Documentation Verification Report

Erdos392

📁 Source: PrimeNumberTheoremAnd/Erdos392.lean

Statistics

MetricCount
DefinitionsFactorization, a, addFactor, balance, deficitMultiset, prod, replace, score, sum, total_imbalance, waste, Params, L, M, initial, initial_full, n, rough_k, rough_q, rough_set, pairProd
21
TheoremsaddFactor_balance, addFactor_deficit_balance_eq_zero, addFactor_submultiset_total_imbalance, addFactor_waste, card_bound, count_deficitMultiset, deficitMultiset_prod_pos, deficit_implies_le_n, ha, hpos, lower_score_1, lower_score_2, lower_score_3, lower_score_3_case1, lower_score_3_case2a, lower_score_3_case2b, lower_score_3_clean, lowest_score, mem_deficitMultiset, replace_balance, replace_div_balance, replace_div_score_le, replace_div_total_imbalance, replace_sum, score_eq, score_le_of_add_submultiset, score_sum_change, score_sum_change_multiset, waste_eq, zero_total_imbalance, L_sub_log_ge_one, balance_inequality_aux, exists_large_prime_of_rough, hL, hL', hL_pos, hM, balance_ge_neg_M_mul_log, balance_large_prime_ge, balance_large_prime_le, balance_medium_prime_ge, balance_medium_prime_le, balance_small_prime_ge, balance_small_prime_le, balance_tiny_prime_ge, bound_score_1, bound_score_2, bound_score_3, bound_score_4, bound_score_5, card, count_bound_aux, count_multiples_le, count_multiples_lower_bound, count_multiples_lower_bound_pow, div_le, factorial_factorization_eq_div, mem_range, score, score_bound, smooth_of_dvd_small_prime, smooth_of_multiple, sum_valuation_eq, sum_valuation_eq_small, sum_valuation_le, sum_valuation_le_M_mul_interval_count, term_bound, valuation_eq_indicator, valuation_eq_one, waste, initial_balance_eq, initial_full_balance_eq, initial_full_balance_ge, initial_full_sum_valuation_eq, initial_full_term_bound, primeCounting_ge_log, rough_qk_prop, rough_set_card_le, rough_set_structure, rough_valuation_eq_k_valuation, rough_valuation_le_log, rough_valuation_sum_le, valuation_eq_one_of_large_prime, Solution_1, Solution_2, exists_phi_div_self_lt, exists_submultiset_prod_between, factorization_prod_eq_count, pairProd_bound, pairProd_length, pairProd_prod, primeCounting_is_o_id, primeCounting_le_bound, prod_one_sub_one_div_prime_tendsto_zero, sum_factorization_eq_sum_multiples, tendsto_primeCounting_div_id_zero
96
Total117
⚠️ With sorryscore_bound
1

Erdos392

Definitions

NameCategoryTheorems
Factorization 📖CompData
1 mathmath: Solution_1
Params 📖CompData
1 mathmath: Params.initial.score
pairProd 📖CompOp
2 mathmath: pairProd_length, pairProd_prod

Theorems

NameKindAssumesProvesValidatesDepends On
Solution_1 📖mathematicalFactorization
Factorization.total_imbalance
Factorization.a
Params.initial.score
Factorization.card_bound
Solution_2 📖Solution_1
Factorization.zero_total_imbalance
pairProd_prod
pairProd_length
pairProd_bound
Factorization.ha
exists_phi_div_self_lt 📖prod_one_sub_one_div_prime_tendsto_zero
exists_submultiset_prod_between 📖
factorization_prod_eq_count 📖
pairProd_bound 📖pairProdpairProd.induct
pairProd.eq_3
pairProd_length 📖mathematicalpairProdpairProd.induct
pairProd_prod 📖mathematicalpairProdpairProd.induct
primeCounting_is_o_id 📖exists_phi_div_self_lt
primeCounting_le_bound 📖
prod_one_sub_one_div_prime_tendsto_zero 📖
sum_factorization_eq_sum_multiples 📖
tendsto_primeCounting_div_id_zero 📖primeCounting_le_bound

