Step |
Hyp |
Ref |
Expression |
1 |
|
eqeq2 |
|
2 |
|
oveq2 |
|
3 |
|
fzo01 |
|
4 |
2 3
|
eqtrdi |
|
5 |
4
|
sumeq1d |
|
6 |
5
|
eqeq2d |
|
7 |
1 6
|
imbi12d |
|
8 |
7
|
ralbidv |
|
9 |
|
eqeq2 |
|
10 |
|
oveq2 |
|
11 |
10
|
sumeq1d |
|
12 |
11
|
eqeq2d |
|
13 |
9 12
|
imbi12d |
|
14 |
13
|
ralbidv |
|
15 |
|
eqeq2 |
|
16 |
|
oveq2 |
|
17 |
16
|
sumeq1d |
|
18 |
17
|
eqeq2d |
|
19 |
15 18
|
imbi12d |
|
20 |
19
|
ralbidv |
|
21 |
|
eqeq2 |
|
22 |
|
oveq2 |
|
23 |
22
|
sumeq1d |
|
24 |
23
|
eqeq2d |
|
25 |
21 24
|
imbi12d |
|
26 |
25
|
ralbidv |
|
27 |
|
0cnd |
|
28 |
|
2nn |
|
29 |
28
|
a1i |
|
30 |
|
0zd |
|
31 |
|
nn0rp0 |
|
32 |
|
digvalnn0 |
|
33 |
29 30 31 32
|
syl3anc |
|
34 |
33
|
nn0cnd |
|
35 |
|
1cnd |
|
36 |
34 35
|
mulcld |
|
37 |
27 36
|
jca |
|
38 |
37
|
adantr |
|
39 |
|
oveq1 |
|
40 |
|
oveq2 |
|
41 |
|
2cn |
|
42 |
|
exp0 |
|
43 |
41 42
|
ax-mp |
|
44 |
40 43
|
eqtrdi |
|
45 |
39 44
|
oveq12d |
|
46 |
45
|
sumsn |
|
47 |
38 46
|
syl |
|
48 |
34
|
adantr |
|
49 |
48
|
mulid1d |
|
50 |
|
blen1b |
|
51 |
50
|
biimpa |
|
52 |
|
vex |
|
53 |
52
|
elpr |
|
54 |
51 53
|
sylibr |
|
55 |
|
0dig2pr01 |
|
56 |
54 55
|
syl |
|
57 |
47 49 56
|
3eqtrrd |
|
58 |
57
|
ex |
|
59 |
58
|
rgen |
|
60 |
|
nn0sumshdiglem1 |
|
61 |
8 14 20 26 59 60
|
nnind |
|