Documentation Verification Report

Operations

📁 Source: Mathlib/RingTheory/Ideal/Operations.lean

Statistics

MetricCount
DefinitionsIsRadical, finsuppTotal, instIdemCommSemiring, radical, radicalInfTopHom, uniqueUnits, algebraIdeal, mapAlgEquiv, mapAlgHom, moduleSubmodule
10
Theoremsmk_ne_zero', mem_ideal_span_range_iff_exists_finsupp, inf_le, inf_le', isRadical, le_of_pow_le, mul_le, multiset_prod_le, multiset_prod_map_le, multiset_prod_mem_iff_exists_mem, notMem_of_isCoprime_of_mem, pow_le_iff, prod_le, prod_mem_iff, prod_mem_iff_exists_mem, radical, radical_le_iff, inf, radical, radical_le_iff, instHMul, instHPowNat, mul_one, pow_add, pow_succ, add_eq_one_iff, add_eq_sup, bot_mul, bot_pow, coprime_of_no_prime_ge, disjoint_powers_iff_notMem, dvd_bot, eq_inf_of_isPrime_inf, eq_span_singleton_mul, exists_subset_radical_span_sup_of_subset_radical_sup, finset_inf_span_singleton, finsuppTotal_apply, finsuppTotal_apply_eq_of_fintype, iInf_span_singleton, iInf_span_singleton_natCast, iInf_sup_eq_top, iSup_mul, inf_eq_mul_of_isCoprime, instIsTorsionFreeSubtypeMemSubmodule, instNoZeroDivisors, isCoprime_biInf, isCoprime_iff_add, isCoprime_iff_codisjoint, isCoprime_iff_exists, isCoprime_iff_sup_eq, isCoprime_of_isMaximal, isCoprime_span_singleton_iff, isCoprime_tfae, isRadical_bot, isRadical_bot_iff, isRadical_bot_of_noZeroDivisors, isRadical_iInf, isRadical_iff_pow_one_lt, isUnit_iff, le_of_dvd, le_radical, le_span_singleton_mul_iff, mem_mul_span_singleton, mem_radical_iff, mem_radical_of_pow_mem, mem_span_range_iff_exists_fun, mem_span_singleton_mul, mul_assoc, mul_bot, mul_comm, mul_eq_bot, mul_eq_inf_of_coprime, mul_iSup, mul_le, mul_le_inf, mul_le_left, mul_le_right, mul_left_self_sup, mul_mem_mul, mul_mem_mul_rev, mul_mono, mul_mono_left, mul_mono_right, mul_right_self_sup, mul_sup, mul_sup_eq_of_coprime_left, mul_sup_eq_of_coprime_right, mul_top, multiset_prod_eq_bot, multiset_prod_le_inf, multiset_prod_span_singleton, natCast_eq_top, ofNat_eq_top, one_eq_top, pow_eq_top_iff, pow_eq_zero_of_mem, pow_le_pow_right, pow_le_self, pow_mem_pow, pow_right_mono, pow_sup_eq_top, pow_sup_eq_top', pow_sup_pow_eq_top, pow_sup_pow_eq_top', primeCompl_le_nonZeroDivisors, prod_le_inf, prod_mem_prod, prod_span, prod_span_singleton, prod_sup_eq_top, radicalInfTopHom_apply, radical_bot_of_noZeroDivisors, radical_eq_iff, radical_eq_sInf, radical_eq_top, radical_finset_inf, radical_iInf_le, radical_idem, radical_inf, radical_isRadical, radical_le_radical_iff, radical_mono, radical_mul, radical_pow, radical_sup, radical_top, range_finsuppTotal, range_mul, range_mul', smul_eq_mul, span_mul_span, span_mul_span', span_pair_mul_span_pair, span_singleton_mul_eq_span_singleton_mul, span_singleton_mul_le_iff, span_singleton_mul_le_span_singleton_mul, span_singleton_mul_left_inj, span_singleton_mul_left_injective, span_singleton_mul_left_mono, span_singleton_mul_right_inj, span_singleton_mul_right_injective, span_singleton_mul_right_mono, span_singleton_mul_span_singleton, span_singleton_nonZeroDivisors, span_singleton_pow, span_singleton_toAddSubgroup_eq_zmultiples, subset_union, subset_union_prime, subset_union_prime', subset_union_prime_finite, sum_eq_sup, sup_eq_top_iff_isCoprime, sup_iInf_eq_top, sup_mul, sup_mul_eq_of_coprime_left, sup_mul_eq_of_coprime_right, sup_mul_left_self, sup_mul_right_self, sup_multiset_prod_eq_top, sup_pow_add_le_pow_sup_pow, sup_pow_eq_top, sup_pow_eq_top', sup_prod_eq_top, top_mul, top_pow, zero_eq_bot, add_eq, codisjoint, exists, sup_eq, coe_mapAlgEquiv_apply, coe_mapAlgEquiv_symm_apply, coe_mapAlgHom_apply, coe_span_smul, comap_smul'', ideal_span_singleton_smul, map_le_smul_top, map_pointwise_smul, map_smul'', mem_ideal_smul_span_iff_exists_sum, mem_ideal_smul_span_iff_exists_sum', mem_of_span_eq_top_of_smul_pow_mem, mem_of_span_top_of_smul_mem, mem_smul_span, mem_smul_span_singleton, mem_smul_top_iff, mul_smul, set_smul_top_eq_span, smul_comap_le_comap_smul, smul_eq_map₂, smul_le_right, smul_le_span, span_singleton_toAddSubgroup_eq_zmultiples, span_smul_eq, span_smul_span, top_smul, instNonUnitalSubringClassIdeal, instNonUnitalSubsemiringClassIdeal
198
Total208

Associates

Theorems

NameKindAssumesProvesValidatesDepends On
mk_ne_zero' 📖mk_ne_zero
Ideal.zero_eq_bot
Ideal.span_singleton_eq_bot

Finsupp

Theorems

NameKindAssumesProvesValidatesDepends On
mem_ideal_span_range_iff_exists_finsupp 📖mathematicalIdeal
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.span
Set.range
sum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
mem_span_range_iff_exists_finsupp

