Documentation Verification Report

Basic

📁 Source: Mathlib/Algebra/ContinuedFractions/Basic.lean

Statistics

MetricCount
DefinitionsContFract, instCoeGenContFract, instCoeSimpContFract, instInhabited, ofInteger, GenContFract, IsSimpContFract, Pair, a, b, coeFn, instCoe, instRepr, map, TerminatedAt, Terminates, coeFn, conts, contsAux, convs, convs', convs'Aux, dens, h, instCoe, instDecidableTerminatedAt, instInhabited, instInhabitedPair, default, nextConts, nextDen, nextNum, nums, ofInteger, partDens, partNums, s, SimpContFract, IsContFract, instCoeGenContFract, instInhabited, ofInteger
42
Theoremscoe_toPair, coe_toGenContFract, ext, ext_iff
4
Total46

ContFract

Definitions

NameCategoryTheorems
instCoeGenContFract 📖CompOp
instCoeSimpContFract 📖CompOp
instInhabited 📖CompOp
ofInteger 📖CompOp

GenContFract

Definitions

NameCategoryTheorems
IsSimpContFract 📖MathDef
4 mathmath: ContFract.convs_eq_convs', SimpContFract.determinant, of_isSimpContFract, SimpContFract.determinant_aux
Pair 📖CompData
26 mathmath: coe_of_s_rat_eq, exists_gcf_pair_rat_eq_nth_conts, exists_conts_b_of_den, coe_of_rat_eq, exists_gcf_pair_rat_eq_of_nth_contsAux, squashSeq_succ_n_tail_eq_squashSeq_tail_n, of_s_head_aux, coe_of_s_get?_rat_eq, convs'Aux_succ_some, of_s_of_int, of_s_head, squashSeq_nth_of_lt, coe_toGenContFract, exists_conts_a_of_num, exists_s_b_of_partDen, of_s_tail, get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, partNum_none_iff_s_none, get?_of_eq_some_of_succ_get?_intFractPair_stream, terminatedAt_iff_s_none, exists_s_a_of_partNum, squashSeq_nth_of_not_terminated, terminatedAt_iff_s_terminatedAt, squashGCF_nth_of_lt, of_s_succ, partDen_none_iff_s_none
TerminatedAt 📖MathDef
7 mathmath: terminatedAt_iff_partNum_none, of_terminatedAt_n_iff_succ_nth_intFractPair_stream_eq_none, terminated_stable, of_terminatedAt_iff_intFractPair_seq1_terminatedAt, terminatedAt_iff_s_none, terminatedAt_iff_s_terminatedAt, terminatedAt_iff_partDen_none
Terminates 📖MathDef
3 mathmath: of_terminates_iff_of_rat_terminates, terminates_iff_rat, terminates_of_rat
coeFn 📖CompOp
1 mathmath: coe_toGenContFract
conts 📖CompOp
12 mathmath: nth_cont_eq_succ_nth_contAux, exists_gcf_pair_rat_eq_nth_conts, first_cont_eq, exists_conts_b_of_den, conts_recurrenceAux, conv_eq_conts_a_div_conts_b, zeroth_cont_eq_h_one, num_eq_conts_a, conts_stable_of_terminated, den_eq_conts_b, exists_conts_a_of_num, conts_recurrence
contsAux 📖CompOp
15 mathmath: nth_cont_eq_succ_nth_contAux, compExactValue_correctness_of_stream_eq_some, exists_gcf_pair_rat_eq_of_nth_contsAux, first_contAux_eq_h_one, contsAux_eq_contsAux_squashGCF_of_le, le_of_succ_succ_get?_contsAux_b, zeroth_contAux_eq_one_zero, fib_le_of_contsAux_b, contsAux_stable_of_terminated, second_contAux_eq, zero_le_of_contsAux_b, sub_convs_eq, SimpContFract.determinant_aux, contsAux_stable_step_of_terminated, contsAux_recurrence
convs 📖CompOp
21 mathmath: of_convergence, convs_stable_of_terminated, ContFract.convs_eq_convs', abs_sub_convergents_le', of_correctness_of_terminates, succ_nth_conv_eq_squashGCF_nth_conv, conv_eq_conts_a_div_conts_b, of_convergence_epsilon, convs_eq_convs', convs_succ, Real.exists_convs_eq_rat, Real.convs_eq_convergent, of_convs_eq_convs', sub_convs_eq, of_correctness_of_nth_stream_eq_none, exists_rat_eq_nth_conv, conv_eq_num_div_den, of_correctness_atTop_of_terminates, zeroth_conv_eq_h, of_correctness_of_terminatedAt, abs_sub_convs_le
convs' 📖CompOp
8 mathmath: ContFract.convs_eq_convs', convs'_succ, zeroth_conv'_eq_h, convs_eq_convs', convs'_of_int, succ_nth_conv'_eq_squashGCF_nth_conv', convs'_stable_of_terminated, of_convs_eq_convs'
convs'Aux 📖CompOp
6 mathmath: convs'Aux_stable_step_of_terminated, convs'Aux_succ_some, succ_succ_nth_conv'Aux_eq_succ_nth_conv'Aux_squashSeq, zeroth_conv'Aux_eq_zero, convs'Aux_stable_of_terminated, convs'Aux_succ_none
dens 📖CompOp
14 mathmath: dens_stable_of_terminated, dens_recurrence, succ_nth_fib_le_of_nth_den, abs_sub_convergents_le', SimpContFract.determinant, zero_le_of_den, den_eq_conts_b, of_den_mono, first_den_eq, zeroth_den_eq_one, le_of_succ_get?_den, conv_eq_num_div_den, abs_sub_convs_le, exists_rat_eq_nth_den
h 📖CompOp
14 mathmath: coe_of_h_rat_eq, first_cont_eq, zeroth_num_eq_h, first_num_eq, zeroth_cont_eq_h_one, zeroth_conv'_eq_h, ext_iff, coe_of_rat_eq, first_contAux_eq_h_one, coe_toGenContFract, of_h_eq_intFractPair_seq1_fst_b, second_contAux_eq, of_h_eq_floor, zeroth_conv_eq_h
instCoe 📖CompOp
instDecidableTerminatedAt 📖CompOp
instInhabited 📖CompOp
instInhabitedPair 📖CompOp
nextConts 📖CompOp
nextDen 📖CompOp
nextNum 📖CompOp
nums 📖CompOp
8 mathmath: nums_stable_of_terminated, exists_rat_eq_nth_num, zeroth_num_eq_h, first_num_eq, SimpContFract.determinant, num_eq_conts_a, nums_recurrence, conv_eq_num_div_den
ofInteger 📖CompOp
partDens 📖CompOp
3 mathmath: partDen_eq_s_b, terminatedAt_iff_partDen_none, partDen_none_iff_s_none
partNums 📖CompOp
3 mathmath: terminatedAt_iff_partNum_none, partNum_eq_s_a, partNum_none_iff_s_none
s 📖CompOp
19 mathmath: coe_of_s_rat_eq, ext_iff, coe_of_rat_eq, of_s_head_aux, coe_of_s_get?_rat_eq, of_s_of_int, of_s_head, coe_toGenContFract, exists_s_b_of_partDen, of_s_tail, get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, partNum_none_iff_s_none, get?_of_eq_some_of_succ_get?_intFractPair_stream, terminatedAt_iff_s_none, exists_s_a_of_partNum, terminatedAt_iff_s_terminatedAt, squashGCF_nth_of_lt, of_s_succ, partDen_none_iff_s_none

