Documentation Verification Report

Single

πŸ“ Source: Mathlib/Data/Finsupp/Single.lean

Statistics

MetricCount
Definitionserase, single, update
3
Theoremsindicator_singleton_eq, apply_single', apply_surjective, card_support_eq_one, card_support_eq_one', card_support_le_one, card_support_le_one', coe_update, embDomain_single, eq_single_iff, equivFunOnFinite_single, equivFunOnFinite_symm_single, erase_apply, erase_eq_update_zero, erase_idem, erase_ne, erase_of_notMem_support, erase_same, erase_single, erase_single_ne, erase_update_eq_erase, erase_update_of_ne, erase_zero, instNontrivial, mapRange_single, mem_support_single, range_single_subset, single_apply, single_apply_eq_zero, single_apply_left, single_apply_mem, single_apply_ne_zero, single_eq_of_ne, single_eq_of_ne', single_eq_pi_single, single_eq_same, single_eq_set_indicator, single_eq_single_iff, single_eq_update, single_eq_zero, single_injective, single_left_inj, single_left_injective, single_ne_zero, single_of_embDomain_single, single_of_single_apply, single_swap, single_zero, support_eq_singleton, support_eq_singleton', support_erase, support_single_disjoint, support_single_ne_bot, support_single_ne_zero, support_single_subset, support_subset_singleton, support_subset_singleton', support_update, support_update_ne_zero, support_update_subset, support_update_zero, unique_single, unique_single_eq_iff, update_apply, update_comm, update_erase_eq_update, update_idem, update_self, zero_update, zipWith_single_single
70
Total73

