Documentation Verification Report

Basic

πŸ“ Source: Mathlib/Algebra/GCDMonoid/Basic.lean

Statistics

MetricCount
DefinitionsinstGCDMonoid, out, instNormalizedGCDMonoid, gcd, lcm, NormalizationMonoid, normUnit, ofUniqueUnits, NormalizedGCDMonoid, toGCDMonoid, toNormalizationMonoid, associatesEquivOfUniqueUnits, gcdMonoidOfExistsGCD, gcdMonoidOfExistsLCM, gcdMonoidOfGCD, gcdMonoidOfLCM, normalizationMonoidOfMonoidHomRightInverse, normalize, normalizedGCDMonoidOfExistsGCD, normalizedGCDMonoidOfExistsLCM, normalizedGCDMonoidOfGCD, normalizedGCDMonoidOfLCM, uniqueNormalizationMonoidOfUniqueUnits
23
Theoremseq_of_normalized, gcd, gcd_eq_left, gcd_eq_right, lcm, dvd_out_iff, gcd_mk_mk, lcm_mk_mk, mk_normalize, mk_out, normalize_out, out_dvd_iff, out_eq_zero_iff, out_injective, out_mk, out_mul, out_one, out_top, out_zero, coe_normUnit, normalize_eq_one, lcm_left, lcm_right, dvd_gcd, gcd_dvd_left, gcd_dvd_right, gcd_mul_lcm, lcm_zero_left, lcm_zero_right, toIsCancelMulZero, gcd_eq_one_iff, isUnit_gcd_iff, normUnit_coe_units, normUnit_mul, normUnit_zero, normalize_gcd, normalize_lcm, dvd_lcm, dvd_or_dvd_of_dvd_lcm, not_dvd_lcm, associated_gcd_left_iff, associated_gcd_right_iff, associated_normalize, associated_normalize_iff, associatesEquivOfUniqueUnits_apply, associatesEquivOfUniqueUnits_symm_apply, dvd_antisymm_of_normalize_eq, dvd_gcd_iff, dvd_gcd_mul_iff_dvd_mul, dvd_gcd_mul_of_dvd_mul, dvd_lcm_left, dvd_lcm_of_dvd_left, dvd_lcm_of_dvd_right, dvd_lcm_right, dvd_mul_gcd_iff_dvd_mul, dvd_mul_gcd_of_dvd_mul, dvd_normalize_iff, dvd_of_lcm_left_dvd, dvd_of_lcm_right_dvd, exists_associated_pow_of_mul_eq_pow, exists_eq_pow_of_mul_eq_pow, extract_gcd, gcd_assoc, gcd_assoc', gcd_comm, gcd_comm', gcd_dvd_gcd, gcd_dvd_gcd_mul_left, gcd_dvd_gcd_mul_left_right, gcd_dvd_gcd_mul_right, gcd_dvd_gcd_mul_right_right, gcd_eq_left_iff, gcd_eq_normalize, gcd_eq_of_dvd_sub_left, gcd_eq_of_dvd_sub_right, gcd_eq_right_iff, gcd_eq_zero_iff, gcd_greatest, gcd_greatest_associated, gcd_isUnit_iff_isRelPrime, gcd_mul_dvd_mul_gcd, gcd_mul_lcm, gcd_mul_left, gcd_mul_left', gcd_mul_right, gcd_mul_right', gcd_ne_zero_of_left, gcd_ne_zero_of_right, gcd_neg, gcd_neg', gcd_one_left, gcd_one_left', gcd_one_right, gcd_one_right', gcd_pow_left_dvd_pow_gcd, gcd_pow_right_dvd_pow_gcd, gcd_same, gcd_zero_left, gcd_zero_left', gcd_zero_right, gcd_zero_right', instAssociativeGcd, instAssociativeLcm, instCommutativeGcd, instCommutativeLcm, instDecompositionMonoidOfNonemptyGCDMonoid, instNonemptyGCDMonoid, instNonemptyGCDMonoidOfNormalizedGCDMonoid, instNonemptyNormalizationMonoid, instNonemptyNormalizationMonoidOfNormalizedGCDMonoid, instNonemptyNormalizedGCDMonoid, isUnit_gcd_of_eq_mul_gcd, isUnit_gcd_one_left, isUnit_gcd_one_right, lcm_assoc, lcm_assoc', lcm_comm, lcm_comm', lcm_dvd, lcm_dvd_iff, lcm_dvd_lcm, lcm_dvd_lcm_mul_left, lcm_dvd_lcm_mul_left_right, lcm_dvd_lcm_mul_right, lcm_dvd_lcm_mul_right_right, lcm_dvd_mul, lcm_eq_left_iff, lcm_eq_normalize, lcm_eq_of_associated_left, lcm_eq_of_associated_right, lcm_eq_one_iff, lcm_eq_right_iff, lcm_eq_zero_iff, lcm_mul_left, lcm_mul_right, lcm_one_left, lcm_one_right, lcm_same, lcm_units_coe_left, lcm_units_coe_right, neg_gcd, neg_gcd', normUnit_eq_one, normUnit_mul_normUnit, normUnit_one, normalize_apply, normalize_associated, normalize_associated_iff, normalize_coe_units, normalize_dvd_iff, normalize_eq, normalize_eq_normalize, normalize_eq_normalize_iff, normalize_eq_normalize_iff_associated, normalize_eq_one, normalize_eq_zero, normalize_gcd, normalize_idem, normalize_lcm, normalize_one, normalize_zero, pow_dvd_of_mul_eq_pow, subsingleton_gcdMonoid_of_unique_units, subsingleton_normalizedGCDMonoid_of_unique_units
164
Total187

Associated

Theorems

NameKindAssumesProvesValidatesDepends On
eq_of_normalized πŸ“–β€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”β€”dvd_antisymm_of_normalize_eq
dvd
dvd'
gcd πŸ“–mathematicalAssociated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcdβ€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
gcd_dvd_gcd
dvd
dvd'
gcd_eq_left πŸ“–mathematicalAssociated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
gcd_dvd_gcd
dvd
dvd_rfl
symm
gcd_eq_right πŸ“–mathematicalAssociated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
gcd_dvd_gcd
dvd_rfl
dvd
symm
lcm πŸ“–mathematicalAssociated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
lcm_dvd_lcm
dvd
dvd'

