Documentation Verification Report

Defs

📁 Source: Mathlib/Data/Nat/Prime/Defs.lean

Statistics

MetricCount
DefinitionsPrimes, coeNat, inhabitedPrimes, instRepr, decidablePrime, decidablePrime', instDecidableEqPrimes, instDecidablePredIrreducible, instDecidablePredPrime, minFac, minFacAux, primePow
12
Theoremscoprime_iff_not_dvd, dvd_mul, dvd_or_dvd, eq_one_or_self_of_dvd, minFac_eq, ne_one, ne_zero, not_dvd_one, one_le, one_lt, one_lt', pos, prime, two_le, coe_nat_inj, coe_nat_injective, coprime_of_dvd, decidablePrime_csimp, dvd_prime, dvd_prime_two_le, exists_prime_and_dvd, fact_prime_three, fact_prime_two, factors_lemma, irreducible_iff_nat_prime, irreducible_iff_prime, le_minFac, le_minFac', minFacAux_has_prop, minFac_dvd, minFac_eq, minFac_eq_one_iff, minFac_eq_two_iff, minFac_has_prop, minFac_le, minFac_le_div, minFac_le_of_dvd, minFac_lemma, minFac_one, minFac_pos, minFac_prime, minFac_prime_iff, minFac_sq_le_self, minFac_two, minFac_zero, not_prime_iff_minFac_lt, not_prime_one, not_prime_zero, prime_def, prime_def_le_sqrt, prime_def_lt, prime_def_lt', prime_def_minFac, prime_dvd_prime_iff_eq, prime_eleven, prime_five, prime_iff, prime_iff_not_exists_mul_eq, prime_of_coprime, prime_one_false, prime_seven, prime_three, prime_two, prime_zero_false, nat_prime
65
Total77

Nat

Definitions

NameCategoryTheorems
Primes 📖CompOp
38 mathmath: Primes.prodNatEquiv_symm_apply, DirichletCharacter.LSeries_eulerProduct_tprod, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Primes.coe_pnat_injective, FirstOrder.Field.ACF_zero_realize_iff_finite_ACF_prime_not_realize, EulerProduct.eulerProduct_hasProd, ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, tsum_eq_tsum_primes_of_support_subset_prime_powers, riemannZeta_eulerProduct_exp_log, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, EulerProduct.eulerProduct_tprod, PNat.count_factorMultiset, Primes.prodNatEquiv_apply, ArithmeticFunction.IsMultiplicative.eulerProduct_tprod, EulerProduct.eulerProduct_completely_multiplicative_tprod, Primes.not_summable_one_div, FirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realize, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, PadicInt.coe_adicCompletionIntegersEquiv_apply, EulerProduct.eulerProduct_completely_multiplicative_hasProd, tprod_eq_tprod_primes_mul_tprod_primes_of_mulSupport_subset_prime_powers, Primes.coe_prodNatEquiv_apply, FirstOrder.Field.ACF_zero_realize_iff_infinite_ACF_prime_realize, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, DirichletCharacter.LSeries_eulerProduct_hasProd, Primes.countable, DirichletCharacter.LSeries_eulerProduct_exp_log, tprod_eq_tprod_primes_of_mulSupport_subset_prime_powers, Primes.summable_rpow, ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, riemannZeta_eulerProduct_tprod, riemannZeta_eulerProduct_hasProd, tsum_eq_tsum_primes_add_tsum_primes_of_support_subset_prime_powers, EulerProduct.exp_tsum_primes_log_eq_tsum, PrimeMultiset.card_ofPrime, Primes.infinite
decidablePrime 📖CompOp
16 mathmath: ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, schnirelmannDensity_setOf_prime, Chebyshev.psi_sub_theta_eq_sum_not_prime, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, primorial_add, primeFactors_eq_to_filter_divisors_prime, Chebyshev.sum_PrimePow_eq_sum_sum, EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, prod_pow_prime_padicValNat, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, primesBelow_succ, Chebyshev.theta_eq_sum_Icc, decidablePrime_csimp, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum
decidablePrime' 📖CompOp
1 mathmath: decidablePrime_csimp
instDecidableEqPrimes 📖CompOp
1 mathmath: PNat.count_factorMultiset
instDecidablePredIrreducible 📖CompOp
instDecidablePredPrime 📖CompOp
minFac 📖CompOp
39 mathmath: Num.minFac_to_nat, Primes.prodNatEquiv_symm_apply, IsPrimePow.minFac_pow_factorization_eq, minFac_eq_two_iff, Prime.minFac_eq, Mathlib.Meta.NormNum.isNat_minFac_1, ZMod.minOrder, primeFactorsList_add_two, le_minFac, factors_lemma, minFac_eq, minFac_le, minFac_le_of_dvd, IsPrimitiveRoot.sub_one_norm_isPrimePow, minFac_one, minFac_dvd, le_minFac', IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow, Mathlib.Meta.NormNum.isNat_minFac_3, not_prime_iff_minFac_lt, minFac_le_div, minFac_has_prop, minFac_eq_one_iff, minFac_two, ArithmeticFunction.vonMangoldt_apply, minFac_prime_iff, minFac_zero, Prime.pow_minFac, coprime_factorial_iff, Mathlib.Meta.NormNum.isNat_minFac_4, pow_minFac, minFac_pos, isPrimePow_nat_iff_bounded_log_minFac, Mathlib.Meta.NormNum.isNat_minFac_2, prime_def_minFac, isPrimePow_iff_minFac_pow_factorization_eq, minFac_prime, minFac_sq_le_self, PosNum.minFac_to_nat
minFacAux 📖CompOp
3 mathmath: minFacAux_has_prop, minFac_eq, PosNum.minFacAux_to_nat