Finsupp

Definitions

NameCategoryTheorems
erase πŸ“–CompOp
32 mathmath: SkewMonoidAlgebra.erase_apply_toFinsupp, erase_same, mapDomain_comapDomain_nat_add_one, erase_ne, erase_apply, erase_of_notMem_support, update_erase_eq_update, erase_add, erase_update_of_ne, erase_single_ne, erase_eq_sub_single, support_erase, erase_neg, update_eq_single_add_erase, erase_zero, erase_add_single, single_add_erase, add_sum_erase', erase_eq_update_zero, Polynomial.ofFinsupp_erase, Nat.factorization_ordCompl, mul_prod_erase, erase_update_eq_erase, add_sum_erase, eraseAddHom_apply, mul_prod_erase', erase_single, Polynomial.toFinsupp_erase, erase_idem, erase_sub, Polynomial.erase_def, update_eq_erase_add_single
single πŸ“–CompOp
412 mathmath: zero_update, MvPolynomial.mul_X_divMonomial, Module.Relations.Solution.ofΟ€'_var, Algebra.Presentation.differentials.comm₁₂_single, single_injective, List.toFinsupp_eq_sum_mapIdx_single, groupHomology.d₁₀_single_one, Rep.diagonalSuccIsoFree_inv_hom_single, single_eq_indicator, MvPolynomial.coeff_X_mul', singleAddHom_apply, supportedEquivFinsupp_symm_single, groupHomology.d₃₂_single, MvPolynomial.X_pow_eq_monomial, KaehlerDifferential.mvPolynomialBasis_repr_D_X, MonomialOrder.degree_X, single_eq_single_iff, Ordinal.CNF.coeff_zero_left, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, MvPowerSeries.coeff_X_pow, List.toFinsupp_cons_eq_single_add_embDomain, Rep.diagonalHomEquiv_symm_apply, single_eq_same, groupHomology.mem_cyclesβ‚‚_iff, MvPowerSeries.X_pow_eq, groupHomology.single_isCycleβ‚‚_iff_inv, SkewMonoidAlgebra.toFinsupp_eq_single_one_one_iff, support_single_add_single, sum_single_add_single, update_eq_add_single, MvPolynomial.scalarRTensor_apply_X_tmul_apply, add_sub_single_one, equivMapDomain_single, Algebra.Presentation.differentials.hom₁_single, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, Lex.single_strictAnti, single_smul, Rep.linearization_single, Nat.Prime.factorization_pow, groupHomology.d₃₂_single_one_thd, eq_single_iff, SkewMonoidAlgebra.toFinsupp_single, finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, Rep.finsuppToCoinvariantsTensorFree_single, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, Module.Basis.repr_algebraMap, univ_sum_single_apply', sum_single_index, AddEquiv.finsuppUnique_symm, MvPowerSeries.coeff_X, Representation.ofMulAction_single, groupHomology.single_one_snd_sub_single_one_fst_mem_boundariesβ‚‚, MvPolynomial.esymmAlgHomMonomial_single, comapSMul_single, groupHomology.d₂₁_single_inv_mul_ρ_add_single, LinearEquiv.finsuppUnique_symm_apply, Rep.diagonalSuccIsoFree_inv_hom_single_single, LinearIndependent.repr_eq_single, supported_eq_span_single, support_add_single, Pi.basis_repr_single, isPrimePow_iff_factorization_eq_single, MvPowerSeries.coeff_index_single_X, Module.Basis.sumQuot_repr_left, embDomain_single, PiTensorProduct.ofFinsuppEquiv'_tprod_single, single_eq_zero, Module.Relations.Solution.ofQuotient_var, TensorProduct.finsuppScalarRight_apply_tmul, MvPowerSeries.X_def, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, update_eq_single_add, DegLex.single_lt_iff, MvPolynomial.single_eq_monomial, finsuppTensorFinsupp'_single_tmul_single, single_eq_of_ne, weight_single, Rep.coindVEquiv_symm_apply_coe, antidiagonal_single, MvPolynomial.coeff_X, single_sub, sub_add_single_one_cancel, PiTensorProduct.ofFinsuppEquiv_tprod_single, unique_single, groupHomology.single_one_fst_sub_single_one_snd_mem_boundariesβ‚‚, finsuppTensorFinsuppLid_symm_single_smul, MvPolynomial.scalarRTensor_apply_tmul, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, finsuppTensorFinsupp'_symm_single_mul, MvPolynomial.C_mul_X_eq_monomial, MvPowerSeries.coeff_index_single_self_X, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupHomology.chainsMap_f_single, TensorProduct.finsuppLeft_symm_apply_single, PiTensorProduct.ofFinsuppEquiv_symm_single_tprod, Module.Basis.reindexRange_repr_self, single_eq_of_ne', single_apply_left, Module.Basis.repr_eq_iff, MvPolynomial.coeff_X_pow, KaehlerDifferential.kerTotal_mkQ_single_add, HahnSeries.SummableFamily.embDomain_succ_smul_powers, MvPolynomial.rTensor_apply_X_tmul, groupHomology.single_one_fst_sub_single_one_fst_mem_boundariesβ‚‚, frange_single, Nat.Prime.factorization, toFreeAbelianGroup_single, single_eq_update, MvPolynomial.eq_divMonomial_single, Module.Presentation.finsupp_var, MvPolynomial.eq_modMonomial_single_iff, MvPolynomial.rTensor_apply_tmul, FiniteDimensional.basisSingleton_repr_apply, mapDomain_single, lsum_single, linearEquivFunOnFinite_single, single_finset_sum, MvPolynomial.mkDerivationβ‚—_monomial, support_single_ne_zero, CategoryTheory.Free.single_comp_single, finsuppTensorFinsupp_single, extendDomain_single, DegLex.single_antitone, Lex.single_lt_iff, MvPolynomial.coeff_single_X, erase_single_ne, single_eq_set_indicator, filter_eq_sum, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, erase_eq_sub_single, CategoryTheory.Free.embedding_map, MvPolynomial.coeff_single_X_pow, support_subset_singleton, MvPolynomial.dvd_X_mul_iff, MonomialOrder.degree_X_sub_C, curry_single, Rep.freeLiftLEquiv_apply, Module.Basis.repr_symm_single, Representation.finsuppToCoinvariants_single_mk, finsuppTensorFinsuppRid_symm_single_smul, uncurry_single, Representation.finsupp_single, isCompl_range_lmapDomain_span, Module.Relations.map_single, single_left_injective, DFinsupp.toFinsupp_single, MvPolynomial.coeff_sumSMulX, single_mul, KaehlerDifferential.derivationQuotKerTotal_apply, linearIndependent_single_of_ne_zero, FreeAbelianGroup.toFinsupp_of, MvPolynomial.supDegree_esymm, Module.Relations.Quotient.linearMap_ext_iff, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, Rep.linearization_Ξ·_hom_apply, MvPolynomial.monomial_add_single, smul_single', single_le_single, update_eq_single_add_erase, groupHomology.H1AddEquivOfIsTrivial_single, MvPolynomial.eq_modMonomial_single, single_mono, card_support_le_one', MonomialOrder.degLex_single_le_iff, MvPolynomial.support_mul_X, support_eq_singleton, single_nonpos, KaehlerDifferential.kerTotal_map, univ_sum_single_apply, MvPolynomial.support_esymm', TensorProduct.finsuppScalarRight_symm_apply_single, List.toFinsupp_concat_eq_toFinsupp_add_single, groupHomology.single_isCycle₁_iff, groupHomology.inhomogeneousChains.d_single, MvPolynomial.mkDerivation_monomial, linearCombination_single, Module.Basis.reindexFinsetRange_repr_self, Representation.coind'_apply_apply, single_tsub, Module.Basis.repr_symm_single_one, groupHomology.isBoundaryβ‚‚_iff, AddMonoidAlgebra.GradesBy.decompose_single, Multiset.toFinsupp_singleton, coe_basis, single_apply_eq_zero, Module.Relations.solutionFinsupp_var, counit_single, RootPairing.Base.toCoweightBasis_repr_coroot, single_swap, groupHomology.single_isCycleβ‚‚_iff, filter_single_of_neg, MvPolynomial.modMonomial_X, Rep.standardComplex.d_of, MvPolynomial.coeff_mul_X', MvPolynomial.coeff_mul_X, SkewMonoidAlgebra.toFinsupp_one, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, finsuppTensorFinsuppRid_single_tmul_single, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, llift_symm_apply, apply_single