Ideal

Definitions

NameCategoryTheorems
IsRadical 📖MathDef
15 mathmath: isRadical_jacobson, PrimeSpectrum.isClosed_iff_zeroLocus_radical_ideal, IsSemisimpleModule.annihilator_isRadical, RingHom.ker_isRadical_iff_reduced_of_surjective, isRadical_bot, PrimeSpectrum.isRadical_vanishingIdeal, isRadical_bot_iff, isRadical_iff_span_singleton, isRadical_bot_of_noZeroDivisors, IsPrime.isRadical, isRadical_of_eq_jacobson, isRadical_iff_pow_one_lt, radical_isRadical, radical_eq_iff, isRadical_iff_quotient_reduced
finsuppTotal 📖CompOp
3 mathmath: finsuppTotal_apply_eq_of_fintype, finsuppTotal_apply, range_finsuppTotal
instIdemCommSemiring 📖CompOp
81 mathmath: FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, NumberField.isCoprime_differentIdeal_of_isCoprime_discr, Submodule.isInternal_prime_power_torsion_of_pid, Submodule.coe_mapAlgEquiv_symm_apply, prime_of_mem_primesOver, Associates.finite_factors, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, IsPrime.prod_le, FractionalIdeal.count_well_defined, isPrime_iff_bot_or_prime, Factors.fact_ramificationIdx_neZero, prod_normalizedFactors_eq_self, IsDedekindDomain.HeightOneSpectrum.intValuationDef_if_neg, count_normalizedFactors_eq, gcd_eq_sup, prime_span_singleton_iff, isCoprime_iff_gcd, Submodule.isInternal_prime_power_torsion_of_is_torsion_by_ideal, IsDedekindDomain.ramificationIdx_eq_normalizedFactors_count, FractionalIdeal.finprod_heightOneSpectrum_factorization, normalizedFactorsEquivOfQuotEquiv_symm, IsPrime.multiset_prod_map_le, instWfDvdMonoidIdeal, FractionalIdeal.count_ne_zero, Factors.isScalarTower, Associates.le_singleton_iff, IsLocalization.OverPrime.mem_normalizedFactors_of_isPrime, Submodule.coe_mapAlgEquiv_apply, IsDedekindDomain.HeightOneSpectrum.prime, IsPrime.multiset_prod_le, count_span_normalizedFactors_eq_of_normUnit, irreducible_pow_sup, PrimeSpectrum.exists_primeSpectrum_prod_le, finite_mulSupport_coe, mem_normalizedFactors_iff, Factors.liesOver, count_le_of_ideal_ge, IsDedekindDomain.HeightOneSpectrum.intValuation_def, prime_iff_isPrime, Factors.finrank_pow_ramificationIdx, mem_primesOver_iff_mem_normalizedFactors, count_associates_eq, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity, map_algebraMap_eq_finset_prod_pow, count_span_normalizedFactors_eq, factors_span_eq, Submodule.isInternal_prime_power_torsion, finprod_count, IsDedekindDomain.ramificationIdx_eq_factors_count, uniqueFactorizationMonoid, IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiset_count, lcm_eq_inf, eq_prime_pow_mul_coprime, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, Factors.finiteDimensional_quotient_pow, finprod_heightOneSpectrum_factorization_coe, exists_multiset_prod_cons_le_and_prod_not_le, FractionalIdeal.finite_factors', count_associates_factors_eq, Factors.isPrime, count_associates_eq', Submodule.coe_mapAlgHom_apply, sup_eq_prod_inf_factors, dvdNotUnit_iff_lt, prime_of_isPrime, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, Factors.piQuotientEquiv_mk, finprod_not_dvd, IsDedekindDomain.HeightOneSpectrum.associates_irreducible, finite_quotient_prod, PrimeSpectrum.exists_primeSpectrum_prod_le_and_ne_bot_of_domain, finite_mulSupport_inv, IsDedekindDomain.quotientEquivPiFactors_mk, singleton_span_mem_normalizedFactors_of_mem_normalizedFactors, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, finprod_heightOneSpectrum_factorization, FractionalIdeal.count_coe, Factors.piQuotientEquiv_map, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_emultiplicity, FractionalIdeal.coeIdeal_finprod, KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span
radical 📖CompOp
69 mathmath: radical_mono, IsLocalization.map_radical, radical_sup, MvPolynomial.radical_le_vanishingIdeal_zeroLocus, jacobson_eq_radical, exists_minimal_isPrimary_decomposition_of_isPrimary_decomposition, ringKrullDim_eq_one_iff_of_isLocalRing_isDomain, Submodule.IsPrimary.radical_colon_singleton_of_notMem, Ring.KrullDimLE.radical_eq_maximalIdeal, PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radical, PrimeSpectrum.vanishingIdeal_range_comap, le_radical, PrimeSpectrum.zeroLocus_subset_zeroLocus_iff, minimalPrimes_eq_subsingleton, Submodule.IsPrimary.isPrime_radical_colon, radical_inf, radical_idem, jacobson_radical_eq_jacobson, PrimeSpectrum.zeroLocus_radical, PrimeSpectrum.isIrreducible_zeroLocus_iff, radical_bot_of_noZeroDivisors, isStronglyTranscendental_mk_radical_conductor, HomogeneousIdeal.coe_radical, IsMinimalPrimaryDecomposition.minimalPrimes_subset_image_radical, PrimeSpectrum.zeroLocus_subset_zeroLocus_singleton_iff, map_radical_of_surjective, AlgebraicGeometry.Scheme.zeroLocus_radical, PrimeSpectrum.zeroLocus_ideal_mem_irreducibleComponents, radical_eq_jacobson, IsAssociatedPrime.eq_radical, Submodule.IsMinimalPrimaryDecomposition.distinct, IsHomogeneous.radical, PrimeSpectrum.zeroLocus_eq_iff, associatedPrimes.eq_singleton_of_isPrimary, IsRadical.radical_le_iff, map_radical_le, radical_eq_sInf, Submodule.isPrimary_decomposition_pairwise_ne_radical, radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot, radical_le_radical_iff, Polynomial.coeff_mem_radical_span_coeff_of_dvd, radical_pow, radical_le_jacobson, radical_minimalPrimes, radical_iInf_le, radicalInfTopHom_apply, radical_isRadical, Submodule.exists_minimal_isPrimary_decomposition_of_isPrimary_decomposition, isPrime_radical, AlgebraicGeometry.Scheme.IdealSheafData.radical_ideal, PrimeSpectrum.basicOpen_le_basicOpen_iff, radical_top, isPrimary_iff, mem_radical_iff, sInf_minimalPrimes, isPrimary_decomposition_pairwise_ne_radical, iUnion_minimalPrimes, radical_eq_top, IsRadical.radical, comap_radical, IsHomogeneous.radical_eq, IsPrime.radical_le_iff, IsPrime.radical, Polynomial.mul_contentIdeal_le_radical_contentIdeal_mul, MvPolynomial.vanishingIdeal_zeroLocus_eq_radical, Submodule.IsPrimary.mem_or_mem, IsArtinianRing.jacobson_eq_radical, radical_eq_iff, radical_mul
radicalInfTopHom 📖CompOp
1 mathmath: radicalInfTopHom_apply
uniqueUnits 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
add_eq_one_iff 📖mathematicalIdeal
Submodule.pointwiseAdd
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.one
SetLike.instMembership
Submodule.setLike
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
one_eq_top
eq_top_iff_one
add_eq_sup
Submodule.mem_sup
add_eq_sup 📖mathematicalIdeal
Submodule.pointwiseAdd
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
bot_mul 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Bot.bot
Submodule.instBot
IsScalarTower.left
Submodule.bot_mul
bot_pow 📖mathematicalIdeal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Bot.bot
Submodule.instBot
Submodule.bot_pow
IsScalarTower.left
coprime_of_no_prime_ge 📖mathematicalIsPrime
CommSemiring.toSemiring
IsCoprime
Ideal
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
isCoprime_iff_sup_eq
exists_le_maximal
le_trans
le_sup_left
le_sup_right
IsMaximal.isPrime
disjoint_powers_iff_notMem 📖mathematicalIsRadicalDisjoint
Set
OmegaCompletePartialOrder.toPartialOrder
CompleteLattice.instOmegaCompletePartialOrder
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
SetLike.coe
Submonoid
Monoid.toMulOneClass
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Submonoid.instSetLike
Submonoid.powers