Associates

Definitions

NameCategoryTheorems
instGCDMonoid πŸ“–CompOp
2 mathmath: lcm_mk_mk, gcd_mk_mk
out πŸ“–CompOp
12 mathmath: mk_out, out_one, out_dvd_iff, out_mk, normalize_out, out_eq_zero_iff, out_zero, associatesEquivOfUniqueUnits_apply, out_mul, dvd_out_iff, out_injective, out_top

Theorems

NameKindAssumesProvesValidatesDepends On
dvd_out_iff πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
out
Associates
MonoidWithZero.toMonoid
Preorder.toLE
instPreorder
CommMonoidWithZero.toCommMonoid
β€”β€”
gcd_mk_mk πŸ“–mathematicalβ€”GCDMonoid.gcd
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
instCommMonoidWithZero
instGCDMonoid
β€”β€”
lcm_mk_mk πŸ“–mathematicalβ€”GCDMonoid.lcm
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
instCommMonoidWithZero
instGCDMonoid
β€”β€”
mk_normalize πŸ“–mathematicalβ€”MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”mk_eq_mk_iff_associated
normalize_associated
mk_out πŸ“–mathematicalβ€”MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
out
β€”mk_normalize
normalize_out πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
out
β€”normalize_idem
out_dvd_iff πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
out
Associates
MonoidWithZero.toMonoid
Preorder.toLE
instPreorder
CommMonoidWithZero.toCommMonoid
β€”β€”
out_eq_zero_iff πŸ“–mathematicalβ€”out
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
Associates
MonoidWithZero.toMonoid
instZero
β€”β€”
out_injective πŸ“–mathematicalβ€”Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
out
β€”mk_out
out_mk πŸ“–mathematicalβ€”out
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”β€”
out_mul πŸ“–mathematicalβ€”out
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
instMul
CommMonoidWithZero.toCommMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”MonoidWithZeroHom.map_mul
out_one πŸ“–mathematicalβ€”out
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
instOne
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
β€”normalize_one
out_top πŸ“–mathematicalβ€”out
Top.top
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
instTopOfZero
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”normalize_zero
out_zero πŸ“–mathematicalβ€”out
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
instZero
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”β€”

CommGroupWithZero

Definitions

NameCategoryTheorems
instNormalizedGCDMonoid πŸ“–CompOp
24 mathmath: Polynomial.degree_normalize, Polynomial.coe_normUnit_of_ne_zero, coe_normUnit, RatFunc.num_div, Polynomial.abc, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, RatFunc.numDenom_div, PowerSeries.normalized_count_X_eq_of_coe, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, natDegree_radical_le, RatFunc.denom_div, divRadical_dvd_wronskian_right, Polynomial.normalize_eq_self_iff_monic, RatFunc.num_div_dvd', Polynomial.mem_normalizedFactors_iff, normalize_eq_one, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, divRadical_dvd_wronskian_left, Polynomial.monic_normalize, Polynomial.normalizedFactors_cyclotomic_card, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Polynomial.map_normalize, degree_radical_le

Theorems

NameKindAssumesProvesValidatesDepends On
coe_normUnit πŸ“–mathematicalβ€”Units.val
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
toCommMonoidWithZero
NormalizationMonoid.normUnit
NormalizedGCDMonoid.toNormalizationMonoid
instNormalizedGCDMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
toDivisionCommMonoid
β€”Units.val_inv_eq_inv_val
normalize_eq_one πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
toCommMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
instNormalizedGCDMonoid
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
toDivisionCommMonoid
β€”coe_normUnit
mul_inv_cancelβ‚€

Dvd.dvd

Theorems

NameKindAssumesProvesValidatesDepends On
lcm_left πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”dvd_lcm_of_dvd_right
lcm_right πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”dvd_lcm_of_dvd_left