', AddMonoidAlgebra.single_mem_grade, MultilinearMap.freeFinsuppEquiv_apply, groupHomology.d₃₂_single_one_fst, Rep.coind'_ext_iff, MvPolynomial.X_dvd_iff_modMonomial_eq_zero, finsuppLEquivDirectSum_single, some_single_none, MvPolynomial.X_mul_divMonomial, comul_single, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, support_single_add_single_subset, groupHomology.H1ToTensorOfIsTrivial_H1Ο€_single, DegLex.single_le_iff, coe_basisSingleOne, indicator_eq_sum_attach_single, support_single_add, exteriorPower.presentation_relation, MvPolynomial.pderiv_monomial_single, erase_add_single, KaehlerDifferential.kerTotal_mkQ_single_mul, linearIndependent_single_iff, MultilinearMap.freeFinsuppEquiv_single, Rep.leftRegularHom_hom_single, MvPolynomial.support_X_pow, MvPolynomial.rTensor_symm_apply_single, update_eq_sub_add_single, optionElim_zero, Representation.free_single_single, MvPolynomial.pderiv_monomial, lcongr_symm_single, Module.Basis.apply_eq_iff, sigmaFinsuppEquivDFinsupp_single, Ordinal.CNF.coeff_one_left, single_add_erase, MvPolynomial.esymmAlgHomMonomial_single_one, Module.Basis.coe_ofRepr, support_single_disjoint, AddMonoidAlgebra.grade.decompose_single, single_add, MvPolynomial.X_mul_modMonomial, Finset.sum_single_ite, List.toFinsupp_singleton, mem_support_single, univ_sum_single, lcongr_single, SkewMonoidAlgebra.ofFinsupp_eq_one, KaehlerDifferential.kerTotal_mkQ_single_smul, MvPolynomial.coeff_X', groupHomology.d₂₁_single_one_fst, add_closure_setOf_eq_single, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, TensorProduct.finsuppScalarLeft_apply_tmul, apply_single, degree_single, card_support_eq_one', linearEquivFunOnFinite_symm_single, range_single_subset, single_multiset_sum, groupHomology.single_one_snd_sub_single_one_snd_mem_boundariesβ‚‚, unique_single_eq_iff, Rep.leftRegularHomEquiv_symm_single, Lex.single_antitone, Algebra.TensorProduct.basis_repr_symm_apply, Submodule.mulLeftMap_apply_single, single_mem_span_single, single_apply_mem, CategoryTheory.Free.lift_map_single, filter_single_of_pos, MvPolynomial.esymm_eq_sum_monomial, range_single_one, support_subset_singleton', finsuppTensorFinsupp_symm_single, single_le_iff, lift_symm_apply, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, KaehlerDifferential.mvPolynomialBasis_repr_D, restrictSupportEquiv_symm_single, single_add_single_eq_single_add_single, RootPairing.Base.toWeightBasis_repr_root, MvPolynomial.C_mul_X_pow_eq_monomial, Polynomial.derivativeFinsupp_one, liftAddHom_apply_single, TensorProduct.finsuppRight_symm_apply_single, single_left_inj, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, finsuppTensorFinsuppLid_single_tmul_single, Module.Relations.Solution.ofΟ€_var, single_apply, Representation.leftRegular_norm_apply, weight_sub_single_add, Representation.coinvariantsToFinsupp_mk_single, single_add_apply, MvPolynomial.support_esymm'', TensorProduct.finsuppLeft_apply_tmul, groupHomology.d₂₁_single_one_snd, groupHomology.d₃₂_single_one_snd, exteriorPower.basis_repr, indicator_eq_sum_single, MvPolynomial.divMonomial_add_modMonomial_single, support_single_subset, Rep.leftRegularHomEquiv_apply, SkewMonoidAlgebra.ofFinsupp_single, Colex.single_le_iff, linearIndependent_single, groupHomology.single_mem_cycles₁_of_mem_invariants, liftAddHom_symm_apply_apply, MvPolynomial.coeff_X_mul, GroupAlgebra.mul_average_left, coe_univ_sum_single, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, AddMonoidAlgebra.decomposeAux_single, some_single_some, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, span_single