Ideal
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AddSubmonoid
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SetLike.instMembership
AddSubmonoid.instSetLike
Submodule.toAddSubmonoid
Set.disjoint_left
Submonoid.mem_powers
disjoint_iff
eq_bot_iff
mem_radical_of_pow_mem
le_radical
dvd_bot 📖mathematicalIdeal
CommSemiring.toSemiring
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Submodule.instNonUnitalSemiring
Semiring.toModule
IsScalarTower.right
Algebra.id
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
dvd_zero
IsScalarTower.right
eq_inf_of_isPrime_inf 📖mathematicalFinset
Finset.instMembership
Finset.inf
Ideal
CommSemiring.toSemiring
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instOrderTop
le_antisymm
Finset.inf_le
IsPrime.inf_le'
le_rfl
eq_span_singleton_mul 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.right
exists_subset_radical_span_sup_of_subset_radical_sup 📖mathematicalSet
Set.instHasSubset
SetLike.coe
Ideal
CommSemiring.toSemiring
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
radical
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Set.range
Set.Elem
span
Set.range_subset_iff
add_mem
mem_sup_left
subset_span
mem_sup_right
finset_inf_span_singleton 📖mathematicalSet.Pairwise
SetLike.coe
Finset
Finset.instSetLike
Function.onFun
IsCoprime
Finset.inf
Ideal
CommSemiring.toSemiring
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instOrderTop
span
Set
Set.instSingletonSet
Finset.prod
CommSemiring.toCommMonoid
ext
Finset.prod_dvd_of_coprime
Dvd.dvd.trans
Finset.dvd_prod_of_mem
finsuppTotal_apply 📖mathematicalDFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
Finsupp
Ideal
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
Submodule.zero
Finsupp.instAddCommMonoid
Submodule.addCommMonoid
AddCommGroup.toAddCommMonoid
Finsupp.module
Submodule.module
LinearMap.instFunLike
finsuppTotal
Finsupp.sum
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
LinearMap.map_zero
Finsupp.linearCombination_apply
Finsupp.sum_mapRange_index
zero_smul
finsuppTotal_apply_eq_of_fintype 📖mathematicalDFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
Finsupp
Ideal
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
Submodule.zero
Finsupp.instAddCommMonoid
Submodule.addCommMonoid
AddCommGroup.toAddCommMonoid
Finsupp.module
Submodule.module
LinearMap.instFunLike
finsuppTotal
Finset.sum
Finset.univ
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Finsupp.instFunLike
finsuppTotal_apply
Finsupp.sum_fintype
zero_smul
iInf_span_singleton 📖mathematicalIsCoprimeiInf
Ideal
CommSemiring.toSemiring
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
span
Set
Set.instSingletonSet
Finset.prod
CommSemiring.toCommMonoid
Finset.univ
Finset.inf_univ_eq_iInf
finset_inf_span_singleton
Finset.coe_univ
Set.pairwise_univ
iInf_span_singleton_natCast 📖mathematicalPairwiseiInf
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
span
Set
Set.instSingletonSet
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Finset.prod
Nat.instCommMonoid
Finset.univ
iInf_span_singleton
Nat.Coprime.cast
Nat.cast_prod
iInf_sup_eq_top 📖mathematicalIsTwoSided
Ideal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
iInf
Submodule.instInfSet
Finset
Finset.instMembership
sup_comm
sup_iInf_eq_top
iSup_mul 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.iSup_smul
IsScalarTower.left
inf_eq_mul_of_isCoprime 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
IsScalarTower.right
mul_eq_inf_of_coprime
IsCoprime.sup_eq
instIsTorsionFreeSubtypeMemSubmodule 📖mathematicalModule.IsTorsionFree
Submodule
SetLike.instMembership
Submodule.setLike
Submodule.addCommMonoid
Submodule.module'
Submodule.instIsTorsionFree
instNoZeroDivisors 📖mathematicalNoZeroDivisors
Ideal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Submodule.pointwiseZero
IsScalarTower.left
mul_eq_bot
isCoprime_biInf 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
iInf
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset
Finset.instMembership
one_eq_top
sup_iInf_eq_top
instIsTwoSided
isCoprime_iff_add 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Submodule.pointwiseAdd
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.one
isCoprime_iff_codisjoint
codisjoint_iff
add_eq_sup
one_eq_top
isCoprime_iff_codisjoint 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Codisjoint
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instOrderTop
IsCoprime.eq_1
codisjoint_iff
eq_top_iff_one
IsScalarTower.right
sup_le
LE.le.trans
IsScalarTower.left
mul_le_left
le_sup_left
le_sup_right
one_eq_top
top_mul
isCoprime_iff_exists 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
add_eq_one_iff
isCoprime_iff_add
isCoprime_iff_sup_eq 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
isCoprime_iff_codisjoint
codisjoint_iff
isCoprime_of_isMaximal 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
isCoprime_iff_codisjoint
IsCoatom.codisjoint_of_ne
isMaximal_def
isCoprime_span_singleton_iff 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
span
Set
Set.instSingletonSet
mul_comm
isCoprime_tfae 📖mathematicalList.TFAE
IsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Codisjoint
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instOrderTop
Submodule.pointwiseAdd
Submodule.one
SetLike.instMembership
Submodule.setLike
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Top.top
Submodule.instTop
isCoprime_iff_codisjoint
isCoprime_iff_add
isCoprime_iff_exists
isCoprime_iff_sup_eq
isRadical_bot 📖mathematicalIsRadical
Bot.bot
Ideal
CommSemiring.toSemiring
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
isRadical_bot_iff
isRadical_bot_iff 📖mathematicalIsRadical
Bot.bot
Ideal
CommSemiring.toSemiring
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
IsReduced
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instIsConcreteLE
isRadical_bot_of_noZeroDivisors 📖mathematicalIsRadical
Bot.bot
Ideal
CommSemiring.toSemiring
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
eq_zero_of_pow_eq_zero
isReduced_of_noZeroDivisors
isRadical_iInf 📖mathematicalIsRadicaliInf
Ideal
CommSemiring.toSemiring
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
LE.le.trans
radical_iInf_le
iInf_mono
isRadical_iff_pow_one_lt 📖mathematicalIsRadical
Ideal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Nat.pow_imp_self_of_one_lt
Submodule.smul_mem
isUnit_iff 📖mathematicalIsUnit
Ideal
CommSemiring.toSemiring
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
IdemSemiring.toSemiring
Submodule.idemSemiring
Algebra.id
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
isUnit_iff_dvd_one
eq_top_iff
le_of_dvd
IsScalarTower.left
mul_top
instIsTwoSided
one_eq_top
le_of_dvd 📖mathematicalIdeal
CommSemiring.toSemiring
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Submodule.instNonUnitalSemiring
Semiring.toModule
IsScalarTower.right
Algebra.id
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
IsScalarTower.right
le_trans
mul_le_inf
instIsTwoSided
inf_le_left
le_radical 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
radical
pow_one
le_span_singleton_mul_iff 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
SetLike.instMembership
Submodule.setLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.right
