Step |
Hyp |
Ref |
Expression |
1 |
|
elnn0 |
|
2 |
|
nnm1nn0 |
|
3 |
|
nn0uz |
|
4 |
2 3
|
eleqtrdi |
|
5 |
|
elfznn0 |
|
6 |
5
|
adantl |
|
7 |
6
|
nn0cnd |
|
8 |
|
id |
|
9 |
4 7 8
|
fsum1p |
|
10 |
|
1e0p1 |
|
11 |
10
|
oveq1i |
|
12 |
11
|
sumeq1i |
|
13 |
12
|
oveq2i |
|
14 |
|
fzfid |
|
15 |
|
elfznn |
|
16 |
15
|
adantl |
|
17 |
16
|
nncnd |
|
18 |
14 17
|
fsumcl |
|
19 |
18
|
addid2d |
|
20 |
13 19
|
syl5eqr |
|
21 |
|
arisum |
|
22 |
2 21
|
syl |
|
23 |
|
nncn |
|
24 |
23
|
2timesd |
|
25 |
24
|
oveq2d |
|
26 |
23
|
sqcld |
|
27 |
26 23 23
|
subsub4d |
|
28 |
25 27
|
eqtr4d |
|
29 |
28
|
oveq1d |
|
30 |
|
binom2sub1 |
|
31 |
23 30
|
syl |
|
32 |
26 23
|
subcld |
|
33 |
|
1cnd |
|
34 |
32 23 33
|
subsubd |
|
35 |
29 31 34
|
3eqtr4d |
|
36 |
35
|
oveq1d |
|
37 |
|
ax-1cn |
|
38 |
|
subcl |
|
39 |
23 37 38
|
sylancl |
|
40 |
32 39
|
npcand |
|
41 |
36 40
|
eqtrd |
|
42 |
41
|
oveq1d |
|
43 |
22 42
|
eqtrd |
|
44 |
20 43
|
eqtrd |
|
45 |
9 44
|
eqtrd |
|
46 |
|
oveq1 |
|
47 |
46
|
oveq2d |
|
48 |
|
0re |
|
49 |
|
ltm1 |
|
50 |
48 49
|
ax-mp |
|
51 |
|
0z |
|
52 |
|
peano2zm |
|
53 |
51 52
|
ax-mp |
|
54 |
|
fzn |
|
55 |
51 53 54
|
mp2an |
|
56 |
50 55
|
mpbi |
|
57 |
47 56
|
eqtrdi |
|
58 |
57
|
sumeq1d |
|
59 |
|
sum0 |
|
60 |
58 59
|
eqtrdi |
|
61 |
|
sq0i |
|
62 |
|
id |
|
63 |
61 62
|
oveq12d |
|
64 |
|
0m0e0 |
|
65 |
63 64
|
eqtrdi |
|
66 |
65
|
oveq1d |
|
67 |
|
2cn |
|
68 |
|
2ne0 |
|
69 |
67 68
|
div0i |
|
70 |
66 69
|
eqtrdi |
|
71 |
60 70
|
eqtr4d |
|
72 |
45 71
|
jaoi |
|
73 |
1 72
|
sylbi |
|