Erdos392.Factorization

Definitions

NameCategoryTheorems
a 📖CompOp
7 mathmath: Erdos392.Params.initial.sum_valuation_eq, Erdos392.Params.initial.sum_valuation_eq_small, Erdos392.Solution_1, waste_eq, card_bound, Erdos392.Params.initial.sum_valuation_le_M_mul_interval_count, Erdos392.Params.initial.card
addFactor 📖CompOp
5 mathmath: addFactor_deficit_balance_eq_zero, addFactor_submultiset_total_imbalance, score_le_of_add_submultiset, addFactor_balance, addFactor_waste
balance 📖CompOp
15 mathmath: count_deficitMultiset, Erdos392.Params.initial.balance_ge_neg_M_mul_log, Erdos392.Params.initial.balance_small_prime_ge, Erdos392.Params.initial_full_balance_ge, Erdos392.Params.initial.balance_large_prime_le, Erdos392.Params.initial.balance_small_prime_le, Erdos392.Params.initial_full_balance_eq, replace_balance, replace_div_balance, Erdos392.Params.initial.balance_medium_prime_ge, addFactor_balance, Erdos392.Params.initial_balance_eq, Erdos392.Params.initial.balance_tiny_prime_ge, Erdos392.Params.initial.balance_medium_prime_le, Erdos392.Params.initial.balance_large_prime_ge
deficitMultiset 📖CompOp
2 mathmath: count_deficitMultiset, deficitMultiset_prod_pos
prod 📖CompOp
1 mathmath: zero_total_imbalance
replace 📖CompOp
5 mathmath: replace_sum, replace_div_score_le, replace_balance, replace_div_total_imbalance, replace_div_balance
score 📖CompOp
14 mathmath: lower_score_3_clean, lower_score_3, lower_score_3_case2a, replace_div_score_le, Erdos392.Params.initial.score_bound, score_eq, lower_score_2, card_bound, score_le_of_add_submultiset, lowest_score, lower_score_3_case2b, lower_score_3_case1, Erdos392.Params.initial.score, lower_score_1
sum 📖CompOp
2 mathmath: replace_sum, Erdos392.Params.initial.sum_valuation_le
total_imbalance 📖CompOp
12 mathmath: lower_score_3_clean, lower_score_3, lower_score_3_case2a, Erdos392.Solution_1, addFactor_submultiset_total_imbalance, replace_div_total_imbalance, lower_score_2, card_bound, lowest_score, lower_score_3_case2b, lower_score_3_case1, lower_score_1
waste 📖CompOp
4 mathmath: waste_eq, score_eq, addFactor_waste, Erdos392.Params.initial.waste