mem_mul_span_singleton 📖mathematicalIdeal
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
span
Set
Set.instSingletonSet
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Submodule.mem_smul_span_singleton
mem_radical_iff 📖mathematicalIdeal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
radical
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
mem_radical_of_pow_mem 📖Ideal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
radical
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
radical_idem
mem_span_range_iff_exists_fun 📖mathematicalIdeal
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
span
Set.range
Finset.sum
Finset.univ
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Submodule.mem_span_range_iff_exists_fun
mem_span_singleton_mul 📖mathematicalIdeal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.right
mul_comm
instIsTwoSided
mul_assoc 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Submodule.smul_assoc
IsScalarTower.left
mul_bot 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Bot.bot
Submodule.instBot
IsScalarTower.left
Submodule.mul_bot
mul_comm 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
le_antisymm
IsScalarTower.right
IsScalarTower.left
mul_le
mul_mem_mul_rev
mul_eq_bot 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Bot.bot
Submodule.instBot
IsScalarTower.left
Submodule.eq_bot_iff
Submodule.ne_bot_iff
mul_eq_zero
mul_mem_mul
bot_mul
mul_bot
mul_eq_inf_of_coprime 📖mathematicalIdeal
CommSemiring.toSemiring
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Submodule.instMin
le_antisymm
IsScalarTower.right
mul_le_inf
instIsTwoSided
Submodule.mem_sup
eq_top_iff_one
add_mem
mul_mem_mul_rev
mul_mem_mul
mul_add
Distrib.leftDistribClass
mul_one
mul_iSup 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.smul_iSup
IsScalarTower.left
mul_le 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
SetLike.instMembership
Submodule.setLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Submodule.smul_le
IsScalarTower.left
mul_le_inf 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Submodule.instMin
IsScalarTower.left
mul_le
mul_mem_right
mul_mem_left
mul_le_left 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
mul_le
mul_mem_left
mul_le_right 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
mul_le
mul_mem_right
mul_left_self_sup 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_eq_right
mul_le_left
mul_mem_mul 📖mathematicalIdeal
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Submodule.smul_mem_smul
IsScalarTower.left
mul_mem_mul_rev 📖mathematicalIdeal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Algebra.id
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.right
mul_mem_mul
mul_comm
mul_mono 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Submodule.smul_mono
IsScalarTower.left
mul_mono_left 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Submodule.smul_mono_left
IsScalarTower.left
mul_mono_right 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
smul_mono_right
IsScalarTower.left
Submodule.instCovariantClassHSMulLe_1
mul_right_self_sup 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_eq_right
mul_le_right
mul_sup 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.smul_sup
IsScalarTower.left
mul_sup_eq_of_coprime_left 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_comm
sup_mul_eq_of_coprime_left
mul_sup_eq_of_coprime_right 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_comm
sup_mul_eq_of_coprime_right
mul_top 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Top.top
Submodule.instTop
le_antisymm
IsScalarTower.left
mul_le
mul_mem_right
mul_mem_mul
Submodule.mem_top
mul_one
multiset_prod_eq_bot 📖mathematicalMultiset.prod
Ideal
CommSemiring.toSemiring
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Multiset
Multiset.instMembership
Multiset.prod_eq_zero_iff
instNoZeroDivisors
IsDomain.to_noZeroDivisors
instNontrivial
IsDomain.toNontrivial
multiset_prod_le_inf 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Multiset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Multiset.inf
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.instOrderTop
Multiset.induction_on
Multiset.inf_zero
le_top
Multiset.prod_cons
Multiset.inf_cons
le_trans
mul_le_inf
instIsTwoSided
inf_le_inf
le_rfl
multiset_prod_span_singleton 📖mathematicalMultiset.prod
Ideal
CommSemiring.toSemiring
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Multiset.map
span
Set
Set.instSingletonSet
Multiset.induction_on
one_eq_top
span_singleton_one
IsScalarTower.left
Multiset.map_cons
Multiset.prod_cons
instIsTwoSided
natCast_eq_top 📖mathematicalIdeal
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
Submodule.instAddCommMonoidWithOne
Semiring.toModule
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Nat.cast_one
one_eq_top
Nat.cast_succ
add_eq_sup
top_sup_eq
ofNat_eq_top 📖mathematicalTop.top
Ideal
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
natCast_eq_top
Nat.AtLeastTwo.toNeZero
one_eq_top 📖mathematicalIdeal
Submodule.one
Semiring.toModule
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Submodule.one_eq_span
span.eq_1
span_singleton_one
pow_eq_top_iff 📖mathematicalIdeal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Top.top
Submodule.instTop
IsScalarTower.left
eq_top_iff_one
pow_le_self
top_pow
Submodule.pow_zero
one_eq_top
pow_eq_zero_of_mem 📖mathematicalIdeal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Submodule.pointwiseZero
SetLike.instMembership
Submodule.setLike
Monoid.toNatPow
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
IsScalarTower.left
pow_le_pow_right
pow_mem_pow
pow_le_pow_right 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
Submodule.pow_zero
one_eq_top
le_top
add_comm
Submodule.pow_add
mul_le_left
pow_le_self 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
pow_le_pow_right
Submodule.pow_one
pow_mem_pow 📖mathematicalIdeal
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Monoid.toNatPow
Submodule.pow_mem_pow
IsScalarTower.left
pow_right_mono 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
Submodule.pow_zero
le_refl
Submodule.pow_succ
mul_mono
pow_sup_eq_top 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_comm
sup_pow_eq_top'
pow_sup_eq_top' 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_comm
sup_pow_eq_top
pow_sup_pow_eq_top 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
pow_sup_eq_top
IsScalarTower.left
sup_pow_eq_top
pow_sup_pow_eq_top' 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
pow_sup_eq_top'
IsScalarTower.left
IsTwoSided.instHPowNat
sup_pow_eq_top'
primeCompl_le_nonZeroDivisors 📖mathematicalSubmonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submonoid.instPartialOrder
primeCompl
nonZeroDivisors
Semiring.toMonoidWithZero
le_nonZeroDivisors_of_noZeroDivisors
zero_mem
prod_le_inf 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Finset.inf
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.instOrderTop
multiset_prod_le_inf
prod_mem_prod 📖mathematicalIdeal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Finset.induction_on
prod_span 📖mathematicalFinset.prod
Ideal
CommSemiring.toSemiring
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
