Documentation Verification Report

Finite

πŸ“ Source: Mathlib/Algebra/Group/Pointwise/Set/Finite.lean

Statistics

MetricCount
DefinitionsFinite, decidableMemAdd, decidableMemMul, decidableMemNSMul, decidableMemPow, fintypeAdd, fintypeDiv, fintypeMul, fintypeSub
9
Theoremscard_nsmul_eq_card_nsmul_card_univ, card_pow_eq_card_pow_card_univ, add, div, inv, mul, neg, of_inv, of_neg, smul, smul_set, sub, vadd, vadd_set, vsub, of_smul_set, of_vadd_set, finite_add, finite_div, finite_inv, finite_mul, finite_neg, finite_one, finite_sub, finite_zero, infinite_add, infinite_div, infinite_inv, infinite_mul, infinite_neg, infinite_sub
31
Total40

AddGroup

Theorems

NameKindAssumesProvesValidatesDepends On
card_nsmul_eq_card_nsmul_card_univ πŸ“–mathematicalFintype.cardSet.Elem
Set
Set.NSMul
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
toSubtractionMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
toSubNegMonoid
Subtype.fintype
Set.instMembership
β€”Fintype.card_pos
Zero.instNonempty
Set.eq_empty_or_nonempty
Fintype.card_congr
Set.nsmul_empty
LT.lt.ne'
LT.lt.trans_le
ne_of_gt
Fintype.card_le_of_injective
add_right_cancel
AddRightCancelSemigroup.toIsRightCancelAdd
monotone_nat_of_le_succ
Set.add_mem_add
Nat.stabilises_of_monotone
set_fintype_card_le_univ
le_antisymm
Set.eq_of_subset_of_card_le
Set.add_subset_add
Set.Subset.rfl
Set.singleton_subset_iff
le_trans
ge_of_eq
Set.mem_singleton
succ_nsmul'
add_assoc
Set.add_singleton
Set.forall_mem_image
add_neg_cancel_right

Group

Theorems

NameKindAssumesProvesValidatesDepends On
card_pow_eq_card_pow_card_univ πŸ“–mathematicalFintype.cardSet.Elem
Set
Set.NPow
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
toDivisionMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
toDivInvMonoid
Subtype.fintype
Set.instMembership
β€”Fintype.card_pos
One.instNonempty
Set.eq_empty_or_nonempty
Fintype.card_congr
Set.empty_pow
LT.lt.ne'
LT.lt.trans_le
ne_of_gt
Fintype.card_le_of_injective
mul_right_cancel
RightCancelSemigroup.toIsRightCancelMul
monotone_nat_of_le_succ
Set.mul_mem_mul
Nat.stabilises_of_monotone
set_fintype_card_le_univ
le_antisymm
Set.eq_of_subset_of_card_le
Set.mul_subset_mul
Set.Subset.rfl
Set.singleton_subset_iff
le_trans
ge_of_eq
Set.mem_singleton
pow_succ'
mul_assoc
Set.mul_singleton
Set.forall_mem_image
mul_inv_cancel_right