GCDMonoid

Definitions

NameCategoryTheorems
gcd πŸ“–CompOp
101 mathmath: gcd_one_left', RatFunc.num_div, Ideal.absNorm_span_insert, gcd_dvd_gcd_mul_right, gcd_mul_lcm, gcd_mul_left, gcd_greatest, Polynomial.degree_gcd_le_left, Associated.gcd_eq_left, gcd_mul_lcm, Associated.gcd_eq_right, gcd_assoc', gcd_dvd_gcd_mul_left_right, gcd_zero_right', Ideal.gcd_eq_sup, span_gcd, gcd_mul_right', Ideal.isCoprime_iff_gcd, gcd_assoc, Squarefree.gcd_right, RatFunc.numDenom_div, isUnit_gcd_one_right, dvd_mul_sub_mul_mul_gcd_of_dvd, Multiset.gcd_ndunion, gcd_eq_zero_iff, Squarefree.gcd_left, dvd_mul_gcd_of_dvd_mul, gcd_eq_nat_gcd, Irreducible.isUnit_gcd_iff, Polynomial.gcd_content_eq_of_dvd_sub, gcd_one_left, dvd_gcd, Multiset.gcd_ndinsert, NormalizedGCDMonoid.normalize_gcd, normalize_gcd, Polynomial.content_mul_aux, dvd_mul_gcd_iff_dvd_mul, isCoprime_div_gcd_div_gcd, exists_gcd_eq_mul_add_mul, gcd_eq_of_dvd_sub_left, extract_gcd, gcd_one_right, gcd_mul_dvd_mul_gcd, gcd_comm, UnitAddCircle.mem_approxAddOrderOf_iff, gcd_same, gcd_zero_right, gcd_neg', Finset.gcd_union, Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd, RatFunc.denom_div, gcd_eq_of_dvd_sub_right, gcd_mul_left', Int.coe_gcd, IsBezout.associated_gcd_gcd, gcd_isUnit_iff, Multiset.gcd_add, Finset.gcd_insert, Finset.gcd_eq_of_dvd_sub, IsLocalization.surj_of_gcd_domain, Int.natAbs_gcd, gcd_dvd_gcd_mul_right_right, gcd_zero_left, PUnit.gcd_eq, instCommutativeGcd, RatFunc.num_div_dvd', gcd_one_right', gcd_mul_right, gcd_pow_left_dvd_pow_gcd, gcd_isUnit_iff_isRelPrime, isUnit_gcd_one_left, associated_gcd_right_iff, associated_gcd_left_iff, neg_gcd, UnitAddCircle.mem_addWellApproximable_iff, Multiset.gcd_union, gcd_comm', gcd_dvd_left, dvd_gcd_mul_of_dvd_mul, gcd_eq_left_iff, Polynomial.content_eq_gcd_leadingCoeff_content_eraseLead, gcd_dvd_right, instAssociativeGcd, IsBezout.span_gcd_eq_span_gcd, gcd_greatest_associated, gcd_pow_right_dvd_pow_gcd, dvd_gcd_mul_iff_dvd_mul, Irreducible.gcd_eq_one_iff, neg_gcd', isCoprime_div_gcd_div_gcd_of_gcd_ne_zero, Multiset.gcd_cons, gcd_neg, gcd_zero_left', gcd_dvd_gcd_mul_left, Associates.gcd_mk_mk, gcd_dvd_iff_exists, Associated.gcd, gcd_eq_right_iff, gcd_dvd_gcd, Polynomial.degree_gcd_le_right, dvd_gcd_iff
lcm πŸ“–CompOp
60 mathmath: lcm_zero_right, lcm_dvd_lcm_mul_right, lcm_eq_zero_iff, gcd_mul_lcm, Multiset.lcm_add, gcd_mul_lcm, DihedralGroup.exponent, NormalizedGCDMonoid.normalize_lcm, Dvd.dvd.lcm_left, dvd_lcm_right, lcm_dvd, instCommutativeLcm, Associates.lcm_mk_mk, lcm_eq_left_iff, lcm_mul_left, lcm_comm', dvd_lcm_of_dvd_left, instAssociativeLcm, lcm_dvd_mul, AddMonoid.exponent_prod, lcm_mul_right, lcm_eq_of_associated_right, PUnit.lcm_eq, lcm_assoc', Multiset.lcm_cons, lcm_eq_of_associated_left, dvd_lcm_left, Associated.lcm, lcm_dvd_iff, lcm_dvd_lcm_mul_right_right, Multiset.lcm_union, lcm_one_left, lcm_eq_right_iff, lcm_dvd_lcm_mul_left, normalize_lcm, lcm_same, Multiset.lcm_ndunion, Monoid.exponent_prod, lcm_zero_left, Dvd.dvd.lcm_right, lcm_units_coe_left, lcm_eq_nat_lcm, span_singleton_inf_span_singleton, lcm_comm, dvd_lcm_of_dvd_right, Multiset.lcm_ndinsert, Prime.not_dvd_lcm, lcm_dvd_lcm, lcm_assoc, Int.coe_lcm, Ideal.lcm_eq_inf, Finset.lcm_union, Int.natAbs_lcm, lcm_dvd_lcm_mul_left_right, Finset.lcm_insert, lcm_units_coe_right, QuaternionGroup.exponent, lcm_eq_one_iff, Prime.dvd_lcm, lcm_one_right

Theorems

NameKindAssumesProvesValidatesDepends On
dvd_gcd πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
gcdβ€”β€”
gcd_dvd_left πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
gcd
β€”β€”
gcd_dvd_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
gcd
β€”β€”
gcd_mul_lcm πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
gcd
lcm
β€”β€”
lcm_zero_left πŸ“–mathematicalβ€”lcm
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”β€”
lcm_zero_right πŸ“–mathematicalβ€”lcm
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”β€”
toIsCancelMulZero πŸ“–mathematicalβ€”IsCancelMulZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toZero
β€”β€”

Irreducible

Theorems

NameKindAssumesProvesValidatesDepends On
gcd_eq_one_iff πŸ“–mathematicalIrreducible
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”isUnit_gcd_iff
normalize_eq_one
NormalizedGCDMonoid.normalize_gcd
isUnit_gcd_iff πŸ“–mathematicalIrreducible
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
IsUnit
GCDMonoid.gcd
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”isUnit_iff_not_associated_of_dvd
GCDMonoid.gcd_dvd_left
not_iff_not
associated_gcd_left_iff

NormalizationMonoid

Definitions

NameCategoryTheorems
normUnit πŸ“–CompOp
15 mathmath: Polynomial.coe_normUnit_of_ne_zero, CommGroupWithZero.coe_normUnit, normUnit_eq_one, PUnit.norm_unit_eq, normUnit_mul_normUnit, Int.normUnit_eq, Polynomial.normUnit_content, normUnit_coe_units, PowerSeries.normUnit_X, normUnit_zero, normalize_apply, Polynomial.coe_normUnit, normUnit_mul, normUnit_one, Polynomial.normUnit_X
ofUniqueUnits πŸ“–CompOp
14 mathmath: UniqueFactorizationMonoid.factors_eq_normalizedFactors, normUnit_eq_one, Nat.factors_multiset_prod_of_irreducible, Nat.two_le_radical_iff, Nat.radical_pos, Nat.factors_eq, Nat.radical_le_self_iff, Nat.sum_divisors_filter_squarefree, associatesEquivOfUniqueUnits_apply, UniqueFactorizationMonoid.primeFactors_eq_natPrimeFactors, Nat.one_lt_radical_iff, Nat.divisors_filter_squarefree, Nat.radical_le_one_iff, normalize_eq

Theorems

NameKindAssumesProvesValidatesDepends On
normUnit_coe_units πŸ“–mathematicalβ€”normUnit
Units.val
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
Units
Units.instInv
β€”β€”
normUnit_mul πŸ“–mathematicalβ€”normUnit
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
Units
MonoidWithZero.toMonoid
Units.instMul
β€”β€”
normUnit_zero πŸ“–mathematicalβ€”normUnit
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
Units
MonoidWithZero.toMonoid
Units.instOne
β€”β€”