span
Set
Set.commMonoid
Submodule.prod_span
prod_span_singleton 📖mathematicalFinset.prod
Ideal
CommSemiring.toSemiring
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
span
Set
Set.instSingletonSet
Submodule.prod_span_singleton
prod_sup_eq_top 📖mathematicalIdeal
CommSemiring.toSemiring
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
sup_comm
sup_prod_eq_top
radicalInfTopHom_apply 📖mathematicalDFunLike.coe
InfTopHom
Ideal
CommSemiring.toSemiring
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instTop
InfTopHom.instFunLike
radicalInfTopHom
radical
radical_bot_of_noZeroDivisors 📖mathematicalradical
Bot.bot
Ideal
CommSemiring.toSemiring
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
eq_bot_iff
isRadical_bot_of_noZeroDivisors
radical_eq_iff 📖mathematicalradical
IsRadical
le_antisymm_iff
le_radical
IsRadical.eq_1
radical_eq_sInf 📖mathematicalradical
InfSet.sInf
Ideal
CommSemiring.toSemiring
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
setOf
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
IsPrime
le_antisymm
le_sInf
IsPrime.radical_le_iff
by_contradiction
zorn_le_nonempty₀
Submodule.mem_sSup_of_directed
IsChain.directedOn
instReflLe
le_sSup
Maximal.prop
Maximal.eq_of_le
le_sup_left
Submodule.mem_sup_right
mem_span_singleton_self
radical_top
Submodule.mem_sup
mem_span_singleton'
pow_add
add_mul
Distrib.rightDistribClass
mul_add
Distrib.leftDistribClass
mul_assoc
mul_left_comm
add_mem
mul_mem_right
instIsTwoSided
mul_mem_left
sInf_le
IsPrime.radical
radical_eq_top 📖mathematicalradical
Top.top
Ideal
CommSemiring.toSemiring
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
eq_top_iff_one
one_pow
radical_top
radical_finset_inf 📖mathematicalFinset
Finset.instMembership
radical
Finset.inf
Ideal
CommSemiring.toSemiring
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instOrderTop
radicalInfTopHom_apply
map_finset_inf
InfTopHom.instInfTopHomClass
Finset.inf'_eq_inf
Finset.inf'_eq_of_forall
radical_iInf_le 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
radical
iInf
Submodule.instInfSet
le_iInf
radical_mono
iInf_le
radical_idem 📖mathematicalradicalIsRadical.radical
radical_isRadical
radical_inf 📖mathematicalradical
Ideal
CommSemiring.toSemiring
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
le_antisymm
le_inf
radical_mono
inf_le_left
inf_le_right
mul_mem_right
instIsTwoSided
pow_add
mul_mem_left
radical_isRadical 📖mathematicalIsRadical
radical
pow_mul
radical_le_radical_iff 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
radical
IsRadical.radical_le_iff
radical_isRadical
radical_mono 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
radical
radical_mul 📖mathematicalradical
Ideal
CommSemiring.toSemiring
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
le_antisymm
IsScalarTower.right
IsScalarTower.left
radical_mono
mul_le_inf
instIsTwoSided
radical_inf
mul_mem_mul
pow_add
radical_pow 📖mathematicalradical
Ideal
CommSemiring.toSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
IdemSemiring.toSemiring
Submodule.idemSemiring
Algebra.id
pow_one
pow_succ
IsScalarTower.right
radical_mul
inf_idem
radical_sup 📖mathematicalradical
Ideal
CommSemiring.toSemiring
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
le_antisymm
radical_mono
sup_le_sup
le_radical
radical_le_radical_iff
sup_le
le_sup_left
le_sup_right
radical_top 📖mathematicalradical
Top.top
Ideal
CommSemiring.toSemiring
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
eq_top_iff_one
Submodule.mem_top
range_finsuppTotal 📖mathematicalLinearMap.range
Finsupp
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.zero
Finsupp.instAddCommMonoid
Submodule.addCommMonoid
AddCommGroup.toAddCommMonoid
Finsupp.module
Submodule.module
RingHom.id
RingHomSurjective.ids
finsuppTotal
Submodule
Submodule.instSMul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Submodule.span
Set.range
Submodule.ext
RingHomSurjective.ids
IsScalarTower.left
Submodule.mem_ideal_smul_span_iff_exists_sum
instIsTwoSided_1
finsuppTotal_apply
Finsupp.sum_mapRange_index
zero_smul
Finsupp.sum_congr
range_mul 📖mathematicalLinearMap.range
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
RingHom.id
RingHomSurjective.ids
DFunLike.coe
LinearMap
LinearMap.addCommMonoid
LinearMap.module
smulCommClass_self
CommSemiring.toCommMonoid
DistribMulAction.toMulAction
CommMonoid.toMonoid
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
LinearMap.instFunLike
LinearMap.mul
Submodule.restrictScalars
Semiring.toModule
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
span
Set
Set.instSingletonSet
Submodule.ext
RingHomSurjective.ids
smulCommClass_self
range_mul' 📖mathematicalLinearMap.range
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.id
RingHomSurjective.ids
DFunLike.coe
LinearMap
LinearMap.addCommMonoid
LinearMap.module
smulCommClass_self
CommSemiring.toCommMonoid
DistribMulAction.toMulAction
CommMonoid.toMonoid
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
LinearMap.instFunLike
LinearMap.mul
Algebra.to_smulCommClass
Algebra.id
IsScalarTower.right
span
Set
Set.instSingletonSet
range_mul
Algebra.to_smulCommClass
IsScalarTower.right
smul_eq_mul 📖mathematicalIdeal
Submodule.instSMul
Semiring.toModule
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Submodule.mul
IsScalarTower.left
span_mul_span 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
span
Set
Set.mul
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Submodule.span_smul_span
span_mul_span' 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
span
Set
Set.mul
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.left
span_mul_span
Set.ext
span_pair_mul_span_pair 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
span
Set
Set.instInsert
Set.instSingletonSet
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.left
span_mul_span'
Set.ext
span_singleton_mul_eq_span_singleton_mul 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.right
span_singleton_mul_le_iff 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
SetLike.instMembership
Submodule.setLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.right
instIsConcreteLE
span_singleton_mul_le_span_singleton_mul 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
SetLike.instMembership
Submodule.setLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.right
span_singleton_mul_left_inj 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
span
Set
Set.instSingletonSet
IsScalarTower.left
span_singleton_mul_left_mono
span_singleton_mul_left_injective 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
IsScalarTower.left
instIsTwoSided
span_singleton_mul_left_mono 📖mathematicalIdeal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
span
Set
Set.instSingletonSet
IsScalarTower.left
instIsConcreteLE
IsCancelMulZero.toIsRightCancelMulZero
IsDomain.toIsCancelMulZero
span_singleton_mul_right_inj 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
IsScalarTower.right
span_singleton_mul_right_mono
span_singleton_mul_right_injective 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
IsScalarTower.right
span_singleton_mul_right_mono 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Algebra.id
span
Set
Set.instSingletonSet
IsScalarTower.right
mul_right_inj'