Set

Definitions

NameCategoryTheorems
Finite πŸ“–MathDef
502 mathmath: SimpleGraph.Finsubgraph.coe_sSup, finite_diff_iUnion_Ioo, MvPowerSeries.hasSubst_def, Monoid.exponent_ne_zero_iff_range_orderOf_finite, Finsupp.finite_of_degree_le, Finite.of_vadd_set, IsArtinianRing.setOf_isPrime_finite, AddAntidiagonal.finite_of_isWF, MeasureTheory.mem_generateSetAlgebra_elim, IsCompact.sigma_exists_finite_sigma_eq, finite_iff_finite_of_encard_eq_encard, Finite.inf_of_right, DirectSum.finite_support, Finite.union, Ideal.finite_setOf_absNorm_leβ‚€, Setoid.finite_classes_ker, ContinuousMap.hasBasis_nhds, finite_empty, Filter.HasBasis.pi_self, Matroid.IsBasis.finite_iff_isRkFinite, Subgroup.IsComplement.finite_right, IsAntichain.finite_of_wellQuasiOrdered, SimpleGraph.Finsubgraph.coe_top, Filter.mem_iInf, List.finite_toSet, Summable.finite_support_of_discreteTopology, IsOfFinOrder.finite_zpowers, locallyFinite_iff_smallSets, finite_one, Filter.mem_cofinite, Function.mulSupport_along_fiber_finite_of_finite, AddMonoid.fg_iff, finite_of_finite_preimage, finite_subset_iUnion, BumpCovering.point_finite, Ideal.finite_setOf_absNorm_eq, SimpleGraph.Finsubgraph.coe_hnot, LocallyConstant.range_finite, NumberField.FinitePlace.mulSupport_finite, finite_mem_finset, finite_smul_set, Finite.powerset, IsNoetherian.finite_basis_index, Filter.HasBasis.iInf, finite_sub, Finite.smul, finite_uIcc, isCompact_iff_finite, Matroid.IsBasis.finite_of_isRkFinite, finite_memPartition, SimpleGraph.Coloring.colorClasses_finite, eq_finite_iUnion_of_isTopologicalBasis_of_isCompact_open, Finite.sInter, List.finite_length_le, Matroid.IsBasis'.finite_of_isRkFinite, finite_or_infinite, ProbabilityTheory.finite_of_uniformOn_ne_zero, Matroid.finite_setOf_matroid', finsum_def', SimpleGraph.Finsubgraph.coe_sdiff, genericPoints.finite, finite_powers, ContinuousMap.mem_nhds_iff, instWellFoundedLTSubtypeSetFinite, Finite.inter_of_left, finite_zpowers, memβ„“p_zero_iff, Function.locallyFinsuppWithin.supportLocallyFiniteWithinDomain, UniformOnFun.isEmbedding_toFun_finite, Multipliable.finite_mulSupport_of_discreteTopology, Finite.vsub, TopologicalSpace.NoetherianSpace.exists_finite_set_isClosed_irreducible, AddCircle.finite_torsion_of_isSMulRegular, ENat.finite_of_sSup_lt_top, forall_finite_image_eval_iff, Matroid.Indep.subset_finite_isBasis_of_subset_of_isRkFinite, finite_range_iff, Matroid.IsRkFinite.finite_of_indep_subset, Matroid.Indep.subset_finite_isBasis'_of_subset_of_isRkFinite, Polynomial.finite_range_coeff, Finite.mul, ruzsa_covering_add, finite_mulSupport_of_finprod_ne_one, FirstOrder.Field.ACF_zero_realize_iff_finite_ACF_prime_not_realize, Function.locallyFinsuppWithin.finiteSupport, Finite.infClosure, Finite.preimage_embedding, Matroid.IsCircuit.finite, finite_union, Finite.of_prod_left, Metric.exists_set_encard_eq_coveringNumber, WellFoundedGT.finite_ne_bot_of_iSupIndep, Finsupp.finite_support, IsCompact.finite_cover_balls, SMulAntidiagonal.finite_of_isPWO, Filter.hasBasis_cofinite, Matroid.isRkFinite_iff_exists_isBasis', Finite.finite_mulAction_orbit, MeasureTheory.ae_finite_setOf_mem, Filter.hasBasis_pi_pure, BijOn.finite_iff_finite, CofiniteTopology.mem_nhds_iff, MeasureTheory.SimpleFunc.finite_range, associatedPrimes.finite, Matroid.finitary_iff_forall_isCircuit_finite, ProperlyDiscontinuousVAdd.finite_stabilizer, WellFoundedGT.finite_of_sSupIndep, Subgroup.IsComplement.finite_left, VAddAntidiagonal.finite_of_isPWO, mem_closure_isSwap, Cardinal.mk_strictMonoOn, Finite.submoduleSpan, AddGroup.fg_iff, union_finset_finite_of_range_finite, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