_image, Ordinal.CNF.coeff_of_le_one, equivFunOnFinite_symm_single, toMultiset_single, single_neg, toDFinsupp_single, MvPolynomial.scalarRTensor_symm_apply_single, zipWith_single_single, range_lmapDomain, Rep.freeLift_hom_single_single, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, groupHomology.single_one_mem_boundaries₁, single_sum, MonomialOrder.degree_X_add_C, MvPolynomial.mul_X_modMonomial, Rep.diagonalHomEquiv_apply, groupHomology.d₂₁_single, SkewMonoidAlgebra.ofFinsupp_one, embSigma_single, card_support_le_one, single_eq_pi_single, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, MonomialOrder.degLex_single_lt_iff, MvPolynomial.modMonomial_add_divMonomial_single, equivFunOnFinite_single, smul_single_one, Colex.single_lt_iff, sub_single_one_add, single_zero, groupHomology.single_mem_cyclesβ‚‚_iff, TensorProduct.finsuppScalarLeft_symm_apply_single, equivFunOnFinite_symm_eq_sum, MvPolynomial.X_divMonomial, single_nonneg, Rep.diagonalSuccIsoFree_hom_hom_single, Lex.single_le_iff, AddMonoidAlgebra.single_mem_gradeBy, erase_single, Rep.free_ext_iff, Module.Basis.repr_eq_iff', smul_single, AList.singleton_lookupFinsupp, Module.End.ringEquivEndFinsupp_symm_apply_apply, sum_single, groupHomology.single_isCycle₁_of_mem_fixedPoints, MvPolynomial.support_esymm, Module.Presentation.tautologicalRelations_relation, mapRange_single, prod_single_index, nsmul_single_one_image, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.single_mem_cycles₁_iff, groupHomology.d₂₁_single_ρ_add_single_inv_mul, sum_eq_one_iff, single_mem_supported, Rep.linearization_map_hom_single, MvPolynomial.support_X, toMultiset_sum_single, KaehlerDifferential.kerTotal_map', Rep.barComplex.d_single, Module.Presentation.tautological_relation, MvPolynomial.monomial_single_add, Module.Basis.repr_self, MvPolynomial.support_X_mul, exteriorPower.presentation.relations_relation, lcomapDomain_eq_linearProjOfIsCompl, support_eq_singleton', TensorProduct.finsuppRight_apply_tmul, groupHomology.isBoundary₁_iff, Set.indicator_singleton_eq, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, linearIndependent_single_one, Module.Relations.Solution.Ο€_single, DegLex.single_strictAnti, Module.presentationFinsupp_var, domLCongr_single, groupHomology.single_mem_cyclesβ‚‚_iff_inv, groupHomology.d₁₀_single, lsingle_apply, MvPolynomial.vars_monomial_single, Colex.single_strictMono, Polynomial.derivativeFinsupp_C, TensorProduct.finsuppRight_tmul_single, Submodule.mulRightMap_apply_single, card_support_eq_one, Polynomial.derivativeFinsupp_X, finsuppLEquivDirectSum_symm_lof, GroupAlgebra.mul_average_right, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, Polynomial.homogenize_monomial, single_of_single_apply, update_eq_erase_add_single, MonomialOrder.degree_X_le_single, KaehlerDifferential.kerTotal_mkQ_single_algebraMap
update πŸ“–CompOp
31 mathmath: zero_update, update_eq_add_single, Finset.mem_finsuppAntidiag_insert, update_self, eq_option_embedding_update_none_iff, update_eq_single_add, update_erase_eq_update, update_apply, erase_update_of_ne, support_update_ne_zero, multinomial_update, update_idem, update_eq_single_add_erase, coe_update, support_update, tail_update_zero, SkewMonoidAlgebra.update_toFinsupp, sum_update_add, update_eq_sub_add_single, support_update_subset, some_update_none, tail_update_succ, erase_eq_update_zero, update_comm, erase_update_eq_erase, support_update_zero, Finset.finsuppAntidiag_insert, optionEquiv_symm_apply, AList.insert_lookupFinsupp, Polynomial.homogenize_monomial, update_eq_erase_add_single