NormalizedGCDMonoid

Definitions

NameCategoryTheorems
toGCDMonoid πŸ“–CompOp
70 mathmath: RatFunc.num_div, gcd_mul_left, gcd_greatest, Multiset.lcm_add, Polynomial.degree_gcd_le_left, Associated.gcd_eq_left, normalize_lcm, Associated.gcd_eq_right, Ideal.gcd_eq_sup, Ideal.isCoprime_iff_gcd, instCommutativeLcm, gcd_assoc, lcm_eq_left_iff, RatFunc.numDenom_div, lcm_mul_left, Multiset.gcd_ndunion, instAssociativeLcm, Polynomial.gcd_content_eq_of_dvd_sub, gcd_one_left, lcm_mul_right, Multiset.gcd_ndinsert, normalize_gcd, normalize_gcd, Polynomial.content_mul_aux, lcm_eq_of_associated_right, PUnit.lcm_eq, Multiset.lcm_cons, gcd_eq_of_dvd_sub_left, lcm_eq_of_associated_left, gcd_one_right, gcd_comm, gcd_same, Multiset.lcm_union, gcd_zero_right, lcm_one_left, lcm_eq_right_iff, Finset.gcd_union, RatFunc.denom_div, gcd_eq_of_dvd_sub_right, normalize_lcm, lcm_same, Multiset.lcm_ndunion, Multiset.gcd_add, Finset.gcd_insert, Finset.gcd_eq_of_dvd_sub, lcm_units_coe_left, gcd_zero_left, PUnit.gcd_eq, instCommutativeGcd, RatFunc.num_div_dvd', lcm_comm, gcd_mul_right, Multiset.lcm_ndinsert, neg_gcd, lcm_assoc, Multiset.gcd_union, Ideal.lcm_eq_inf, Finset.lcm_union, gcd_eq_left_iff, Polynomial.content_eq_gcd_leadingCoeff_content_eraseLead, Finset.lcm_insert, instAssociativeGcd, lcm_units_coe_right, Irreducible.gcd_eq_one_iff, Multiset.gcd_cons, gcd_neg, lcm_eq_one_iff, gcd_eq_right_iff, lcm_one_right, Polynomial.degree_gcd_le_right
toNormalizationMonoid πŸ“–CompOp
56 mathmath: Polynomial.degree_normalize, Polynomial.coe_normUnit_of_ne_zero, CommGroupWithZero.coe_normUnit, PUnit.norm_unit_eq, gcd_mul_left, gcd_greatest, Polynomial.abc, normalize_lcm, Multiset.lcm_singleton, Polynomial.normUnit_content, Finset.lcm_singleton, gcd_eq_normalize, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, lcm_mul_left, Finset.gcd_mul_left, Finset.normalize_lcm, PowerSeries.normalized_count_X_eq_of_coe, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, Multiset.gcd_singleton, Polynomial.content_C_mul, lcm_mul_right, Polynomial.normalize_content, normalize_gcd, normalize_gcd, gcd_same, natDegree_radical_le, gcd_zero_right, lcm_one_left, divRadical_dvd_wronskian_right, Finset.gcd_singleton, normalize_lcm, lcm_same, Polynomial.normalize_eq_self_iff_monic, lcm_units_coe_left, gcd_zero_left, Polynomial.mem_normalizedFactors_iff, gcd_mul_right, Multiset.normalize_lcm, CommGroupWithZero.normalize_eq_one, Finset.gcd_mul_right, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, divRadical_dvd_wronskian_left, Polynomial.content_C, lcm_units_coe_right, Multiset.normalize_gcd, Polynomial.monic_normalize, Multiset.gcd_map_mul, Finset.normalize_gcd, lcm_eq_normalize, Polynomial.normalizedFactors_cyclotomic_card, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Polynomial.content_monomial, Polynomial.map_normalize, lcm_one_right, degree_radical_le

Theorems

NameKindAssumesProvesValidatesDepends On
normalize_gcd πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
toNormalizationMonoid
GCDMonoid.gcd
toGCDMonoid
β€”β€”
normalize_lcm πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
toNormalizationMonoid
GCDMonoid.lcm
toGCDMonoid
β€”β€”

Prime

Theorems

NameKindAssumesProvesValidatesDepends On
dvd_lcm πŸ“–mathematicalPrimesemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”dvd_or_dvd_of_dvd_lcm
dvd_lcm_of_dvd_left
dvd_lcm_of_dvd_right
dvd_or_dvd_of_dvd_lcm πŸ“–β€”Prime
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”β€”dvd_or_dvd
Dvd.dvd.trans
lcm_dvd_mul
not_dvd_lcm πŸ“–mathematicalPrime
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”Iff.not
dvd_lcm

(root)