Theorems

NameKindAssumesProvesValidatesDepends On
coprime_of_dvd 📖exists_prime_and_dvd
dvd_trans
decidablePrime_csimp 📖mathematicaldecidablePrime
decidablePrime'
dvd_prime 📖PrimePrime.eq_one_or_self_of_dvd
one_dvd
dvd_rfl
dvd_prime_two_le 📖Primedvd_prime
exists_prime_and_dvd 📖mathematicalPrimeminFac_prime
minFac_dvd
fact_prime_three 📖mathematicalFact
Prime
prime_three
fact_prime_two 📖mathematicalFact
Prime
prime_two
factors_lemma 📖mathematicalminFacPrime.one_lt
minFac_prime
irreducible_iff_nat_prime 📖mathematicalIrreducible
instMonoid
Prime
irreducible_iff_prime 📖mathematicalIrreducible
instMonoid
Prime
instCommMonoidWithZero
prime_iff
le_minFac 📖mathematicalminFacPrime.not_dvd_one
le_trans
minFac_le_of_dvd
Prime.two_le
minFac_prime
minFac_dvd
le_minFac' 📖mathematicalminFacnot_le_of_gt
le_trans
minFac_le_of_dvd
le_minFac
Prime.two_le
minFacAux_has_prop 📖mathematicalminFacAuxminFacAux.eq_1
prime_def_le_sqrt
not_lt_of_ge
lt_of_lt_of_le
sqrt_lt
dvd_rfl
le_of_eq
dvd_prime_two_le
minFac_lemma
add_right_comm
mul_one
le_rfl
dvd_of_mul_right_dvd
minFac_dvd 📖mathematicalminFacminFac_one
minFac_has_prop
minFac_eq 📖mathematicalminFac
minFacAux
minFac_eq_one_iff 📖mathematicalminFacminFac_prime
not_prime_one
minFacAux.eq_1
minFac_eq_two_iff 📖mathematicalminFacminFac_dvd
minFac_le_of_dvd
le_refl
minFac_pos
LE.le.eq_or_lt
le_antisymm
minFac_has_prop 📖mathematicalminFaczero_add
le_rfl
minFacAux_has_prop
minFac_le 📖mathematicalminFacminFac_dvd
minFac_le_div 📖mathematicalPrimeminFacminFac_dvd
MulZeroClass.mul_zero
le_antisymm
not_le
mul_one
not_and_or
prime_def_minFac
minFac_one
le_refl
minFac_pos
minFac_le_of_dvd
mul_comm
minFac_le_of_dvd 📖mathematicalminFacle_trans
minFac_one
minFac_has_prop
minFac_lemma 📖le_sqrt
le_of_not_gt
minFac_one 📖mathematicalminFacminFacAux.eq_1
minFac_pos 📖mathematicalminFacminFac_one
Prime.pos
minFac_prime
minFac_prime 📖mathematicalPrime
minFac
minFac_has_prop
prime_def_lt'
not_le_of_gt
Dvd.dvd.trans
minFac_prime_iff 📖mathematicalPrime
minFac
minFac_one
minFac_prime
minFac_sq_le_self 📖mathematicalPrimeMonoid.toNatPow
instMonoid
minFac
minFac_le_div
sq
minFac_two 📖mathematicalminFac
minFac_zero 📖mathematicalminFac
not_prime_iff_minFac_lt 📖mathematicalPrime
minFac
prime_def_minFac
lt_iff_le_and_ne
minFac_le
not_prime_one 📖mathematicalPrimeIrreducible.ne_one
not_prime_zero 📖mathematicalPrimeIrreducible.ne_zero
prime_def 📖mathematicalPrimePrime.two_le
Prime.eq_one_or_self_of_dvd
LT.lt.trans_le
isUnit_iff
LT.lt.ne'
mul_right_inj'
IsCancelMulZero.toIsLeftCancelMulZero
instIsCancelMulZero
mul_one
dvd_mul_right
prime_def_le_sqrt 📖mathematicalPrimeprime_def_lt'
lt_of_le_of_lt
sqrt_lt_self
le_sqrt_of_eq_mul
one_mul
mul_comm
prime_def_lt 📖mathematicalPrimeprime_def
LE.le.lt_or_eq_dec
prime_def_lt' 📖mathematicalPrimeprime_def_lt
not_lt_of_ge
prime_def_minFac 📖mathematicalPrime
minFac
Prime.two_le
minFac_has_prop
Prime.one_lt
dvd_prime
minFac_prime
prime_dvd_prime_iff_eq 📖Primedvd_prime_two_le
Prime.two_le
prime_eleven 📖mathematicalPrime
prime_five 📖mathematicalPrime
prime_iff 📖mathematicalPrime
Prime
instCommMonoidWithZero
Prime.ne_zero
Irreducible.not_isUnit
Prime.dvd_mul
Prime.irreducible
instIsCancelMulZero
prime_iff_not_exists_mul_eq 📖mathematicalPrimeMathlib.Tactic.Push.not_and_eq
one_mul
mul_ne_zero_iff
IsRightCancelMulZero.to_noZeroDivisors
IsCancelMulZero.toIsRightCancelMulZero
instIsCancelMulZero
LE.le.antisymm
prime_of_coprime 📖mathematicalPrimeprime_def_lt
LT.lt.ne'
zero_dvd_iff
prime_one_false 📖Primenot_prime_one
prime_seven 📖mathematicalPrime
prime_three 📖mathematicalPrime
prime_two 📖mathematicalPrime
prime_zero_false 📖Primenot_prime_zero