Theorems

NameKindAssumesProvesValidatesDepends On
apply_single' πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”β€”
apply_surjective πŸ“–mathematicalβ€”Finsupp
DFunLike.coe
instFunLike
β€”single_eq_same
card_support_eq_one πŸ“–mathematicalβ€”Finset.card
support
single
DFunLike.coe
Finsupp
instFunLike
β€”β€”
card_support_eq_one' πŸ“–mathematicalβ€”Finset.card
support
single
β€”β€”
card_support_le_one πŸ“–mathematicalβ€”Finset.card
support
single
DFunLike.coe
Finsupp
instFunLike
β€”β€”
card_support_le_one' πŸ“–mathematicalβ€”Finset.card
support
single
β€”β€”
coe_update πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
update
Function.update
β€”β€”
embDomain_single πŸ“–mathematicalβ€”embDomain
single
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
β€”ext
eq_single_iff πŸ“–mathematicalβ€”single
Finset
Finset.instHasSubset
support
Finset.instSingleton
DFunLike.coe
Finsupp
instFunLike
β€”support_single_subset
single_eq_same
ext
single_eq_of_ne
notMem_support_iff
Finset.mem_singleton
equivFunOnFinite_single πŸ“–mathematicalβ€”DFunLike.coe
Equiv
Finsupp
EquivLike.toFunLike
Equiv.instEquivLike
equivFunOnFinite
single
Pi.single
β€”single_eq_pi_single
equivFunOnFinite_symm_single πŸ“–mathematicalβ€”DFunLike.coe
Equiv
Finsupp
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
equivFunOnFinite
Pi.single
single
β€”equivFunOnFinite_single
Equiv.symm_apply_apply
erase_apply πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
erase
β€”erase.eq_1
erase_eq_update_zero πŸ“–mathematicalβ€”erase
update
β€”β€”
erase_idem πŸ“–mathematicalβ€”eraseβ€”β€”
erase_ne πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
erase
β€”β€”
erase_of_notMem_support πŸ“–mathematicalFinset
Finset.instMembership
support
eraseβ€”β€”
erase_same πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
erase
β€”β€”
erase_single πŸ“–mathematicalβ€”erase
single
Finsupp
instZero
β€”β€”
erase_single_ne πŸ“–mathematicalβ€”erase
single
β€”β€”
erase_update_eq_erase πŸ“–mathematicalβ€”erase
update
β€”β€”
erase_update_of_ne πŸ“–mathematicalβ€”erase
update
β€”β€”
erase_zero πŸ“–mathematicalβ€”erase
Finsupp
instZero
β€”erase_of_notMem_support
instNontrivial πŸ“–mathematicalβ€”Nontrivial
Finsupp
β€”exists_ne
nontrivial_of_ne
single_eq_zero
mapRange_single πŸ“–mathematicalβ€”mapRange
single
β€”β€”
mem_support_single πŸ“–mathematicalβ€”Finset
Finset.instMembership
support
single
β€”β€”
range_single_subset πŸ“–mathematicalβ€”Set
Set.instHasSubset
Set.range
DFunLike.coe
Finsupp
instFunLike
single
Set.instInsert
Set.instSingletonSet
β€”Set.range_subset_iff
single_apply_mem
single_apply πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”Pi.single_apply
single_apply_eq_zero πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”single_eq_set_indicator
single_apply_left πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”single_apply
single_apply_mem πŸ“–mathematicalβ€”Set
Set.instMembership
Set.instInsert
Set.instSingletonSet
DFunLike.coe
Finsupp
instFunLike
single
β€”β€”
single_apply_ne_zero πŸ“–β€”β€”β€”β€”β€”
single_eq_of_ne πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”Pi.single_eq_of_ne
single_eq_of_ne' πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”Pi.single_eq_of_ne'
single_eq_pi_single πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
Pi.single
β€”single_eq_update
single_eq_same πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”Pi.single_eq_same
single_eq_set_indicator πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
Set.indicator
Set
Set.instSingletonSet
β€”single_apply
single_eq_single_iff πŸ“–mathematicalβ€”singleβ€”single_injective