Definitions

NameCategoryTheorems
NormalizationMonoid πŸ“–CompData
2 mathmath: instNonemptyNormalizationMonoid, instNonemptyNormalizationMonoidOfNormalizedGCDMonoid
NormalizedGCDMonoid πŸ“–CompData
3 mathmath: instNonemptyNormalizedGCDMonoidOfUniqueFactorizationMonoid, instNonemptyNormalizedGCDMonoid, subsingleton_normalizedGCDMonoid_of_unique_units
associatesEquivOfUniqueUnits πŸ“–CompOp
4 mathmath: associatesEquivOfUniqueUnits_symm_apply, mkFactorOrderIsoOfFactorDvdEquiv_apply_coe, associatesEquivOfUniqueUnits_apply, mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe
gcdMonoidOfExistsGCD πŸ“–CompOpβ€”
gcdMonoidOfExistsLCM πŸ“–CompOpβ€”
gcdMonoidOfGCD πŸ“–CompOpβ€”
gcdMonoidOfLCM πŸ“–CompOpβ€”
normalizationMonoidOfMonoidHomRightInverse πŸ“–CompOpβ€”
normalize πŸ“–CompOp
81 mathmath: normalize_one, Polynomial.degree_normalize, Polynomial.roots_normalize, normalize_dvd_iff, gcd_mul_left, gcd_greatest, normalize_eq_normalize, NormalizedGCDMonoid.normalize_lcm, Int.normalize_of_nonneg, Multiset.lcm_singleton, Finset.lcm_singleton, Polynomial.Monic.normalize_eq_self, gcd_eq_normalize, UniqueFactorizationMonoid.normalize_normalized_factor, Associates.out_mk, normalize_eq_normalize_iff, Polynomial.leadingCoeff_normalize, lcm_mul_left, Finset.gcd_mul_left, Finset.normalize_lcm, Multiset.gcd_singleton, Associates.normalize_out, UniqueFactorizationMonoid.radical_of_prime, Polynomial.content_C_mul, Int.normalize_coe_nat, normalize_eq_zero, lcm_mul_right, Polynomial.normalize_content, NormalizedGCDMonoid.normalize_gcd, normalize_gcd, normalize_apply, normalize_coe_units, Associates.mk_normalize, gcd_same, gcd_zero_right, lcm_one_left, Int.normalize_of_nonpos, Finset.gcd_singleton, normalize_lcm, lcm_same, Polynomial.normalize_eq_self_iff_monic, Irreducible.normalizedFactors_pow, UniqueFactorizationMonoid.normalizedFactors_irreducible, Int.abs_eq_normalize, lcm_units_coe_left, gcd_zero_left, UniqueFactorizationMonoid.normalizedFactors_prod_eq, UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors, count_span_normalizedFactors_eq, gcd_mul_right, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, dvd_normalize_iff, associated_normalize_iff, Multiset.normalize_lcm, CommGroupWithZero.normalize_eq_one, Finset.gcd_mul_right, UniqueFactorizationMonoid.mem_normalizedFactors_iff', UniqueFactorizationMonoid.normalizedFactors_of_irreducible_pow, Polynomial.content_C, UniqueFactorizationMonoid.prod_normalizedFactors_eq, UniqueFactorizationMonoid.radical_pow_of_prime, normalize_eq_one, lcm_units_coe_right, Multiset.normalize_gcd, normalize_associated, Polynomial.monic_normalize, Multiset.gcd_map_mul, normalize_zero, normalize_idem, Finset.normalize_gcd, lcm_eq_normalize, Int.nonneg_iff_normalize_eq_self, normalize_eq_normalize_iff_associated, PowerSeries.X_eq_normalizeX, normalize_associated_iff, Polynomial.X_eq_normalize, Polynomial.content_monomial, Polynomial.map_normalize, normalize_eq, lcm_one_right, associated_normalize
normalizedGCDMonoidOfExistsGCD πŸ“–CompOpβ€”
normalizedGCDMonoidOfExistsLCM πŸ“–CompOpβ€”
normalizedGCDMonoidOfGCD πŸ“–CompOpβ€”
normalizedGCDMonoidOfLCM πŸ“–CompOpβ€”
uniqueNormalizationMonoidOfUniqueUnits πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
associated_gcd_left_iff πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”Dvd.dvd.trans
Associated.dvd
GCDMonoid.gcd_dvd_right
associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.dvd_gcd
dvd_rfl
GCDMonoid.gcd_dvd_left
associated_gcd_right_iff πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”Dvd.dvd.trans
Associated.dvd
GCDMonoid.gcd_dvd_left
associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.dvd_gcd
dvd_rfl
GCDMonoid.gcd_dvd_right
associated_normalize πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”β€”
associated_normalize_iff πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”Associated.trans
normalize_associated
associated_normalize
associatesEquivOfUniqueUnits_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
Associates.instMul
CommMonoidWithZero.toCommMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
EquivLike.toFunLike
MulEquiv.instEquivLike
associatesEquivOfUniqueUnits
Associates.out
NormalizationMonoid.ofUniqueUnits
β€”β€”
associatesEquivOfUniqueUnits_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Associates
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Associates.instMul
CommMonoidWithZero.toCommMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
associatesEquivOfUniqueUnits
β€”β€”
dvd_antisymm_of_normalize_eq πŸ“–β€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”β€”normalize_eq_normalize
dvd_gcd_iff πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
β€”Dvd.dvd.trans
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
GCDMonoid.dvd_gcd
dvd_gcd_mul_iff_dvd_mul πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GCDMonoid.gcd
β€”Dvd.dvd.trans
mul_dvd_mul
GCDMonoid.gcd_dvd_right
dvd_rfl
dvd_gcd_mul_of_dvd_mul
dvd_gcd_mul_of_dvd_mul πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GCDMonoid.gcdβ€”Dvd.dvd.trans
GCDMonoid.dvd_gcd
dvd_mul_right
Associated.dvd
gcd_mul_right'
dvd_lcm_left πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”lcm_dvd_iff
dvd_refl
dvd_lcm_of_dvd_left πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”Dvd.dvd.trans
dvd_lcm_left
dvd_lcm_of_dvd_right πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”Dvd.dvd.trans
dvd_lcm_right
dvd_lcm_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”lcm_dvd_iff
dvd_refl
dvd_mul_gcd_iff_dvd_mul πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GCDMonoid.gcd
β€”Dvd.dvd.trans
mul_dvd_mul
dvd_rfl
GCDMonoid.gcd_dvd_right
dvd_mul_gcd_of_dvd_mul
dvd_mul_gcd_of_dvd_mul πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GCDMonoid.gcdβ€”mul_comm
dvd_gcd_mul_of_dvd_mul
dvd_normalize_iff πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”Units.dvd_mul_right
dvd_of_lcm_left_dvd πŸ“–β€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”β€”Dvd.dvd.trans
dvd_lcm_right
dvd_of_lcm_right_dvd πŸ“–β€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”β€”Dvd.dvd.trans
dvd_lcm_left