IsCancelMulZero.toIsLeftCancelMulZero
IsDomain.toIsCancelMulZero
instIsConcreteLE
span_singleton_mul_span_singleton 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
span
Set
Set.instSingletonSet
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsScalarTower.left
span_mul_span'
Set.singleton_mul_singleton
span_singleton_nonZeroDivisors 📖mathematicalIdeal
CommSemiring.toSemiring
Submonoid
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
Semiring.toMonoidWithZero
IdemSemiring.toSemiring
Submodule.idemSemiring
Algebra.id
SetLike.instMembership
Submonoid.instSetLike
nonZeroDivisors
span
Set
Set.instSingletonSet
subsingleton_or_nontrivial
Subsingleton.eq_zero
Unique.instSubsingleton
mem_nonZeroDivisors_iff_ne_zero
instNoZeroDivisors
instNontrivial
zero_eq_bot
span_singleton_eq_bot
span_singleton_pow 📖mathematicalIdeal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
span
Set
Set.instSingletonSet
Monoid.toNatPow
IsScalarTower.left
one_eq_top
pow_zero
span_one
eq_or_ne
zero_add
Submodule.pow_one
pow_one
Submodule.pow_succ'
span_singleton_mul_span_singleton
pow_succ'
span_singleton_toAddSubgroup_eq_zmultiples 📖mathematicalSubmodule.toAddSubgroup
Int.instRing
Int.instAddCommGroup
Semiring.toModule
Int.instSemiring
span
Set
Set.instSingletonSet
AddSubgroup.zmultiples
Int.instAddGroup
Submodule.span_singleton_toAddSubgroup_eq_zmultiples
subset_union 📖mathematicalSet
Set.instHasSubset
SetLike.coe
Ideal
Ring.toSemiring
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Set.instUnion
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
AddSubgroupClass.subset_union
Submodule.addSubgroupClass
instIsConcreteLE
subset_union_prime 📖mathematicalIsPrime
CommSemiring.toSemiring
CommRing.toCommSemiring
Set
Set.instHasSubset
SetLike.coe
Ideal
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Set.iUnion
Set.instMembership
Finset
Finset.instSetLike
Finset.instMembership
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
Finset.notMem_erase
Finset.insert_erase
Finset.mem_insert_of_mem
Finset.exists_mem_insert
subset_union_prime'
Set.union_assoc
Set.biUnion_insert
Finset.coe_insert
Set.union_self
Finset.eq_empty_or_nonempty
Set.biUnion_empty
Finset.coe_empty
zero_mem
bex_def
Set.Subset.trans
Set.subset_biUnion_of_mem
subset_union_prime' 📖mathematicalIsPrime
CommSemiring.toSemiring
CommRing.toCommSemiring
Set
Set.instHasSubset
SetLike.coe
Ideal
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Set.instUnion
Set.iUnion
Set.instMembership
Finset
Finset.instSetLike
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
Finset.instMembership
subset_union
Set.union_empty
Set.biUnion_empty
Finset.coe_empty
Finset.card_eq_zero
Finset.card_eq_succ
Finset.forall_mem_insert
Finset.notMem_erase
Finset.insert_erase
Finset.mem_insert_of_mem
Finset.card_insert_of_notMem
Finset.coe_insert
Set.biUnion_insert
Set.union_eq_self_of_subset_right
Set.union_assoc
Finset.insert_subset_insert
Finset.subset_insert
Set.union_eq_self_of_subset_left
Set.union_right_comm
Finset.mem_insert_self
IsPrime.inf_le
IsPrime.inf_le'
Set.not_subset
ne_of_not_le
Mathlib.Tactic.Push.not_and_eq
le_antisymm
le_trans
le_refl
Mathlib.Tactic.Order.le_of_not_lt_le
Mathlib.Tactic.Order.not_lt_of_not_le
add_mem
sub_mem
add_sub_cancel_left
add_sub_cancel_right
Set.mem_iUnion₂
Set.mem_biUnion
Finset.inf_eq_iInf
Set.Subset.trans
Set.subset_union_left
Set.subset_union_right
Set.subset_biUnion_of_mem
Finset.mem_coe
subset_union_prime_finite 📖mathematicalIsPrime
CommSemiring.toSemiring
CommRing.toCommSemiring
Set
Set.instHasSubset
SetLike.coe
Ideal
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Set.iUnion
Set.instMembership
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
Set.Finite.exists_finset
Set.ext
subset_union_prime
sum_eq_sup 📖mathematicalFinset.sum
Ideal
Submodule.pointwiseAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.sup
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.instOrderBot
sup_eq_top_iff_isCoprime 📖mathematicalIdeal
CommSemiring.toSemiring
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
span
Set
Set.instSingletonSet
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
IsCoprime
eq_top_iff_one
Submodule.mem_sup
mem_span_singleton'
sup_iInf_eq_top 📖mathematicalIsTwoSided
Ideal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
iInf
Submodule.instInfSet
Finset
Finset.instMembership
Finset.induction_on'
iInf_congr_Prop
iInf_neg
iInf_top
sup_of_le_right
top_unique
Finset.iInf_insert
inf_comm
le_trans
IsScalarTower.left
sup_mul_eq_of_coprime_right
instIsTwoSidedIInf
Eq.ge
sup_le_sup_left
mul_le_inf
sup_mul 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.sup_smul
IsScalarTower.left
sup_mul_eq_of_coprime_left 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
le_antisymm
IsScalarTower.left
sup_le_sup_left
mul_le_left
Submodule.mem_sup
eq_top_iff_one
AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
Submodule.addSubmonoidClass
mul_mem_right
mul_mem_mul
add_assoc
add_mul
Distrib.rightDistribClass
one_mul
sup_mul_eq_of_coprime_right 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
le_antisymm
IsScalarTower.left
sup_le_sup_left
mul_le_right
Submodule.mem_sup
eq_top_iff_one
AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
Submodule.addSubmonoidClass
mul_mem_left
mul_mem_mul
add_assoc
mul_add
Distrib.leftDistribClass
mul_one
sup_mul_left_self 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_eq_left
mul_le_left
sup_mul_right_self 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
sup_eq_left
mul_le_right
sup_multiset_prod_eq_top 📖mathematicalIdeal
CommSemiring.toSemiring
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Multiset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Multiset.prod_induction
IsScalarTower.left
sup_mul_eq_of_coprime_left
instIsTwoSided
one_eq_top
sup_of_le_right
sup_pow_add_le_pow_sup_pow 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instPowNat
IsScalarTower.right
Algebra.id
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
IsScalarTower.right
add_eq_sup
add_pow
sum_eq_sup
Finset.sup_le
LE.le.trans
IsScalarTower.left
mul_le_right
instIsTwoSided
pow_le_pow_right
le_sup_left
mul_le_left
le_sup_right
sup_pow_eq_top 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
one_eq_top
sup_of_le_right
Submodule.pow_succ
sup_mul_eq_of_coprime_left
sup_pow_eq_top' 📖mathematicalIdeal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Top.top
Submodule.instTop
Submodule.instPowNat
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
one_eq_top
sup_of_le_right
eq_or_ne
zero_add
Submodule.pow_one
Submodule.pow_succ'
sup_mul_eq_of_coprime_right
sup_prod_eq_top 📖mathematicalIdeal
CommSemiring.toSemiring
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Finset.prod_induction
IsScalarTower.left
sup_mul_eq_of_coprime_left
instIsTwoSided
one_eq_top
sup_top_eq
top_mul 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Top.top
Submodule.instTop
Submodule.top_smul
top_pow 📖mathematicalIdeal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Top.top
Submodule.instTop
IsScalarTower.left
one_eq_top
Submodule.pow_succ
top_mul
zero_eq_bot 📖mathematicalIdeal
Submodule.pointwiseZero
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Bot.bot
Submodule.instBot