, DiscreteTiling.PlacedTile.coe_finite_iff, OrderIso.finsetSetFinite_symm_apply, LocallyFinite.exists_mem_basis, DiscreteTiling.PlacedTile.coe_mk_finite_iff, Rat.finite_rat_abs_sub_lt_one_div_den_sq, finite_insert, Submodule.fg_def, IsOfFinOrder.finite_powers, FirstOrder.Language.Substructure.fg_def, Matrix.finite_spectrum, LinearIndependent.set_finite_of_isNoetherian, MeasurableSet.setOf_finite, spectralValueTerms_finite_range, Finsupp.finite_range, Filter.hasBasis_pi_same_index, finite_Iic, Subgroup.fg_iff, IsArtinian.finite_of_linearIndependent, finite_compl_fixedBy_swap, Metric.exists_finite_isCover_of_isCompact, sUnion_finite_eq_univ, Polynomial.bUnion_roots_finite, finite_of_ncard_pos, LieModule.finite_genWeightSpaceOf_ne_bot, Nat.finite_setOf_setGcd_dvd_and_mem_span, CategoryTheory.Precoverage.mem_finite_iff, Ideal.finite_minimalPrimes_of_isNoetherianRing, Matroid.IsBasis'.finite_iff_isRkFinite, Equiv.set_finite_iff, eq_finite_iUnion_of_finite_subset_iUnion, Algebra.QuasiFinite.iff_finite_primesOver, finite_support_of_finsum_ne_zero, Filter.cofinite.bliminf_set_eq, HahnSeries.SummableFamily.smul_support_finite, BddAbove.finite, NumberField.hermiteTheorem.finite_of_finite_generating_set, Filter.eventually_cofinite, Filter.disjoint_cofinite_right, finite_Iio, Matroid.Indep.finite, finite_zero, not_finite, encard_lt_top_iff, AddCircle.finite_setOf_addOrderOf_eq, Finsupp.finite_of_nat_weight_le, Filter.disjoint_cofinite_left, SimpleGraph.Finsubgraph.coe_iInf, finite_preimage_inl_and_inr, ENNReal.finite_const_le_of_tsum_ne_top, Matroid.finite_setOf_isRestriction, Countable.setOf_finite, Equiv.Perm.IsSwap.finite_compl_fixedBy, Algebra.QuasiFinite.iff_finite_comap_preimage_singleton, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, Filter.TotallyBounded.exists_subset_of_mem, finite_range, AddSubgroup.fg_iff, MvPowerSeries.HasSubst.coeff_zero, Group.fg_iff, Matroid.Indep.finite_of_isRkFinite, minimalPrimes.finite_of_isNoetherianRing, MeasureTheory.Measure.count_apply_lt_top, Subalgebra.fg_def, Finite.Set.finite_pure, Finite.sub, FirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realize, MeasureTheory.SimpleFunc.finite_range', Finite.add, SimpleGraph.Finsubgraph.coe_bot, Matroid.isRkFinite_iff, ProperlyDiscontinuousSMul.finite_stabilizer', Finite.subset, AddSubmonoid.fg_iff, Language.isRegular_iff_finite_range_leftQuotient, finprod_def', IntermediateField.fg_def, Finite.div, Finite.image, Finite.dependent_image, Metric.finite_isBounded_inter_isClosed, Algebra.QuasiFinite.finite_comap_preimage, finite_range_findGreatest, infinite_or_finite, IsSemisimpleModule.finite_tfae, finite_Ico, finite_isTop, Finite.neg, ProperlyDiscontinuousSMul.finite_stabilizer, Filter.mem_biInf_principal, AddSubgroup.IsComplement.finite_left, Function.locallyFinsuppWithin.supportLocallyFiniteWithinDomain', Matroid.IsRkFinite.finite_of_isBasis', SmoothBumpCovering.point_finite, Multiset.finite_toSet, finite_Icc, WellQuasiOrderedLE.finite_of_isAntichain, SimpleGraph.Walk.finite_neighborSet_toSubgraph, NumberField.FinitePlace.mulSupport_finite_int, Metric.finite_minimalCover, Finite.finite_addAction_orbit, primesOver_finite, Filter.hasBasis_iInf_principal_finite, Finite.image2, Finite.diff, finite_coe_iff, Finite.inf_of_left, finite_of_encard_eq_coe, finite_iff_bddBelow, AlgebraicGeometry.isCompactOpen_iff_eq_finset_affine_union, Finite.of_subsingleton, Finite.supClosure, Filter.HasBasis.filter_totallyBounded_iff, BoxIntegral.unitPartition.setFinite_index, Matroid.IsRkFinite.exists_finite_isBasis', Height.AdmissibleAbsValues.