddGrpCat.coe_id`, `CategoryTheory.Iso.addCommGroupIsoToAddEquiv_apply`, `RCLike.geometric_hahn_banach_open_point`, `WeierstrassCurve.Affine.Point.map_id`, `Finsupp.image_pow_eq_finsuppProd_image`, `CategoryTheory.whiskering_preadditiveCoyoneda`, `ModuleCat.forget₂_map`, `AddSubgroup.map_centralizer_le_centralizer_image`, `AddGrpCat.forget₂Mon_preservesLimits`, `subAddMonoidHom_apply`, `AddSubmonoid.coe_inclusion`, `AddCommGrpCat.coyoneda_obj_map`, `AddCommGrpCat.forget_reflects_isos`, `uliftZMultiplesHom_symm_apply`, `SkewMonoidAlgebra.mapDomain_comp`, `QuotientAddGroup.map_id_apply`, `DirectSum.of_eq_of_ne`

---

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