Documentation Verification Report

Consequences

📁 Source: PrimeNumberTheoremAnd/Consequences.lean

Statistics

MetricCount
DefinitionsR, mu_log
2
Theoremsneg_apply, add_isLittleO', add_isLittleO'', Icc_zero_eq_insert, M_isLittleO, M_isLittleO', M_log_identity, R_isLittleO, R_linear_bound, R_locally_bounded, Ico_subset_Ico_of_Icc_subset_Icc, WeakPNT', WeakPNT'', bound_f_first_term, bound_f_second_term, chebyshev_asymptotic, chebyshev_asymptotic', chebyshev_asymptotic'', chebyshev_asymptotic_finsum, chebyshev_asymptotic_pnt, continuousOn_log0, continuousOn_log1, dirichlet_thm, filter_prime_Iic_eq_Icc, finsum_range_eq_sum_range, finsum_range_eq_sum_range', integral_div_log_asymptotic, integral_log_inv, integral_log_inv', integral_log_inv'', integral_log_inv_ne_zero, integral_log_inv_pialt, integral_log_inv_pos, inv_div_log_asy, isLittleO_sqrt_mul_log, isTheta_self_div_const, lambda_eq_sum_sq_dvd_mu, lambda_pnt, log2_pos, log_nth_prime_asymp, mu_log_apply, mu_log_eq_mu_mul_neg_lambda, mu_log_mul_zeta, mu_pnt, mu_pnt_alt, nth_prime_asymp, pi_alt, pi_alt', pi_asymp, pi_asymp'', pi_asymp_aux, pi_nth_prime, pi_nth_prime_asymp, pn_asymptotic, pn_pn_plus_one, prime_between, prime_in_gap, prime_in_gap', primorial_bounds, primorial_bounds_finprod, second_smaller_terms, smaller_terms, sum_abs_R_isLittleO, sum_abs_R_isLittleO', sum_bounded_of_linear_bound, sum_lambda_eq_sum_mu_div_sq, sum_log_div_isBigO, sum_mobius_div_approx, sum_mobius_div_isBigO, sum_mobius_div_self_le, sum_mobius_floor, sum_mobius_floor_tail_isLittleO, sum_mobius_mul_floor, sum_mu_Lambda, sum_mu_div_sq_isLittleO, tendsto_by_squeeze, tendsto_floor_add_one_div_self, tendsto_nth_prime_atTop, th43_b, x_log_x_atTop
80
Total82

ArithmeticFunction

Theorems

NameKindAssumesProvesValidatesDepends On
neg_apply 📖

Asymptotics.IsEquivalent

Theorems

NameKindAssumesProvesValidatesDepends On
add_isLittleO' 📖
add_isLittleO'' 📖

Set

Theorems

NameKindAssumesProvesValidatesDepends On
Ico_subset_Ico_of_Icc_subset_Icc 📖

(root)

Definitions

NameCategoryTheorems
R 📖CompOp
5 mathmath: sum_abs_R_isLittleO, R_isLittleO, R_linear_bound, R_locally_bounded, sum_abs_R_isLittleO'
mu_log 📖CompOp
3 mathmath: mu_log_mul_zeta, mu_log_apply, mu_log_eq_mu_mul_neg_lambda