Ideal.IsPrime

Theorems

NameKindAssumesProvesValidatesDepends On
inf_le 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instMin
IsScalarTower.right
mul_le
LE.le.trans
IsScalarTower.left
Ideal.mul_le_inf
Ideal.instIsTwoSided
inf_le_left
inf_le_right
inf_le' 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.inf
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Submodule.instOrderTop
Finset
Finset.instMembership
prod_le
LE.le.trans
Ideal.prod_le_inf
Finset.inf_le
isRadical 📖mathematicalIdeal.IsRadicalmem_of_pow_mem
le_of_pow_le 📖Ideal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instPowNat
IsScalarTower.right
Algebra.id
IsScalarTower.right
Ideal.one_eq_top
pow_zero
Submodule.mem_top
pow_le_iff
mul_le 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.mul
IsScalarTower.right
Algebra.id
IsScalarTower.right
IsScalarTower.left
Ideal.mul_le
mul_mem_iff_mem_or_mem
Ideal.instIsTwoSided
instIsConcreteLE
multiset_prod_le 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Multiset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Ideal.instIdemCommSemiring
Multiset
Multiset.instMembership
Multiset.induction_on
Ideal.one_eq_top
ne_top
Multiset.prod_cons
IsScalarTower.right
mul_le
multiset_prod_map_le 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Multiset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Ideal.instIdemCommSemiring
Multiset.map
Multiset
Multiset.instMembership
multiset_prod_le
multiset_prod_mem_iff_exists_mem 📖mathematicalIdeal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Multiset.prod
CommSemiring.toCommMonoid
Multiset
Multiset.instMembership
Ideal.multiset_prod_span_singleton
multiset_prod_map_le
notMem_of_isCoprime_of_mem 📖IsCoprime
Ideal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
one_notMem
Ideal.add_mem
Ideal.mul_mem_left
pow_le_iff 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instPowNat
IsScalarTower.right
Algebra.id
multiset_prod_le
Multiset.prod_replicate
prod_le 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.prod
CommSemiring.toCommMonoid
IdemCommSemiring.toCommSemiring
Ideal.instIdemCommSemiring
Finset
Finset.instMembership
multiset_prod_map_le
prod_mem_iff 📖mathematicalIdeal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.prod
CommSemiring.toCommMonoid
Finset
Finset.instMembership
prod_le
prod_mem_iff_exists_mem 📖mathematicalIdeal
CommSemiring.toSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Finset.prod
CommSemiring.toCommMonoid
Finset
Finset.instMembership
Finset.prod_eq_multiset_prod
Multiset.map_id'
multiset_prod_mem_iff_exists_mem
radical 📖mathematicalIdeal.radicalIdeal.IsRadical.radical
isRadical
radical_le_iff 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.radical
Ideal.IsRadical.radical_le_iff
isRadical

Ideal.IsRadical

Theorems

NameKindAssumesProvesValidatesDepends On
inf 📖mathematicalIdeal.IsRadicalIdeal
CommSemiring.toSemiring
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
eq_1
Ideal.radical_inf
inf_le_inf
radical 📖mathematicalIdeal.IsRadicalIdeal.radicalIdeal.radical_eq_iff
radical_le_iff 📖mathematicalIdeal.IsRadicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.radical
le_trans
Ideal.le_radical
Ideal.radical_mono
radical

Ideal.IsTwoSided

Theorems

NameKindAssumesProvesValidatesDepends On
instHMul 📖mathematicalIdeal.IsTwoSided
Ideal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
IsScalarTower.left
Submodule.mul_induction_on
mul_assoc
Ideal.mul_mem_mul
Ideal.mul_mem_right
right_distrib
Distrib.rightDistribClass
AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
Submodule.addSubmonoidClass
instHPowNat 📖mathematicalIdeal.IsTwoSided
Ideal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
IsScalarTower.left
Submodule.pow_zero
Ideal.one_eq_top
Ideal.instIsTwoSidedTop
Submodule.pow_succ
instHMul
mul_one 📖mathematicalIdeal
Submodule.mul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Submodule.one
LE.le.antisymm
IsScalarTower.left
Ideal.mul_le_right
Ideal.mul_mem_mul
Submodule.mem_top
Ideal.one_eq_top
mul_one
pow_add 📖mathematicalIdeal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Submodule.mul
IsScalarTower.left
eq_or_ne
add_zero
Submodule.pow_zero
mul_one
instHPowNat
Submodule.pow_add
pow_succ 📖mathematicalIdeal
Submodule.instPowNat
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Submodule.mul
IsScalarTower.left
add_comm
pow_add
Submodule.pow_one

IsCoprime

Theorems

NameKindAssumesProvesValidatesDepends On
add_eq 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Submodule.pointwiseAdd
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.one
Ideal.isCoprime_iff_add
codisjoint 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
Codisjoint
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instOrderTop
Ideal.isCoprime_iff_codisjoint
exists 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Ideal.isCoprime_iff_exists
sup_eq 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
IdemCommSemiring.toCommSemiring
Submodule.instIdemCommSemiring
Algebra.id
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Top.top
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.isCoprime_iff_sup_eq