exists_associated_pow_of_mul_eq_pow πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
Associatedβ€”subsingleton_or_nontrivial
Associated.refl
eq_or_ne
MulZeroClass.zero_mul
pow_zero
NeZero.one
zero_pow
one_pow
Associated.trans
Associated.symm
associated_one_iff_isUnit
gcd_zero_right'
instIsDedekindFiniteMonoid
Units.val_mkOfMulEqOne
one_mul
dvd_pow_self
LT.lt.ne'
exists_dvd_and_dvd_of_dvd_mul
instDecompositionMonoidOfNonemptyGCDMonoid
instNonemptyGCDMonoid
pow_dvd_of_mul_eq_pow
Associated.isUnit_iff
gcd_comm'
mul_comm
mul_right_inj'
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
mul_one
mul_pow
mul_assoc
exists_eq_pow_of_mul_eq_pow πŸ“–β€”IsUnit
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
β€”β€”exists_associated_pow_of_mul_eq_pow
associated_iff_eq
extract_gcd πŸ“–mathematicalβ€”MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
IsUnit
MonoidWithZero.toMonoid
β€”gcd_eq_zero_iff
MulZeroClass.zero_mul
gcd_one_left'
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
isUnit_gcd_of_eq_mul_gcd
gcd_assoc πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
GCDMonoid.dvd_gcd
Dvd.dvd.trans
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
gcd_assoc' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
β€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.dvd_gcd
Dvd.dvd.trans
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
gcd_comm πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
GCDMonoid.dvd_gcd
GCDMonoid.gcd_dvd_right
GCDMonoid.gcd_dvd_left
gcd_comm' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
β€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.dvd_gcd
GCDMonoid.gcd_dvd_right
GCDMonoid.gcd_dvd_left
gcd_dvd_gcd πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcdβ€”GCDMonoid.dvd_gcd
Dvd.dvd.trans
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
gcd_dvd_gcd_mul_left πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”Mathlib.Tactic.GCongr.rel_imp_rel
instIsTransDvd
dvd_refl
gcd_dvd_gcd
dvd_mul_left
gcd_dvd_gcd_mul_left_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”Mathlib.Tactic.GCongr.rel_imp_rel
instIsTransDvd
dvd_refl
gcd_dvd_gcd
dvd_mul_left
gcd_dvd_gcd_mul_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”Mathlib.Tactic.GCongr.rel_imp_rel
instIsTransDvd
dvd_refl
gcd_dvd_gcd
dvd_mul_right
gcd_dvd_gcd_mul_right_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”Mathlib.Tactic.GCongr.rel_imp_rel
instIsTransDvd
dvd_refl
gcd_dvd_gcd
dvd_mul_right
gcd_eq_left_iff πŸ“–mathematicalDFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”GCDMonoid.gcd_dvd_right
dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
GCDMonoid.gcd_dvd_left
GCDMonoid.dvd_gcd
dvd_refl
gcd_eq_normalize πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”normalize_eq_normalize
GCDMonoid.toIsCancelMulZero
normalize_gcd
gcd_eq_of_dvd_sub_left πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
CommRing.toNonUnitalCommRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
GCDMonoid.gcd
CommSemiring.toCommMonoidWithZero
CommRing.toCommSemiring
NormalizedGCDMonoid.toGCDMonoid
β€”gcd_comm
gcd_eq_of_dvd_sub_right
gcd_eq_of_dvd_sub_right πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
CommRing.toNonUnitalCommRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
GCDMonoid.gcd
CommSemiring.toCommMonoidWithZero
CommRing.toCommSemiring
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
dvd_gcd_iff
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
mul_sub
mul_assoc
sub_sub_cancel
mul_add
Distrib.leftDistribClass
add_sub_assoc
add_comm
add_sub_cancel_right
gcd_eq_right_iff πŸ“–mathematicalDFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”gcd_comm
gcd_eq_left_iff
gcd_eq_zero_iff πŸ“–mathematicalβ€”GCDMonoid.gcd
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
MulZeroClass.zero_mul
zero_dvd_iff
GCDMonoid.dvd_gcd
dvd_refl
gcd_greatest πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”gcd_eq_normalize
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
GCDMonoid.dvd_gcd
gcd_greatest_associated πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
Associated
MonoidWithZero.toMonoid
GCDMonoid.gcd
β€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.dvd_gcd
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
gcd_isUnit_iff_isRelPrime πŸ“–mathematicalβ€”IsUnit
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
IsRelPrime
β€”isUnit_of_dvd_unit
GCDMonoid.dvd_gcd
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
gcd_mul_dvd_mul_gcd πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”exists_dvd_and_dvd_of_dvd_mul
instDecompositionMonoidOfNonemptyGCDMonoid
instNonemptyGCDMonoid
GCDMonoid.gcd_dvd_right
GCDMonoid.gcd_dvd_left
mul_dvd_mul
Dvd.dvd.trans
dvd_mul_right
GCDMonoid.dvd_gcd
dvd_mul_left
gcd_mul_lcm πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GCDMonoid.gcd
GCDMonoid.lcm
β€”GCDMonoid.gcd_mul_lcm
gcd_mul_left πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”by_cases
MulZeroClass.zero_mul
gcd_zero_left
normalize_zero
GCDMonoid.dvd_gcd
dvd_mul_right
gcd_eq_normalize
mul_dvd_mul_left
mul_dvd_mul_iff_left
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
map_mul
MonoidHomClass.toMulHomClass
MonoidWithZeroHomClass.toMonoidHomClass
MonoidWithZeroHom.monoidWithZeroHomClass
normalize_gcd
gcd_mul_left' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”eq_or_ne
MulZeroClass.zero_mul
GCDMonoid.dvd_gcd
dvd_mul_right
associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
mul_dvd_mul_left
mul_dvd_mul_iff_left
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
gcd_mul_right πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”mul_comm
gcd_mul_left
gcd_mul_right' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”mul_comm
gcd_ne_zero_of_left πŸ“–β€”β€”β€”β€”β€”
gcd_ne_zero_of_right πŸ“–β€”β€”β€”β€”β€”
gcd_neg πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
NegZeroClass.toNeg
MulZeroClass.negZeroClass
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”Associated.eq_of_normalized
GCDMonoid.toIsCancelMulZero
gcd_neg'
normalize_gcd
gcd_neg' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
NegZeroClass.toNeg
MulZeroClass.negZeroClass