Theorems

NameKindAssumesProvesValidatesDepends On
addFactor_balance 📖mathematicalbalance
addFactor
addFactor_deficit_balance_eq_zero 📖mathematicalbalance
deficitMultiset
addFactoraddFactor.congr_simp
addFactor_balance
Erdos392.factorization_prod_eq_count
mem_deficitMultiset
count_deficitMultiset
deficit_implies_le_n
addFactor_submultiset_total_imbalance 📖mathematicalbalance
deficitMultiset
total_imbalance
addFactor
addFactor_balance
Erdos392.factorization_prod_eq_count
mem_deficitMultiset
count_deficitMultiset
addFactor_waste 📖mathematicalwaste
addFactor
card_bound 📖mathematicaltotal_imbalance
a
score
lowest_score
waste_eq
score_eq
count_deficitMultiset 📖mathematicaldeficitMultiset
balance
deficitMultiset_prod_pos 📖mathematicaldeficitMultiset
deficit_implies_le_n 📖balance
ha 📖a
hpos 📖a
lower_score_1 📖mathematicalbalancetotal_imbalance
score
ha
hpos
replace_div_total_imbalance
replace_div_score_le
lower_score_2 📖mathematicalbalancetotal_imbalance
score
ha
hpos
lower_score_3 📖mathematicalbalancetotal_imbalance
score
lower_score_1
lower_score_2
lower_score_3_clean
ha
hpos
deficit_implies_le_n
lower_score_3_case1 📖mathematicalbalance
deficitMultiset
total_imbalance
score
deficitMultiset_prod_pos
addFactor_deficit_balance_eq_zero
score_eq
addFactor_waste
lower_score_3_case2a 📖mathematicalbalancetotal_imbalance
score
addFactor_submultiset_total_imbalance
addFactor_balance
score_sum_change
addFactor_waste
lower_score_3_case2b 📖mathematicalbalance
deficitMultiset
total_imbalance
score
Erdos392.exists_submultiset_prod_between
mem_deficitMultiset
addFactor_submultiset_total_imbalance
score_le_of_add_submultiset
lower_score_3_clean 📖mathematicalbalancetotal_imbalance
score
lower_score_3_case1
lower_score_3_case2a
lower_score_3_case2b
lowest_score 📖mathematicaltotal_imbalance
score
lower_score_1
lower_score_2
lower_score_3
mem_deficitMultiset 📖deficitMultiset
replace_balance 📖mathematicalabalance
replace
replace_div_balance 📖mathematicalabalance
replace
ha
hpos
hpos
ha
replace_balance
replace_div_score_le 📖mathematicala
balance
score
replace
ha
hpos
ha
hpos
replace_sum
replace_div_balance
replace.congr_simp
replace_div_total_imbalance 📖mathematicala
balance
total_imbalance
replace
ha
hpos
hpos
ha
replace_div_balance
replace_sum 📖mathematicalasum
replace
score_eq 📖mathematicaltotal_imbalancescore
waste
score_le_of_add_submultiset 📖mathematicaldeficitMultisetscore
addFactor
score_sum_change_multiset
addFactor_balance
Erdos392.factorization_prod_eq_count
mem_deficitMultiset
addFactor_waste
score_sum_change 📖balance
score_sum_change_multiset 📖deficitMultiset
balance
count_deficitMultiset
waste_eq 📖mathematicaltotal_imbalancea
waste
zero_total_imbalance
prod.eq_1
hpos
ha
zero_total_imbalance 📖mathematicaltotal_imbalanceprodhpos
ha

Erdos392.Params

Definitions

NameCategoryTheorems
L 📖CompOp
11 mathmath: exists_large_prime_of_rough, hL_pos, hL, initial.score_bound, rough_set_card_le, balance_inequality_aux, hL', L_sub_log_ge_one, rough_qk_prop, initial.score, rough_set_structure
M 📖CompOp
21 mathmath: initial.balance_ge_neg_M_mul_log, initial_full_sum_valuation_eq, initial.balance_small_prime_ge, initial_full_balance_ge, initial.mem_range, initial.sum_valuation_eq, initial.sum_valuation_eq_small, initial.balance_small_prime_le, initial.term_bound, initial.score_bound, initial_full_balance_eq, hM, initial.balance_medium_prime_ge, initial_balance_eq, initial_full_term_bound, initial.sum_valuation_le_M_mul_interval_count, initial.balance_tiny_prime_ge, initial.sum_valuation_le, initial.balance_medium_prime_le, initial.waste, initial.div_le
initial 📖CompOp
17 mathmath: initial.balance_ge_neg_M_mul_log, initial.balance_small_prime_ge, initial.sum_valuation_eq, initial.balance_large_prime_le, initial.sum_valuation_eq_small, initial.balance_small_prime_le, initial.score_bound, initial.balance_medium_prime_ge, initial_balance_eq, initial.sum_valuation_le_M_mul_interval_count, initial.score, initial.balance_tiny_prime_ge, initial.sum_valuation_le, initial.balance_medium_prime_le, initial.card, initial.balance_large_prime_ge, initial.waste
initial_full 📖CompOp
3 mathmath: initial_full_balance_ge, initial_full_balance_eq, initial_balance_eq
n 📖CompOp
21 mathmath: exists_large_prime_of_rough, initial_full_sum_valuation_eq, initial_full_balance_ge, hL, initial.balance_small_prime_le, initial.term_bound, initial.score_bound, rough_valuation_sum_le, rough_set_card_le, initial_full_balance_eq, balance_inequality_aux, hL', initial_balance_eq, rough_qk_prop, initial_full_term_bound, initial.score, initial.balance_tiny_prime_ge, initial.sum_valuation_le, initial.card, rough_set_structure, initial.waste
rough_k 📖CompOp
2 mathmath: rough_valuation_eq_k_valuation, rough_qk_prop
rough_q 📖CompOp
1 mathmath: rough_qk_prop
rough_set 📖CompOp
3 mathmath: rough_valuation_sum_le, rough_set_card_le, initial_balance_eq