Nat.Prime

Theorems

NameKindAssumesProvesValidatesDepends On
coprime_iff_not_dvd 📖Nat.Primenot_dvd_one
mul_one
Nat.coprime_of_dvd
Nat.prime_dvd_prime_iff_eq
dvd_mul 📖Nat.Primecoprime_iff_not_dvd
Dvd.dvd.mul_right
Dvd.dvd.mul_left
dvd_or_dvd 📖Nat.Primedvd_mul
eq_one_or_self_of_dvd 📖Nat.PrimeIrreducible.isUnit_or_isUnit
mul_one
Nat.isUnit_iff
minFac_eq 📖mathematicalNat.PrimeNat.minFacNat.prime_def_minFac
ne_one 📖Nat.PrimeLT.lt.ne'
one_lt
ne_zero 📖Nat.PrimeIrreducible.ne_zero
not_dvd_one 📖Nat.PrimeIrreducible.not_dvd_one
one_le 📖Nat.PrimeLT.lt.le
one_lt
one_lt 📖Nat.Primetwo_le
one_lt' 📖mathematicalFactone_lt
Fact.out
pos 📖Nat.Primene_zero
prime 📖mathematicalNat.PrimePrime
Nat.instCommMonoidWithZero
Nat.prime_iff
two_le 📖Nat.PrimeNat.not_prime_zero
Nat.not_prime_one

Nat.Primes

Definitions

NameCategoryTheorems
coeNat 📖CompOp
inhabitedPrimes 📖CompOp
instRepr 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
coe_nat_inj 📖mathematicalNat.Prime
coe_nat_injective 📖mathematicalNat.PrimeSubtype.coe_injective

Nat.monoid

Definitions

NameCategoryTheorems
primePow 📖CompOp

Prime

Theorems

NameKindAssumesProvesValidatesDepends On
nat_prime 📖mathematicalPrime
Nat.instCommMonoidWithZero
Nat.PrimeNat.prime_iff

---

← Back to Index