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”Associated.gcd
Associated.rfl
Associated.neg_left
gcd_one_left πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
normalize_one
GCDMonoid.gcd_dvd_left
one_dvd
gcd_one_left' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
β€”β€”
gcd_one_right πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_gcd
normalize_one
GCDMonoid.gcd_dvd_right
one_dvd
gcd_one_right' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
β€”β€”
gcd_pow_left_dvd_pow_gcd πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
Monoid.toNatPow
MonoidWithZero.toMonoid
β€”instIsTransDvd
Associated.dvd
gcd_comm'
gcd_pow_right_dvd_pow_gcd
pow_dvd_pow_of_dvd
gcd_pow_right_dvd_pow_gcd πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
Monoid.toNatPow
MonoidWithZero.toMonoid
β€”gcd_eq_zero_iff
Dvd.dvd.trans
Associated.dvd
gcd_zero_left'
pow_dvd_pow_of_dvd
Associated.symm
pow_zero
gcd_one_right'
pow_succ'
instIsTransDvd
gcd_mul_dvd_mul_gcd
mul_dvd_mul_iff_left
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
gcd_same πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”gcd_eq_normalize
GCDMonoid.gcd_dvd_left
GCDMonoid.dvd_gcd
dvd_refl
gcd_zero_left πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”gcd_eq_normalize
GCDMonoid.gcd_dvd_right
GCDMonoid.dvd_gcd
dvd_zero
dvd_refl
gcd_zero_left' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.gcd_dvd_right
GCDMonoid.dvd_gcd
dvd_zero
dvd_refl
gcd_zero_right πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”gcd_eq_normalize
GCDMonoid.gcd_dvd_left
GCDMonoid.dvd_gcd
dvd_refl
dvd_zero
gcd_zero_right' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.gcd_dvd_left
GCDMonoid.dvd_gcd
dvd_refl
dvd_zero
instAssociativeGcd πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
β€”gcd_assoc
instAssociativeLcm πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
β€”lcm_assoc
instCommutativeGcd πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
β€”gcd_comm
instCommutativeLcm πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
β€”lcm_comm
instDecompositionMonoidOfNonemptyGCDMonoid πŸ“–mathematicalβ€”DecompositionMonoid
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
β€”gcd_eq_zero_iff
dvd_refl
MulZeroClass.zero_mul
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
mul_dvd_mul_iff_left
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
dvd_gcd_mul_of_dvd_mul
instNonemptyGCDMonoid πŸ“–mathematicalβ€”GCDMonoidβ€”β€”
instNonemptyGCDMonoidOfNormalizedGCDMonoid πŸ“–mathematicalβ€”GCDMonoidβ€”instNonemptyGCDMonoid
instNonemptyNormalizationMonoid πŸ“–mathematicalβ€”NormalizationMonoidβ€”β€”
instNonemptyNormalizationMonoidOfNormalizedGCDMonoid πŸ“–mathematicalβ€”NormalizationMonoidβ€”instNonemptyNormalizationMonoid
instNonemptyNormalizedGCDMonoid πŸ“–mathematicalβ€”NormalizedGCDMonoidβ€”β€”
isUnit_gcd_of_eq_mul_gcd πŸ“–mathematicalMulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
IsUnit
MonoidWithZero.toMonoid
β€”associated_one_iff_isUnit
Associated.of_mul_left
GCDMonoid.toIsCancelMulZero
mul_one
Associated.symm
gcd_mul_left'
Associated.refl
isUnit_gcd_one_left πŸ“–mathematicalβ€”IsUnit
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
β€”isUnit_of_dvd_one
GCDMonoid.gcd_dvd_left
isUnit_gcd_one_right πŸ“–mathematicalβ€”IsUnit
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
β€”isUnit_of_dvd_one
GCDMonoid.gcd_dvd_right
lcm_assoc πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_lcm
lcm_dvd
dvd_lcm_left
Dvd.dvd.trans
dvd_lcm_right
lcm_assoc' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
lcm_dvd
dvd_lcm_left
Dvd.dvd.trans
dvd_lcm_right
lcm_comm πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_lcm
lcm_dvd
dvd_lcm_right
dvd_lcm_left
lcm_comm' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
lcm_dvd
dvd_lcm_right
dvd_lcm_left
lcm_dvd πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”lcm_dvd_iff
lcm_dvd_iff πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
β€”GCDMonoid.lcm_zero_left
GCDMonoid.lcm_zero_right
gcd_eq_zero_iff
mul_dvd_mul_iff_left
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
Associated.dvd_iff_dvd_left
gcd_mul_lcm
Associated.dvd_iff_dvd_right
gcd_mul_right'
dvd_gcd_iff
mul_comm
mul_dvd_mul_iff_right
lcm_dvd_lcm πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcmβ€”lcm_dvd
Dvd.dvd.trans
dvd_lcm_left
dvd_lcm_right
lcm_dvd_lcm_mul_left πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”lcm_dvd_lcm
dvd_mul_left
dvd_rfl
lcm_dvd_lcm_mul_left_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”lcm_dvd_lcm
dvd_rfl
dvd_mul_left
lcm_dvd_lcm_mul_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”lcm_dvd_lcm
dvd_mul_right
dvd_rfl
lcm_dvd_lcm_mul_right_right πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”lcm_dvd_lcm
dvd_rfl
dvd_mul_right
lcm_dvd_mul πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”lcm_dvd
lcm_eq_left_iff πŸ“–mathematicalDFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”dvd_lcm_right
dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_lcm
lcm_dvd
dvd_refl
dvd_lcm_left
lcm_eq_normalize πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”normalize_eq_normalize
GCDMonoid.toIsCancelMulZero
normalize_lcm
lcm_eq_of_associated_left πŸ“–mathematicalAssociated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_lcm
lcm_dvd_lcm
Associated.dvd
dvd_rfl
Associated.symm
lcm_eq_of_associated_right πŸ“–mathematicalAssociated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
β€”dvd_antisymm_of_normalize_eq
GCDMonoid.toIsCancelMulZero
normalize_lcm
lcm_dvd_lcm
dvd_rfl
Associated.dvd
Associated.symm
lcm_eq_one_iff πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”dvd_lcm_left
dvd_lcm_right
instIsDedekindFiniteMonoid
lcm_units_coe_left
normalize_coe_units
lcm_eq_right_iff πŸ“–mathematicalDFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”lcm_comm
lcm_eq_left_iff
lcm_eq_zero_iff πŸ“–mathematicalβ€”GCDMonoid.lcm
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”Associated.trans
Associated.symm
gcd_mul_lcm
MulZeroClass.mul_zero
Associated.refl
mul_eq_zero
IsRightCancelMulZero.to_noZeroDivisors
IsCancelMulZero.toIsRightCancelMulZero
GCDMonoid.toIsCancelMulZero