Theorems

NameKindAssumesProvesValidatesDepends On
Icc_zero_eq_insert 📖
M_isLittleO 📖mathematicalMM_log_identity
sum_log_div_isBigO
sum_mobius_div_isBigO
sum_abs_R_isLittleO
M_isLittleO' 📖mathematicalMM_isLittleO
M_log_identity 📖mathematicalM
Psi
sum_mu_Lambda
R_isLittleO 📖mathematicalRWeakPNT''
R_linear_bound 📖mathematicalRR_isLittleO
R_locally_bounded
R_locally_bounded 📖mathematicalR
WeakPNT' 📖WeakPNT
Real.tendsto_pow_log_div_pow_atTop
WeakPNT'' 📖WeakPNT'
bound_f_first_term 📖
bound_f_second_term 📖
chebyshev_asymptotic 📖Asymptotics.IsEquivalent.add_isLittleO''
WeakPNT''
isLittleO_sqrt_mul_log
chebyshev_asymptotic' 📖chebyshev_asymptotic
chebyshev_asymptotic'' 📖chebyshev_asymptotic'
chebyshev_asymptotic_finsum 📖chebyshev_asymptotic
chebyshev_asymptotic_pnt 📖WeakPNT_AP
tendsto_floor_add_one_div_self
Asymptotics.IsEquivalent.add_isLittleO''
Icc_zero_eq_insert
filter_prime_Iic_eq_Icc
isLittleO_sqrt_mul_log
isTheta_self_div_const
continuousOn_log0 📖
continuousOn_log1 📖
dirichlet_thm 📖
filter_prime_Iic_eq_Icc 📖
finsum_range_eq_sum_range 📖
finsum_range_eq_sum_range' 📖
integral_div_log_asymptotic 📖inv_div_log_asy
integral_log_inv_pialt
integral_log_inv 📖continuousOn_log0
integral_log_inv' 📖integral_log_inv
integral_log_inv'' 📖integral_log_inv'
integral_log_inv_ne_zero 📖integral_log_inv_pos
integral_log_inv_pialt 📖integral_log_inv
integral_log_inv_pos 📖
inv_div_log_asy 📖
isLittleO_sqrt_mul_log 📖
isTheta_self_div_const 📖
lambda_eq_sum_sq_dvd_mu 📖
lambda_pnt 📖sum_mu_div_sq_isLittleO
sum_lambda_eq_sum_mu_div_sq
log2_pos 📖
log_nth_prime_asymp 📖mathematicalnth_primepi_nth_prime_asymp
tendsto_nth_prime_atTop
mu_log_apply 📖mathematicalmu_log
mu_log_eq_mu_mul_neg_lambda 📖mathematicalmu_logmu_log_mul_zeta
mu_log_mul_zeta 📖mathematicalmu_logmu_log_apply
mu_pnt 📖M_isLittleO
mu_pnt_alt 📖sum_mobius_div_approx
sum_mobius_floor_tail_isLittleO
nth_prime_asymp 📖mathematicalnth_primepi_nth_prime_asymp
log_nth_prime_asymp
pi_alt 📖pi_asymp
integral_div_log_asymptotic
pi_alt' 📖pi_alt
pi_asymp 📖pi_asymp''
integral_log_inv_pos
pi_asymp'' 📖chebyshev_asymptotic''
pi_asymp_aux
continuousOn_log1
integral_log_inv''
integral_log_inv'
integral_log_inv_pos
integral_log_inv_ne_zero
pi_asymp_aux 📖th43_b
pi_nth_prime 📖mathematicalnth_prime
pi_nth_prime_asymp 📖mathematicalnth_primetendsto_nth_prime_atTop
pi_nth_prime
pi_alt'
pn_asymptotic 📖nth_prime_asymp
pn_pn_plus_one 📖pn_asymptotic
prime_between 📖tendsto_by_squeeze
prime_in_gap
prime_in_gap 📖prime_in_gap'
prime_in_gap' 📖
primorial_bounds 📖chebyshev_asymptotic
primorial_bounds_finprod 📖primorial_bounds
second_smaller_terms 📖bound_f_second_term
smaller_terms 📖bound_f_first_term
sum_abs_R_isLittleO 📖mathematicalRR_isLittleO
R_locally_bounded
sum_bounded_of_linear_bound
sum_abs_R_isLittleO' 📖mathematicalRsum_abs_R_isLittleO
sum_bounded_of_linear_bound 📖
sum_lambda_eq_sum_mu_div_sq 📖lambda_eq_sum_sq_dvd_mu
sum_log_div_isBigO 📖
sum_mobius_div_approx 📖sum_mobius_floor
sum_mobius_div_isBigO 📖sum_mobius_div_self_le
sum_mobius_div_self_le 📖
sum_mobius_floor 📖sum_mobius_mul_floor
sum_mobius_floor_tail_isLittleO 📖mu_pnt
sum_mobius_mul_floor 📖
sum_mu_Lambda 📖mathematicalPsimu_log_eq_mu_mul_neg_lambda
ArithmeticFunction.neg_apply
sum_mu_div_sq_isLittleO 📖M_isLittleO'
tendsto_by_squeeze 📖pi_alt
smaller_terms
second_smaller_terms
x_log_x_atTop
tendsto_floor_add_one_div_self 📖
tendsto_nth_prime_atTop 📖mathematicalnth_prime
th43_b 📖
x_log_x_atTop 📖

---

← Back to Index