Theorems

NameKindAssumesProvesValidatesDepends On
L_sub_log_ge_one 📖mathematicalLhL_pos
balance_inequality_aux 📖mathematicaln
L
primeCounting_ge_log
hL_pos
hL
L_sub_log_ge_one
exists_large_prime_of_rough 📖mathematicalrough_setn
L
hL 📖mathematicaln
L
hL' 📖mathematicaln
L
hL_pos 📖mathematicalL
hM 📖mathematicalM
initial_balance_eq 📖mathematicalErdos392.Factorization.balance
n
initial
initial_full
M
rough_set
initial_full_balance_eq 📖mathematicalErdos392.Factorization.balance
n
initial_full
M
initial_full_balance_ge 📖mathematicalErdos392.Factorization.balance
n
initial_full
M
initial_full_sum_valuation_eq
initial_full_balance_eq
initial_full_term_bound
hL
initial_full_sum_valuation_eq 📖mathematicaln
M
hM
Erdos392.sum_factorization_eq_sum_multiples
initial_full_term_bound 📖mathematicalM
n
initial.count_multiples_lower_bound_pow
hM
primeCounting_ge_log 📖LogTables.log_7_lt
rough_qk_prop 📖mathematicalrough_setrough_q
n
L
rough_k
rough_set_structure
rough_set_card_le 📖mathematicalrough_set
n
L
rough_set_structure
rough_set_structure 📖mathematicalrough_setn
L
exists_large_prime_of_rough
hL
hL_pos
hM
valuation_eq_one_of_large_prime
rough_valuation_eq_k_valuation 📖mathematicalrough_set
L
rough_krough_qk_prop
hL'
hL_pos
hL
rough_valuation_le_log 📖rough_set
L
rough_qk_prop
rough_valuation_eq_k_valuation
rough_valuation_sum_le 📖mathematicalLrough_set
n
rough_set_card_le
rough_valuation_le_log
valuation_eq_one_of_large_prime 📖n
L
hL'