associated_zero_iff_eq_zero
GCDMonoid.lcm_zero_left
GCDMonoid.lcm_zero_right
lcm_mul_left πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”by_cases
MulZeroClass.zero_mul
GCDMonoid.lcm_zero_left
normalize_zero
Dvd.dvd.trans
dvd_mul_right
dvd_lcm_left
lcm_eq_normalize
lcm_dvd
mul_dvd_mul_left
dvd_lcm_right
mul_dvd_mul_iff_left
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
map_mul
MonoidHomClass.toMulHomClass
MonoidWithZeroHomClass.toMonoidHomClass
MonoidWithZeroHom.monoidWithZeroHomClass
normalize_lcm
lcm_mul_right πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”mul_comm
lcm_mul_left
lcm_one_left πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”lcm_units_coe_left
lcm_one_right πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”lcm_units_coe_right
lcm_same πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”lcm_eq_normalize
lcm_dvd
dvd_rfl
dvd_lcm_left
lcm_units_coe_left πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
Units.val
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”lcm_eq_normalize
lcm_dvd
Units.coe_dvd
dvd_rfl
dvd_lcm_right
lcm_units_coe_right πŸ“–mathematicalβ€”GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
Units.val
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
β€”lcm_comm
lcm_units_coe_left
neg_gcd πŸ“–mathematicalβ€”GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
NegZeroClass.toNeg
MulZeroClass.negZeroClass
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
β€”Associated.eq_of_normalized
GCDMonoid.toIsCancelMulZero
neg_gcd'
normalize_gcd
neg_gcd' πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
NegZeroClass.toNeg
MulZeroClass.negZeroClass
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
β€”Associated.gcd
Associated.neg_left
Associated.rfl
normUnit_eq_one πŸ“–mathematicalβ€”NormalizationMonoid.normUnit
NormalizationMonoid.ofUniqueUnits
Units
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
Units.instOne
β€”β€”
normUnit_mul_normUnit πŸ“–mathematicalβ€”NormalizationMonoid.normUnit
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
Units.val
MonoidWithZero.toMonoid
Units
Units.instOne
β€”Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
NormalizationMonoid.normUnit_zero
mul_one
eq_or_ne
MulZeroClass.zero_mul
NormalizationMonoid.normUnit_mul
Units.ne_zero
NormalizationMonoid.normUnit_coe_units
mul_inv_eq_one
normUnit_one πŸ“–mathematicalβ€”NormalizationMonoid.normUnit
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
Units
MonoidWithZero.toMonoid
Units.instOne
β€”NormalizationMonoid.normUnit_coe_units
normalize_apply πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
Units.val
MonoidWithZero.toMonoid
NormalizationMonoid.normUnit
β€”β€”
normalize_associated πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”Associated.symm
associated_normalize
normalize_associated_iff πŸ“–mathematicalβ€”Associated
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”Associated.trans
associated_normalize
normalize_associated
normalize_coe_units πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
Units.val
MonoidWithZero.toMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
β€”NormalizationMonoid.normUnit_coe_units
Units.mul_inv
normalize_dvd_iff πŸ“–mathematicalβ€”semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”Units.mul_right_dvd
normalize_eq πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizationMonoid.ofUniqueUnits
β€”mul_one
normalize_eq_normalize πŸ“–mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
CommMonoidWithZero.toMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
normalize
β€”Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
by_cases
MulZeroClass.zero_mul
Units.mul_inv_cancel_right
mul_right_comm
NormalizationMonoid.normUnit_mul
Units.ne_zero
NormalizationMonoid.normUnit_coe_units
mul_assoc
normalize_eq_normalize_iff πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”Units.dvd_mul_right
normalize_eq_normalize
normalize_eq_normalize_iff_associated πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
Associated
MonoidWithZero.toMonoid
β€”normalize_eq_normalize_iff
dvd_dvd_iff_associated
IsCancelMulZero.toIsLeftCancelMulZero
normalize_eq_one πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
IsUnit
MonoidWithZero.toMonoid
β€”isUnit_iff_exists_inv
instIsDedekindFiniteMonoid
normalize_coe_units
normalize_eq_zero πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
β€”associated_zero_iff_eq_zero
associated_normalize
normalize_zero
normalize_gcd πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
GCDMonoid.gcd
NormalizedGCDMonoid.toGCDMonoid
β€”NormalizedGCDMonoid.normalize_gcd
normalize_idem πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
β€”normUnit_mul_normUnit
mul_one
normalize_lcm πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
NormalizedGCDMonoid.toNormalizationMonoid
GCDMonoid.lcm
NormalizedGCDMonoid.toGCDMonoid
β€”NormalizedGCDMonoid.normalize_lcm
normalize_one πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
β€”MonoidWithZeroHom.map_one
normalize_zero πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
MonoidWithZeroHom.funLike
normalize
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
β€”MonoidWithZeroHom.map_zero
pow_dvd_of_mul_eq_pow πŸ“–β€”IsUnit
MonoidWithZero.toMonoid
CommMonoidWithZero.toMonoidWithZero
GCDMonoid.gcd
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
semigroupDvd
SemigroupWithZero.toSemigroup
MonoidWithZero.toSemigroupWithZero
β€”β€”isUnit_of_dvd_one
instIsTransDvd
gcd_pow_left_dvd_pow_gcd
IsUnit.dvd
IsUnit.pow
Mathlib.Tactic.GCongr.rel_imp_rel
gcd_dvd_gcd
dvd_refl
mul_pow
Dvd.dvd.trans
dvd_gcd_mul_of_dvd_mul
mul_comm
IsUnit.mul_left_dvd
zero_dvd_iff
subsingleton_gcdMonoid_of_unique_units πŸ“–mathematicalβ€”GCDMonoidβ€”associated_iff_eq
associated_of_dvd_dvd
IsCancelMulZero.toIsLeftCancelMulZero
GCDMonoid.toIsCancelMulZero
GCDMonoid.dvd_gcd
GCDMonoid.gcd_dvd_left
GCDMonoid.gcd_dvd_right
lcm_dvd
dvd_lcm_left
dvd_lcm_right
subsingleton_normalizedGCDMonoid_of_unique_units πŸ“–mathematicalβ€”NormalizedGCDMonoidβ€”subsingleton_gcdMonoid_of_unique_units
Unique.instSubsingleton

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