Step |
Hyp |
Ref |
Expression |
1 |
|
abelth.1 |
|
2 |
|
abelth.2 |
|
3 |
|
abelth.3 |
|
4 |
|
abelth.4 |
|
5 |
|
abelth.5 |
|
6 |
|
abelth.6 |
|
7 |
|
abelth.7 |
|
8 |
|
nn0uz |
|
9 |
|
0zd |
|
10 |
|
id |
|
11 |
3 4
|
ge0p1rpd |
|
12 |
|
rpdivcl |
|
13 |
10 11 12
|
syl2anr |
|
14 |
|
eqidd |
|
15 |
7
|
adantr |
|
16 |
8 9 13 14 15
|
climi0 |
|
17 |
13
|
adantr |
|
18 |
|
fzfid |
|
19 |
|
0zd |
|
20 |
1
|
ffvelrnda |
|
21 |
8 19 20
|
serf |
|
22 |
|
elfznn0 |
|
23 |
|
ffvelrn |
|
24 |
21 22 23
|
syl2an |
|
25 |
24
|
abscld |
|
26 |
18 25
|
fsumrecl |
|
27 |
26
|
ad2antrr |
|
28 |
24
|
absge0d |
|
29 |
18 25 28
|
fsumge0 |
|
30 |
29
|
ad2antrr |
|
31 |
27 30
|
ge0p1rpd |
|
32 |
17 31
|
rpdivcld |
|
33 |
1 2 3 4 5
|
abelthlem2 |
|
34 |
33
|
simpld |
|
35 |
|
oveq1 |
|
36 |
|
nn0z |
|
37 |
|
1exp |
|
38 |
36 37
|
syl |
|
39 |
35 38
|
sylan9eq |
|
40 |
39
|
oveq2d |
|
41 |
40
|
sumeq2dv |
|
42 |
|
sumex |
|
43 |
41 6 42
|
fvmpt |
|
44 |
34 43
|
syl |
|
45 |
1
|
ffvelrnda |
|
46 |
45
|
mulid1d |
|
47 |
46
|
eqcomd |
|
48 |
46 45
|
eqeltrd |
|
49 |
8 19 47 48 7
|
isumclim |
|
50 |
44 49
|
eqtrd |
|
51 |
50
|
adantr |
|
52 |
51
|
oveq1d |
|
53 |
|
df-neg |
|
54 |
52 53
|
eqtr4di |
|
55 |
54
|
fveq2d |
|
56 |
1 2 3 4 5 6
|
abelthlem4 |
|
57 |
56
|
ffvelrnda |
|
58 |
57
|
absnegd |
|
59 |
55 58
|
eqtrd |
|
60 |
59
|
adantlr |
|
61 |
60
|
ad2ant2r |
|
62 |
|
fveq2 |
|
63 |
62 50
|
sylan9eqr |
|
64 |
63
|
abs00bd |
|
65 |
64
|
ad5ant15 |
|
66 |
|
simpllr |
|
67 |
66
|
rpgt0d |
|
68 |
67
|
adantr |
|
69 |
65 68
|
eqbrtrd |
|
70 |
1
|
ad3antrrr |
|
71 |
2
|
ad3antrrr |
|
72 |
3
|
ad3antrrr |
|
73 |
4
|
ad3antrrr |
|
74 |
7
|
ad3antrrr |
|
75 |
|
simprll |
|
76 |
|
simprr |
|
77 |
|
eldifsn |
|
78 |
75 76 77
|
sylanbrc |
|
79 |
13
|
ad2antrr |
|
80 |
|
simplrl |
|
81 |
|
simplrr |
|
82 |
|
2fveq3 |
|
83 |
82
|
breq1d |
|
84 |
83
|
cbvralvw |
|
85 |
81 84
|
sylib |
|
86 |
|
simprlr |
|
87 |
|
2fveq3 |
|
88 |
87
|
cbvsumv |
|
89 |
88
|
oveq1i |
|
90 |
89
|
oveq2i |
|
91 |
86 90
|
breqtrdi |
|
92 |
70 71 72 73 5 6 74 78 79 80 85 91
|
abelthlem7 |
|
93 |
|
rpcn |
|
94 |
93
|
adantl |
|
95 |
11
|
adantr |
|
96 |
95
|
rpcnd |
|
97 |
95
|
rpne0d |
|
98 |
94 96 97
|
divcan2d |
|
99 |
98
|
ad2antrr |
|
100 |
92 99
|
breqtrd |
|
101 |
100
|
anassrs |
|
102 |
69 101
|
pm2.61dane |
|
103 |
61 102
|
eqbrtrd |
|
104 |
103
|
expr |
|
105 |
104
|
ralrimiva |
|
106 |
|
breq2 |
|
107 |
106
|
rspceaimv |
|
108 |
32 105 107
|
syl2anc |
|
109 |
16 108
|
rexlimddv |
|