DFunLike.ext_iff
single_eq_update πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
Function.update
Pi.instZero
β€”single_eq_set_indicator
Set.piecewise_eq_indicator
Set.piecewise_singleton
single_eq_zero πŸ“–mathematicalβ€”single
Finsupp
instZero
β€”single_eq_set_indicator
single_injective πŸ“–mathematicalβ€”Finsupp
single
β€”single_eq_same
single_left_inj πŸ“–mathematicalβ€”singleβ€”single_left_injective
single_left_injective πŸ“–mathematicalβ€”Finsupp
single
β€”single_eq_single_iff
single_ne_zero πŸ“–β€”β€”β€”β€”Iff.not
single_eq_zero
single_of_embDomain_single πŸ“–mathematicalembDomain
single
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
β€”support_embDomain
support_single_ne_zero
Finset.mem_map
ext
embDomain_apply_self
single_of_single_apply πŸ“–mathematicalβ€”single
DFunLike.coe
Finsupp
instFunLike
instZero
β€”β€”
single_swap πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
single
β€”single_apply
single_zero πŸ“–mathematicalβ€”single
Finsupp
instZero
β€”DFunLike.coe_injective
single_eq_update
Function.update_eq_self
support_eq_singleton πŸ“–mathematicalβ€”support
Finset
Finset.instSingleton
single
DFunLike.coe
Finsupp
instFunLike
β€”mem_support_iff
Finset.mem_singleton_self
eq_single_iff
subset_of_eq
Finset.instReflSubset
support_single_ne_zero
support_eq_singleton' πŸ“–mathematicalβ€”support
Finset
Finset.instSingleton
single
β€”support_eq_singleton
support_single_ne_zero
support_erase πŸ“–mathematicalβ€”support
erase
Finset.erase
β€”β€”
support_single_disjoint πŸ“–mathematicalβ€”Disjoint
Finset
Finset.partialOrder
Finset.instOrderBot
support
single
β€”support_single_ne_zero
Finset.disjoint_singleton
support_single_ne_bot πŸ“–β€”β€”β€”β€”support_single_ne_zero
Finset.singleton_ne_empty
support_single_ne_zero πŸ“–mathematicalβ€”support
single
Finset
Finset.instSingleton
β€”β€”
support_single_subset πŸ“–mathematicalβ€”Finset
Finset.instHasSubset
support
single
Finset.instSingleton
β€”β€”
support_subset_singleton πŸ“–mathematicalβ€”Finset
Finset.instHasSubset
support
Finset.instSingleton
single
DFunLike.coe
Finsupp
instFunLike
β€”eq_single_iff
support_subset_singleton' πŸ“–mathematicalβ€”Finset
Finset.instHasSubset
support
Finset.instSingleton
single
β€”support_subset_singleton
single_eq_same
support_update πŸ“–mathematicalβ€”support
update
Finset
Finset.erase
Finset.instInsert
β€”β€”
support_update_ne_zero πŸ“–mathematicalβ€”support
update
Finset
Finset.instInsert
β€”β€”
support_update_subset πŸ“–mathematicalβ€”Finset
Finset.instHasSubset
support
update
Finset.instInsert
β€”β€”
support_update_zero πŸ“–mathematicalβ€”support
update
Finset.erase
β€”β€”
unique_single πŸ“–mathematicalβ€”single
Unique.instInhabited
DFunLike.coe
Finsupp
instFunLike
β€”ext
Unique.forall_iff
single_eq_same
unique_single_eq_iff πŸ“–mathematicalβ€”singleβ€”unique_ext_iff
Unique.eq_default
single_eq_same
update_apply πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
instFunLike
update
β€”β€”
update_comm πŸ“–mathematicalβ€”updateβ€”β€”
update_erase_eq_update πŸ“–mathematicalβ€”update
erase
β€”β€”
update_idem πŸ“–mathematicalβ€”updateβ€”β€”
update_self πŸ“–mathematicalβ€”update
DFunLike.coe
Finsupp
instFunLike
β€”β€”
zero_update πŸ“–mathematicalβ€”update
Finsupp
instZero
single
β€”β€”
zipWith_single_single πŸ“–mathematicalβ€”zipWith
single
β€”β€”

Finsupp.Set

Theorems

NameKindAssumesProvesValidatesDepends On
indicator_singleton_eq πŸ“–mathematicalβ€”Set.indicator
Set
Set.instSingletonSet
DFunLike.coe
Finsupp
Finsupp.instFunLike
Finsupp.single
β€”Finsupp.single_apply

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