Erdos392.Params.initial

Theorems

NameKindAssumesProvesValidatesDepends On
balance_ge_neg_M_mul_log 📖mathematicalErdos392.Params.n
Erdos392.Params.L
Erdos392.Factorization.balance
Erdos392.Params.initial
Erdos392.Params.M
Erdos392.Factorization.balance.eq_1
Erdos392.Factorization.sum.eq_1
sum_valuation_eq_small
count_multiples_lower_bound
Erdos392.Params.hM
balance_large_prime_ge 📖mathematicalErdos392.Params.n
Erdos392.Params.L
Erdos392.Factorization.balance
Erdos392.Params.initial
Erdos392.Params.hL_pos
Erdos392.Params.hL
Erdos392.Params.hL'
factorial_factorization_eq_div
balance_large_prime_le 📖mathematicalErdos392.Params.n
Erdos392.Params.L
Erdos392.Factorization.balance
Erdos392.Params.initial
balance_medium_prime_ge 📖mathematicalErdos392.Params.n
Erdos392.Params.L
Erdos392.Factorization.balance
Erdos392.Params.initial
Erdos392.Params.M
count_multiples_lower_bound
Erdos392.Params.hM
sum_valuation_eq
factorial_factorization_eq_div
balance_medium_prime_le 📖mathematicalErdos392.Params.nErdos392.Factorization.balance
Erdos392.Params.initial
Erdos392.Params.M
sum_valuation_le_M_mul_interval_count
count_multiples_le
count_bound_aux
factorial_factorization_eq_div
balance_small_prime_ge 📖mathematicalErdos392.Params.n
Erdos392.Params.L
Erdos392.Factorization.balance
Erdos392.Params.initial
Erdos392.Params.M
Erdos392.Params.hL_pos
balance_ge_neg_M_mul_log
balance_small_prime_le 📖mathematicalErdos392.Factorization.balance
Erdos392.Params.n
Erdos392.Params.initial
Erdos392.Params.M
sum_valuation_le
Erdos392.Params.hM
term_bound
Erdos392.Params.hL
balance_tiny_prime_ge 📖mathematicalErdos392.Params.LErdos392.Factorization.balance
Erdos392.Params.n
Erdos392.Params.initial
Erdos392.Params.M
Erdos392.Params.initial_full_balance_ge
Erdos392.Params.initial_balance_eq
Erdos392.Params.rough_valuation_sum_le
Erdos392.Params.balance_inequality_aux
bound_score_1 📖Erdos392.Params.hM
bound_score_2 📖pi_alt'
bound_score_3 📖pi_alt'
bound_score_4 📖Erdos392.Params.hL_pos
Erdos392.primeCounting_is_o_id
bound_score_5 📖Erdos392.tendsto_primeCounting_div_id_zero
card 📖mathematicalErdos392.Factorization.a
Erdos392.Params.n
Erdos392.Params.initial
count_bound_aux 📖
count_multiples_le 📖
count_multiples_lower_bound 📖
count_multiples_lower_bound_pow 📖count_multiples_lower_bound
div_le 📖mathematicalErdos392.Factorization.a
Erdos392.Params.n
Erdos392.Params.initial
Erdos392.Params.Mmem_range
Erdos392.Params.hM
Erdos392.Factorization.hpos
factorial_factorization_eq_div 📖
mem_range 📖mathematicalErdos392.Factorization.a
Erdos392.Params.n
Erdos392.Params.initial
Erdos392.Params.M
score 📖mathematicalErdos392.Params
Erdos392.Params.n
Erdos392.Factorization.score
Erdos392.Params.initial
Erdos392.Params.L
bound_score_1
bound_score_2
bound_score_3
bound_score_4
bound_score_5
score_bound
score_bound 📖 ⚠️mathematicalErdos392.Factorization.score
Erdos392.Params.n
Erdos392.Params.initial
Erdos392.Params.L
Erdos392.Params.M
smooth_of_dvd_small_prime 📖Erdos392.Params.n
Erdos392.Params.L
Erdos392.Params.M
Erdos392.Params.hL_pos
Erdos392.Params.hL
Erdos392.Params.hM
smooth_of_multiple 📖Erdos392.Params.n
Erdos392.Params.L
sum_valuation_eq 📖mathematicalErdos392.Params.n
Erdos392.Params.L
Erdos392.Factorization.a
Erdos392.Params.initial
Erdos392.Params.M
Erdos392.Params.hM
valuation_eq_indicator
sum_valuation_eq_small 📖mathematicalErdos392.Params.n
Erdos392.Params.L
Erdos392.Factorization.a
Erdos392.Params.initial
Erdos392.Params.M
smooth_of_dvd_small_prime
Erdos392.Params.hM
sum_valuation_le 📖mathematicalErdos392.Factorization.sum
Erdos392.Params.n
Erdos392.Params.initial
Erdos392.Params.M
sum_valuation_le_M_mul_interval_count 📖mathematicalErdos392.Params.nErdos392.Factorization.a
Erdos392.Params.initial
Erdos392.Params.M
term_bound 📖mathematicalErdos392.Params.M
Erdos392.Params.n
count_multiples_le
valuation_eq_indicator 📖Erdos392.Params.n
Erdos392.Params.L
valuation_eq_one
smooth_of_multiple
valuation_eq_one 📖Erdos392.Params.n
waste 📖mathematicalErdos392.Factorization.waste
Erdos392.Params.n
Erdos392.Params.initial
Erdos392.Params.M
Erdos392.Params.hM
Erdos392.Factorization.hpos
mem_range
div_le
card

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