Theorems

NameKindAssumesProvesValidatesDepends On
coe_toGenContFract 📖mathematicalcoeFn
h
Stream'.Seq.map
Pair
Pair.coeFn
s
ext 📖h
s
ext_iff 📖mathematicalh
s
ext

GenContFract.Pair

Definitions

NameCategoryTheorems
a 📖CompOp
17 mathmath: GenContFract.dens_recurrence, GenContFract.of_partNum_eq_one_and_exists_int_partDen_eq, GenContFract.first_cont_eq, GenContFract.first_num_eq, GenContFract.conts_recurrenceAux, GenContFract.conv_eq_conts_a_div_conts_b, GenContFract.num_eq_conts_a, GenContFract.convs'Aux_succ_some, GenContFract.nums_recurrence, GenContFract.partNum_eq_s_a, GenContFract.exists_conts_a_of_num, GenContFract.second_contAux_eq, GenContFract.conts_recurrence, GenContFract.exists_s_a_of_partNum, GenContFract.squashSeq_nth_of_not_terminated, SimpContFract.determinant_aux, GenContFract.contsAux_recurrence
b 📖CompOp
23 mathmath: GenContFract.dens_recurrence, GenContFract.of_partNum_eq_one_and_exists_int_partDen_eq, GenContFract.first_cont_eq, GenContFract.exists_conts_b_of_den, GenContFract.first_num_eq, GenContFract.conts_recurrenceAux, GenContFract.conv_eq_conts_a_div_conts_b, GenContFract.convs'Aux_succ_some, GenContFract.nums_recurrence, GenContFract.den_eq_conts_b, GenContFract.first_den_eq, GenContFract.le_of_succ_succ_get?_contsAux_b, GenContFract.exists_s_b_of_partDen, GenContFract.fib_le_of_contsAux_b, GenContFract.partDen_eq_s_b, GenContFract.second_contAux_eq, GenContFract.IntFractPair.exists_succ_get?_stream_of_gcf_of_get?_eq_some, GenContFract.conts_recurrence, GenContFract.zero_le_of_contsAux_b, GenContFract.sub_convs_eq, GenContFract.squashSeq_nth_of_not_terminated, SimpContFract.determinant_aux, GenContFract.contsAux_recurrence
coeFn 📖CompOp
2 mathmath: GenContFract.coe_toGenContFract, coe_toPair
instCoe 📖CompOp
instRepr 📖CompOp
map 📖CompOp
5 mathmath: GenContFract.coe_of_s_rat_eq, GenContFract.exists_gcf_pair_rat_eq_nth_conts, GenContFract.coe_of_rat_eq, GenContFract.exists_gcf_pair_rat_eq_of_nth_contsAux, GenContFract.coe_of_s_get?_rat_eq

Theorems

NameKindAssumesProvesValidatesDepends On
coe_toPair 📖mathematicalcoeFn

GenContFract.instInhabitedPair

Definitions

NameCategoryTheorems
default 📖CompOp

SimpContFract

Definitions

NameCategoryTheorems
IsContFract 📖MathDef
2 mathmath: ContFract.convs_eq_convs', of_isContFract
instCoeGenContFract 📖CompOp
instInhabited 📖CompOp
ofInteger 📖CompOp

(root)

Definitions

NameCategoryTheorems
ContFract 📖CompOp
GenContFract 📖CompData
3 mathmath: ContFract.convs_eq_convs', SimpContFract.determinant, SimpContFract.determinant_aux
SimpContFract 📖CompOp
1 mathmath: ContFract.convs_eq_convs'

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