mulSupport_finite, finsum_def, MulAntidiagonal.finite_of_isPWO, TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompact, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, Finite.offDiag, Finite.inter_of_right, Function.support_along_fiber_finite_of_finite, TopologicalSpace.Opens.IsBasis.isCompact_open_iff_eq_finite_iUnion, SimpleGraph.Finsubgraph.coe_iSup, PrimeSpectrum.finite_setOf_isMin, MeasurableSpace.finite_countablePartition, MvPolynomial.weightedHomogeneousComponent_finsupp, Matroid.IsBasis.Finite, LinearMap.sInter_polar_finite_subset_eq_polar, finite_of_chainHeight_ne_top, Matroid.exists_mem_finite_closure_of_mem_closure, Algebra.SubmersivePresentation.finite_coeffs, finite_option, Filter.HasBasis.iInf', CofiniteTopology.isClosed_iff, LinearIndependent.setFinite, ProperlyDiscontinuousVAdd.finite_disjoint_inter_image, finite_range_const, Matroid.finite_setOf_matroid, codiscreteWithin_iff_locallyFiniteComplementWithin, finite_cover_balls_of_compact, isCompact_open_iff_eq_finite_iUnion_of_isTopologicalBasis, not_infinite, Polynomial.rootSet_finite, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens, Ideal.finite_mulSupport_coe, Finite.star, toFinite, Monoid.fg_iff, LieModule.finite_genWeightSpace_ne_bot, Cardinal.lt_aleph0_iff_subtype_finite, Module.End.finite_spectrum, finite_image_fst_and_snd_iff, NumberField.finite_of_discr_bdd, Finite.finite_subsets, Finite.sep, finite_isBot, Finsupp.finite_vaddAntidiagonal, encard_le_coe_iff_finite_ncard_le, Module.End.finite_hasEigenvalue, Matroid.Indep.isRkFinite_iff_finite, tendsto_cofinite_cocompact_iff, Finite.of_preimage, Submodule.finite_ne_bot_of_iSupIndep, Matroid.rankFinite_iff, MeasurableSet.sep_finite, MvPowerSeries.coeff_zero_iff, supportDiscreteWithin_iff_locallyFiniteWithin, Finite.symmDiff_congr, Ideal.finite_mulSupport, FiniteExhaustion.finite, finite_range_ite, finite_inv, finite_iff_bddAbove, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, Filter.cofinite.liminf_set_eq, TopologicalSpace.isTopologicalBasis_of_subbasis, Metric.isCompact_closure_iff_exists_finite_isCover, finite_diff_iUnion_Ioo', Matrix.finite_real_spectrum, Matroid.finite_iff, AlgebraicGeometry.IsFinite.finite_preimage_singleton, AffineBasis.finite_set, Finite.prod, finite_Ioo, LocallyFinite.point_finite, finite_add, Finite.inv, Finite.map, finite_set_of_fin_dim_affineIndependent, MeasureTheory.Measure.finite_const_le_meas_of_disjoint_iUnionβ‚€, Filter.hasBasis_generate, Filter.HasBasis.totallyBounded_iff, Submonoid.fg_iff, Matroid.Indep.finite_of_subset_isRkFinite, Filter.hasBasis_pi_principal, isIntegral_iff_isIntegral_closure_finite, SimpleGraph.Finsubgraph.coe_sup, AddSubgroup.IsComplement.finite_right, PowerSeries.exist_eq_span_eq_ncard_of_X_notMem, Finite.of_neg, Ideal.finite_factors, finite_univ, finite_multiples, TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducible, MulAntidiagonal.finite_of_isWF, Finite.of_finite_image, List.finite_length_lt, finite_compl_fixedBy_closure_iff, HahnSeries.SummableFamily.pow_finite_co_support, finite_irreducible, Algebra.QuasiFinite.finite_comap_preimage_singleton, mem_closure_isSwap', Matroid.IsBase.diff_finite_comm, finite_prod, NormedSpace.sInter_polar_eq_closedBall, finite_iff_bddBelow_bddAbove, WellFoundedLT.finite_of_sSupIndep, IsCompact.elim_finite_subcover_image, Infinite.exists_subset_ncard_eq, Finite.of_injOn, AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton, Finite.finite_of_encard_le, finite_of_encard_le_coe, Metric.totallyBounded_iff, finite_iUnion_of_subsingleton, IsCompact.finite_of_discrete, EMetric.totallyBounded_iff, Metric.exists_finite_isCover_of_totallyBounded, Finite.latticeClosure, Matroid.RankFinite.exists_finite_isBase, isTopologicalBasis_biInter_Ioi_Iio_of_generateFrom, ProperlyDiscontinuousSMul.finite_disjoint_inter_image, Finite.symmDiff, Finite.smul_set, instCanLiftFinsetCoeFinite, SimpleGraph.Finsubgraph.coe_inf, encard_le_coe_iff, Filter.mem_generate_iff, totallyBounded_iff_subset, finite_mul, Submonoid.FG.finite_irreducible_mem_submonoidClosure, Matroid.ground_finite, PairwiseDisjoint.finite_biUnion_iff, AddAntidiagonal.finite_of_isPWO, AddCircle.finite_torsion, Finite.lowerClosure, Module.DualBases.finite, List.finite_length_eq, Ideal.finite_setOf_absNorm_le, ruzsa_covering_mul, partiallyWellOrderedOn_iff_finite_antichains, AlgebraicGeometry.Scheme.Hom.finite_preimage, finite_def, SmoothPartitionOfUnity.finite_tsupport, AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens, PowerSeries.coeff_subst_finite, IsOfFinAddOrder.finite_multiples, AddCircle.finite_torsion_of_isSMulRegular_int, finite_image_iff, SimpleGraph.Finsubgraph.coe_himp, WellFoundedLT.finite_ne_bot_of_iSupIndep, Language.IsRegular.finite_range_leftQuotient, Module.Basis.finite_index_of_rank_lt_aleph0, finite_div, exists_finite_iff_finset, Matroid.IsRkFinite.finite_of_isBasis, tprod_def, Metric.exists_finite_isCover_of_isCompact_closure, Algebra.Presentation.finite_coeffs, exists_finite_cover_balls_of_isCompact_closure, NumberField.Embeddings.finite_of_norm_le, MeasureTheory.Measure.finite_const_le_meas_of_disjoint_iUnion, MulAction.stabilizer_finite, Finite.insert, Finset.finite_toSet, one_lt_ncard_iff_nontrivial_and_finite, encard_ne_top_iff, SimpleGraph.singletonFinsubgraph_le_adj_left, AddAction.stabilizer_finite, Filter.generate_eq_generate_inter, HahnSeries.SummableFamily.finite_co_support', finite_interval, finite_Ioc, totallyBounded_iff_subset_finite_iUnion_nhds_one, Finite.ofFinset, IsAntichain.finite_of_partiallyWellOrderedOn, AlgebraicGeometry.locallyQuasiFinite_iff_finite_preimage_singleton, IsLocallyConstant.range_finite, Algebra.QuasiFinite.finite_primesOver, wellQuasiOrderedLE_iff, PartitionOfUnity.finite_tsupport, Filter.mem_pi_principal, Finite.vadd_set, finprod_def, Finite.seq, MeasureTheory.Measure.count_apply_lt_top', MvPowerSeries.coeff_subst_finite, UniformOnFun.isUniformEmbedding_toFun_finite, Filter.mem_iInf', TotallyBounded.exists_subset, exists_subset_image_finite_and, Matroid.Finite.ground_finite, Finite.of_prod_right, Finite.ncard_strictMonoOn, finite_neg, Finite.sup, Submodule.FG.finite_generators, Metric.exists_set_encard_eq_packingNumber, Matroid.set_finite, finite_of_ncard_ne_zero, TopologicalSpace.NoetherianSpace.finite_irreducibleComponents, Finite.vadd, Finite.seq', Finite.upperClosure, LocallyFinite.finite_nonempty_inter_compact, IsOfFinAddOrder.finite_zmultiples, Finite.of_surjOn, finite_Ici, Metric.finite_approx_of_totallyBounded, SimpleGraph.Finsubgraph.coe_sInf, finite_lt_nat, Polynomial.finite_mahlerMeasure_le, Filter.mem_pi, SimpleGraph.Finsubgraph.coe_compl, Infinite.not_finite, Matroid.IsBase.finite_of_finite, finite_image2, finite_singleton, DFinsupp.finite_support, PowerSeries.coeff_subst_finite', finite_support_of_finsum_eq_one, finite_addIrreducible, Finite.of_inv, Matroid.IsBase.finite, EMetric.totallyBounded_iff', tsum_def, finite_of_forall_not_lt_lt, OrderIso.finsetSetFinite_apply_coe, Subsingleton.finite, FreeCommRing.exists_finite_support, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, finite_iUnion_iff, totallyBounded_iff_subset_finite_iUnion_nhds_zero, Ideal.finite_mulSupport_inv, AlgebraicGeometry.finite_irreducibleComponents_of_isNoetherian, CofiniteTopology.isOpen_iff, CofiniteTopology.isOpen_iff', AddMonoid.exponent_ne_zero_iff_range_addOrderOf_finite, finite_univ_iff, LocallyFinite.eventually_smallSets, Cardinal.lt_aleph0_iff_set_finite, Finite.encard_strictMonoOn, IsCompact.finite, ZSpan.setFinite_inter, Matroid.exists_subset_finite_closure_of_subset_closure, Module.Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0, Finite.of_diff, univ_finite_iff_nonempty_fintype, finite_vadd_set, AddSubmonoid.FG.finite_addIrreducible_mem_addSubmonoidClosure, Filter.FilterBasis.ofSets_sets, countable_setOf_finite_subset, ContinuousMap.compactOpen_eq_generateFrom, LocallyFinite.finite_nonempty_of_compact, Finsupp.instCanLift, HahnSeries.SummableFamily.finite_co_support, Filter.hasBasis_pi, IsAntichain.partiallyWellOrderedOn_iff, BddBelow.finite, Finite.of_summable_const, Finite.of_smul_set, finite_Ioi, Memβ„“p.finite_dsupport, LocallyFinite.finite_of_compact, ProperlyDiscontinuousVAdd.finite_stabilizer', Filter.mem_pi_pure, Polynomial.finite_setOf_isRoot, BddBelow.finite_of_bddAbove, IsDedekindDomain.HeightOneSpectrum.Support.finite, finite_le_nat, Finite.preimage, SimpleGraph.singletonFinsubgraph_le_adj_right, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, IsArtinianRing.setOf_isMaximal_finite, finite_zmultiples, FirstOrder.Language.Structure.fg_iff
decidableMemAdd πŸ“–CompOpβ€”
decidableMemMul πŸ“–CompOpβ€”
decidableMemNSMul πŸ“–CompOpβ€”
decidableMemPow πŸ“–CompOpβ€”
fintypeAdd πŸ“–CompOpβ€”
fintypeDiv πŸ“–CompOpβ€”
fintypeMul πŸ“–CompOpβ€”
fintypeSub πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
finite_add πŸ“–mathematicalβ€”Finite
Set
add
instEmptyCollection
β€”finite_image2
Function.Injective.injOn
add_left_injective
add_right_injective
finite_div πŸ“–mathematicalβ€”Finite
Set
div
DivInvMonoid.toDiv
Group.toDivInvMonoid
instEmptyCollection
β€”finite_image2
Function.Injective.injOn
div_left_injective
div_right_injective
finite_inv πŸ“–mathematicalβ€”Finite
Set
inv
InvolutiveInv.toInv
β€”image_inv_eq_inv
finite_image_iff
Function.Injective.injOn
inv_injective
finite_mul πŸ“–mathematicalβ€”Finite
Set
mul
instEmptyCollection
β€”finite_image2
Function.Injective.injOn
mul_left_injective
mul_right_injective
finite_neg πŸ“–mathematicalβ€”Finite
Set
neg
InvolutiveNeg.toNeg
β€”image_neg_eq_neg
finite_image_iff
Function.Injective.injOn
neg_injective
finite_one πŸ“–mathematicalβ€”Finite
Set
one
β€”finite_singleton
finite_sub πŸ“–mathematicalβ€”Finite
Set
sub
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
instEmptyCollection
β€”finite_image2
Function.Injective.injOn
sub_left_injective
sub_right_injective
finite_zero πŸ“–mathematicalβ€”Finite
Set
zero
β€”finite_singleton
infinite_add πŸ“–mathematicalβ€”Infinite
Set
add
Nonempty
β€”infinite_image2
Function.Injective.injOn
add_left_injective
add_right_injective
infinite_div πŸ“–mathematicalβ€”Infinite
Set
div
DivInvMonoid.toDiv
Group.toDivInvMonoid
Nonempty
β€”infinite_image2
Function.Injective.injOn
div_left_injective
div_right_injective
infinite_inv πŸ“–mathematicalβ€”Infinite
Set
inv
InvolutiveInv.toInv
β€”Iff.not
finite_inv
infinite_mul πŸ“–mathematicalβ€”Infinite
Set
mul
Nonempty
β€”infinite_image2
Function.Injective.injOn
mul_left_injective
mul_right_injective
infinite_neg πŸ“–mathematicalβ€”Infinite
Set
neg
InvolutiveNeg.toNeg
β€”Iff.not
finite_neg
infinite_sub πŸ“–mathematicalβ€”Infinite
Set
sub
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
Nonempty
β€”infinite_image2
Function.Injective.injOn
sub_left_injective
sub_right_injective

