Step |
Hyp |
Ref |
Expression |
1 |
|
hdmapglem7.h |
|
2 |
|
hdmapglem7.e |
|
3 |
|
hdmapglem7.o |
|
4 |
|
hdmapglem7.u |
|
5 |
|
hdmapglem7.v |
|
6 |
|
hdmapglem7.p |
|
7 |
|
hdmapglem7.q |
|
8 |
|
hdmapglem7.r |
|
9 |
|
hdmapglem7.b |
|
10 |
|
hdmapglem7.a |
|
11 |
|
hdmapglem7.n |
|
12 |
|
hdmapglem7.k |
|
13 |
|
hdmapglem7.x |
|
14 |
|
hdmapglem7.t |
|
15 |
|
hdmapglem7.z |
|
16 |
|
hdmapglem7.c |
|
17 |
|
hdmapglem7.s |
|
18 |
|
hdmapglem7.g |
|
19 |
|
hdmapglem7.y |
|
20 |
1 2 3 4 5 6 7 8 9 10 11 12 13
|
hdmapglem7a |
|
21 |
1 2 3 4 5 6 7 8 9 10 11 12 19
|
hdmapglem7a |
|
22 |
12
|
ad2antrr |
|
23 |
1 4 12
|
dvhlmod |
|
24 |
8
|
lmodring |
|
25 |
23 24
|
syl |
|
26 |
25
|
ad2antrr |
|
27 |
|
simplrr |
|
28 |
|
simprr |
|
29 |
1 4 8 9 18 22 28
|
hgmapcl |
|
30 |
9 14
|
ringcl |
|
31 |
26 27 29 30
|
syl3anc |
|
32 |
|
eqid |
|
33 |
|
eqid |
|
34 |
|
eqid |
|
35 |
1 32 33 4 5 34 2 12
|
dvheveccl |
|
36 |
35
|
eldifad |
|
37 |
36
|
snssd |
|
38 |
1 4 5 3
|
dochssv |
|
39 |
12 37 38
|
syl2anc |
|
40 |
39
|
ad2antrr |
|
41 |
|
simplrl |
|
42 |
40 41
|
sseldd |
|
43 |
|
simprl |
|
44 |
40 43
|
sseldd |
|
45 |
1 4 5 8 9 17 22 42 44
|
hdmapipcl |
|
46 |
1 4 8 9 16 18 22 31 45
|
hgmapadd |
|
47 |
1 4 8 9 14 18 22 27 29
|
hgmapmul |
|
48 |
1 4 8 9 18 22 28
|
hgmapvv |
|
49 |
48
|
oveq1d |
|
50 |
47 49
|
eqtrd |
|
51 |
|
eqid |
|
52 |
1 2 3 4 5 6 51 7 8 9 14 15 17 18 22 41 43 27 27
|
hdmapglem5 |
|
53 |
50 52
|
oveq12d |
|
54 |
46 53
|
eqtrd |
|
55 |
13
|
ad2antrr |
|
56 |
1 2 3 4 5 6 7 8 9 10 11 22 55 14 15 16 17 18 43 41 28 27
|
hdmapglem7b |
|
57 |
56
|
fveq2d |
|
58 |
1 2 3 4 5 6 7 8 9 10 11 22 55 14 15 16 17 18 41 43 27 28
|
hdmapglem7b |
|
59 |
54 57 58
|
3eqtr4d |
|
60 |
59
|
3adantl3 |
|
61 |
60
|
3adant3 |
|
62 |
|
simp3 |
|
63 |
62
|
fveq2d |
|
64 |
|
simp13 |
|
65 |
63 64
|
fveq12d |
|
66 |
65
|
fveq2d |
|
67 |
64
|
fveq2d |
|
68 |
67 62
|
fveq12d |
|
69 |
61 66 68
|
3eqtr4d |
|
70 |
69
|
3exp |
|
71 |
70
|
rexlimdvv |
|
72 |
71
|
3exp |
|
73 |
72
|
rexlimdvv |
|
74 |
20 21 73
|
mp2d |
|