Step |
Hyp |
Ref |
Expression |
1 |
|
gausslemma2d.p |
|
2 |
|
gausslemma2d.h |
|
3 |
|
gausslemma2d.r |
|
4 |
|
gausslemma2d.m |
|
5 |
|
gausslemma2d.n |
|
6 |
1 2 3 4 5
|
gausslemma2dlem7 |
|
7 |
|
eldifi |
|
8 |
|
prmnn |
|
9 |
8
|
nnred |
|
10 |
|
prmgt1 |
|
11 |
9 10
|
jca |
|
12 |
|
1mod |
|
13 |
1 7 11 12
|
4syl |
|
14 |
13
|
eqcomd |
|
15 |
14
|
eqeq2d |
|
16 |
|
neg1z |
|
17 |
1 4 2 5
|
gausslemma2dlem0h |
|
18 |
|
zexpcl |
|
19 |
16 17 18
|
sylancr |
|
20 |
|
2nn |
|
21 |
20
|
a1i |
|
22 |
1 2
|
gausslemma2dlem0b |
|
23 |
22
|
nnnn0d |
|
24 |
21 23
|
nnexpcld |
|
25 |
24
|
nnzd |
|
26 |
19 25
|
zmulcld |
|
27 |
26
|
zred |
|
28 |
|
1red |
|
29 |
27 28
|
jca |
|
30 |
29
|
adantr |
|
31 |
1
|
gausslemma2dlem0a |
|
32 |
31
|
nnrpd |
|
33 |
19 32
|
jca |
|
34 |
33
|
adantr |
|
35 |
|
simpr |
|
36 |
|
modmul1 |
|
37 |
30 34 35 36
|
syl3anc |
|
38 |
37
|
ex |
|
39 |
19
|
zcnd |
|
40 |
24
|
nncnd |
|
41 |
39 40 39
|
mul32d |
|
42 |
17
|
nn0cnd |
|
43 |
42
|
2timesd |
|
44 |
43
|
eqcomd |
|
45 |
44
|
oveq2d |
|
46 |
|
neg1cn |
|
47 |
46
|
a1i |
|
48 |
47 17 17
|
expaddd |
|
49 |
17
|
nn0zd |
|
50 |
|
m1expeven |
|
51 |
49 50
|
syl |
|
52 |
45 48 51
|
3eqtr3d |
|
53 |
52
|
oveq1d |
|
54 |
40
|
mullidd |
|
55 |
41 53 54
|
3eqtrd |
|
56 |
55
|
oveq1d |
|
57 |
39
|
mullidd |
|
58 |
57
|
oveq1d |
|
59 |
56 58
|
eqeq12d |
|
60 |
2
|
oveq2i |
|
61 |
60
|
oveq1i |
|
62 |
61
|
eqeq1i |
|
63 |
|
2z |
|
64 |
|
lgsvalmod |
|
65 |
63 1 64
|
sylancr |
|
66 |
65
|
eqcomd |
|
67 |
66
|
eqeq1d |
|
68 |
1 4 2 5
|
gausslemma2dlem0i |
|
69 |
67 68
|
sylbid |
|
70 |
62 69
|
biimtrid |
|
71 |
59 70
|
sylbid |
|
72 |
38 71
|
syld |
|
73 |
15 72
|
sylbid |
|
74 |
6 73
|
mpd |
|