Submodule

Definitions

NameCategoryTheorems
algebraIdeal 📖CompOp
3 mathmath: coe_mapAlgEquiv_symm_apply, coe_mapAlgEquiv_apply, coe_mapAlgHom_apply
mapAlgEquiv 📖CompOp
2 mathmath: coe_mapAlgEquiv_symm_apply, coe_mapAlgEquiv_apply
mapAlgHom 📖CompOp
1 mathmath: coe_mapAlgHom_apply
moduleSubmodule 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
coe_mapAlgEquiv_apply 📖mathematicalSetLike.coe
Submodule
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Algebra.toModule
setLike
DFunLike.coe
AlgEquiv
Ideal
IdemCommSemiring.toCommSemiring
Ideal.instIdemCommSemiring
IdemSemiring.toSemiring
idemSemiring
algebraIdeal
AlgEquiv.instFunLike
mapAlgEquiv
Set.image
Set.image_congr
coe_mapAlgEquiv_symm_apply 📖mathematicalSetLike.coe
Submodule
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Algebra.toModule
setLike
DFunLike.coe
AlgEquiv
Ideal
IdemCommSemiring.toCommSemiring
Ideal.instIdemCommSemiring
IdemSemiring.toSemiring
idemSemiring
algebraIdeal
AlgEquiv.instFunLike
AlgEquiv.symm
mapAlgEquiv
Set.image
Set.image_congr
coe_mapAlgHom_apply 📖mathematicalSetLike.coe
Submodule
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Algebra.toModule
setLike
DFunLike.coe
AlgHom
Ideal
IdemCommSemiring.toCommSemiring
Ideal.instIdemCommSemiring
IdemSemiring.toSemiring
idemSemiring
algebraIdeal
AlgHom.funLike
mapAlgHom
Set.image
coe_span_smul 📖mathematicalSet
Submodule
CommSemiring.toSemiring
pointwiseSetSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
SetLike.coe
Ideal
setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.span
set_smul_eq_of_le
span_induction
mem_set_smul_of_mem_mem
zero_smul
zero_mem
add_smul
add_mem
mem_span_set
Finsupp.sum.eq_1
Finset.smul_sum
Finset.sum_smul
sum_mem
SemigroupAction.mul_smul
smul_eq_mul
mul_comm
smul_mem
set_smul_mono_left
subset_span
comap_smul'' 📖mathematicalDFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
LinearMap.instFunLike
Submodule
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
LinearMap.range
RingHomSurjective.ids
comap
Ideal
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
RingHomSurjective.ids
le_antisymm
IsScalarTower.left
map_comap_eq_self
map_smul''
comap_map_eq_of_injective
le_refl
ideal_span_singleton_smul 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Ideal.span
Set
Set.instSingletonSet
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
pointwiseAddCommMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
pointwiseDistribMulAction
smulCommClass_self
CommSemiring.toCommMonoid
CommMonoid.toMonoid
IsScalarTower.left
smulCommClass_self
span_eq
span_smul_span
Ideal.instIsTwoSided
Set.singleton_smul
map_le_smul_top 📖mathematicalSubmodule
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
map
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.id
RingHomSurjective.ids
Ideal
instSMul
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Top.top
instTop
RingHomSurjective.ids
IsScalarTower.left
mul_one
smul_eq_mul
LinearMap.map_smul
smul_mem_smul
mem_top
map_pointwise_smul 📖mathematicalmap
CommSemiring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
RingHomSurjective.ids
Submodule
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
pointwiseAddCommMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
pointwiseDistribMulAction
Module.toDistribMulAction
smulCommClass_self
CommSemiring.toCommMonoid
DistribMulAction.toMulAction
CommMonoid.toMonoid
RingHomSurjective.ids
smulCommClass_self
IsScalarTower.left
map.congr_simp
map_smul''
map_smul'' 📖mathematicalmap
RingHom.id
Semiring.toNonAssocSemiring
RingHomSurjective.ids
Ideal
Submodule
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
le_antisymm
RingHomSurjective.ids
IsScalarTower.left
map_le_iff_le_comap
smul_le
smul_mem_smul
mem_map_of_mem
LinearMap.map_smul
mem_map
mem_ideal_smul_span_iff_exists_sum 📖mathematicalSubmodule
SetLike.instMembership
setLike
Ideal
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
span
Set.range
Finsupp.sum
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
IsScalarTower.left
span_induction
Finsupp.single_apply
Ideal.zero_mem
Finsupp.sum_single_index
zero_smul
Finsupp.sum_zero_index
Ideal.add_mem
Finsupp.sum_add_index'
add_smul
Ideal.mul_mem_left
Finsupp.sum_smul_index
Finsupp.smul_sum
SemigroupAction.mul_smul
mem_smul_span
sum_mem
smul_mem_smul
subset_span
Set.mem_range_self
mem_ideal_smul_span_iff_exists_sum' 📖mathematicalSubmodule
SetLike.instMembership
setLike
Ideal
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
span
Set.image
Finsupp.sum
Set.Elem
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Set
Set.instMembership
IsScalarTower.left
mem_ideal_smul_span_iff_exists_sum
Set.image_eq_range
mem_of_span_eq_top_of_smul_pow_mem 📖Ideal.span
CommSemiring.toSemiring
Top.top
Ideal
instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule
SetLike.instMembership
setLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Monoid.toNatPow
Set
Set.instMembership
mem_of_span_top_of_smul_mem
Ideal.span_range_pow_eq_top
mem_of_span_top_of_smul_mem 📖Ideal.span
Top.top
Ideal
instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule
SetLike.instMembership
setLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.instMembership
RingHomSurjective.ids
LinearMap.range_eq_map
map_le_iff_le_comap
Ideal.span.eq_1
span_le
LinearMap.toSpanSingleton_apply_one
LinearMap.mem_range_self
mem_smul_span 📖mathematicalSubmodule
SetLike.instMembership
setLike
Ideal
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
span
Set
Set.smul
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
SetLike.coe
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
IsScalarTower.left
Ideal.span_eq
span_smul_span
mem_smul_span_singleton 📖mathematicalSubmodule
SetLike.instMembership
setLike
Ideal
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
span
Set
Set.instSingletonSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
IsScalarTower.left
smul_induction_on
mem_span_singleton
Ideal.mul_mem_right
SemigroupAction.mul_smul
Ideal.add_mem
add_smul
smul_mem_smul
subset_span
Set.mem_singleton
mem_smul_top_iff 📖mathematicalSubmodule
SetLike.instMembership
setLike
addCommMonoid
module
Ideal
instSMul
Semiring.toModule
isScalarTower'
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribSMul.toSMulZeroClass
instDistribSMul
NonAssocSemiring.toNonUnitalNonAssocSemiring
SemigroupAction.toSMul
Monoid.toSemigroup
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulAction.toSemigroupAction
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
DistribMulAction.toDistribSMul
NonUnitalNonAssocSemiring.toAddCommMonoid
IsScalarTower.left
Top.top
instTop
RingHomSurjective.ids
isScalarTower'
IsScalarTower.left
map_smul''
map_top
range_subtype
mul_smul 📖mathematicalIdeal
Submodule
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
mul
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
smul_assoc
IsScalarTower.left
set_smul_top_eq_span 📖mathematicalSet
Ideal
CommSemiring.toSemiring
pointwiseSetSMul
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Top.top
instTop
Ideal.span
IsScalarTower.left
span_smul_eq
Ideal.mul_top
Ideal.instIsTwoSided
smul_comap_le_comap_smul 📖mathematicalSubmodule
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Ideal
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
comap
RingHom.id
Semiring.toNonAssocSemiring
IsScalarTower.left
smul_le
mem_comap
LinearMap.map_smul
smul_mem_smul
smul_eq_map₂ 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
map₂
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
LinearMap.lsmul
le_antisymm
IsScalarTower.left
smul_le
apply_mem_map₂
smulCommClass_self
map₂_le
smul_mem_smul
smul_le_right 📖mathematicalSubmodule
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Ideal
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
IsScalarTower.left
smul_le
smul_mem
smul_le_span 📖mathematicalIdeal
CommSemiring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Set
pointwiseSetSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Ideal.span
instCovariantClassSetHSMulLe
span_singleton_toAddSubgroup_eq_zmultiples 📖mathematicaltoAddSubgroup
Int.instRing
Int.instAddCommGroup
AddCommGroup.toIntModule
span
Int.instSemiring
Int.instAddCommMonoid
Set
Set.instSingletonSet
AddSubgroup.zmultiples
Int.instAddGroup
AddSubgroup.ext
span_smul_eq 📖mathematicalIdeal
CommSemiring.toSemiring
Submodule
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Ideal.span
Set
pointwiseSetSMul
IsScalarTower.left
coe_set_smul
coe_span_smul
span_smul_span 📖mathematicalIdeal
Submodule
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Ideal.span
span
Set
Set.smul
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
le_antisymm
IsScalarTower.left
smul_le
span_induction
subset_span
zero_smul
ZeroMemClass.zero_mem
AddSubmonoidClass.toZeroMemClass
addSubmonoidClass
add_smul
AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
smul_assoc
smul_mem
smul_zero
smul_add
SemigroupAction.mul_smul
Ideal.mul_mem_right
span_le
smul_mem_smul
top_smul 📖mathematicalIdeal
Submodule
instSMul
Semiring.toModule
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Top.top
instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
le_antisymm
IsScalarTower.left
smul_le_right
smul_mem_smul
mem_top
one_smul

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
instNonUnitalSubringClassIdeal 📖mathematicalNonUnitalSubringClass
Ideal
Ring.toSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
instNonUnitalSubsemiringClassIdeal
AddSubgroupClass.toNegMemClass
Submodule.addSubgroupClass
instNonUnitalSubsemiringClassIdeal 📖mathematicalNonUnitalSubsemiringClass
Ideal
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
Semiring.toModule
Submodule.addSubmonoidClass
Ideal.mul_mem_left

---

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