Set.Finite

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalβ€”Set.Finite
Set
Set.add
β€”image2
div πŸ“–mathematicalβ€”Set.Finite
Set
Set.div
β€”image2
inv πŸ“–mathematicalβ€”Set.Finite
Set
Set.inv
InvolutiveInv.toInv
β€”Set.finite_inv
mul πŸ“–mathematicalβ€”Set.Finite
Set
Set.mul
β€”image2
neg πŸ“–mathematicalβ€”Set.Finite
Set
Set.neg
InvolutiveNeg.toNeg
β€”Set.finite_neg
of_inv πŸ“–mathematicalβ€”Set.Finiteβ€”Set.finite_inv
of_neg πŸ“–mathematicalβ€”Set.Finiteβ€”Set.finite_neg
smul πŸ“–mathematicalβ€”Set.Finite
Set
Set.smul
β€”image2
smul_set πŸ“–mathematicalβ€”Set.Finite
Set
Set.smulSet
β€”image
sub πŸ“–mathematicalβ€”Set.Finite
Set
Set.sub
β€”image2
vadd πŸ“–mathematicalβ€”Set.Finite
HVAdd.hVAdd
Set
instHVAdd
Set.vadd
β€”image2
vadd_set πŸ“–mathematicalβ€”Set.Finite
HVAdd.hVAdd
Set
instHVAdd
Set.vaddSet
β€”image
vsub πŸ“–mathematicalβ€”Set.Finite
VSub.vsub
Set
Set.vsub
β€”image2

Set.Infinite

Theorems

NameKindAssumesProvesValidatesDepends On
of_smul_set πŸ“–β€”Set.Infinite
Set
Set.smulSet
β€”β€”of_image
of_vadd_set πŸ“–β€”Set.Infinite
HVAdd.hVAdd
Set
instHVAdd
Set.vaddSet
β€”β€”of_image

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