Step |
Hyp |
Ref |
Expression |
1 |
|
hgmapadd.h |
|
2 |
|
hgmapadd.u |
|
3 |
|
hgmapadd.r |
|
4 |
|
hgmapadd.b |
|
5 |
|
hgmapadd.p |
|
6 |
|
hgmapadd.g |
|
7 |
|
hgmapadd.k |
|
8 |
|
hgmapadd.x |
|
9 |
|
hgmapadd.y |
|
10 |
|
eqid |
|
11 |
|
eqid |
|
12 |
1 2 10 11 7
|
dvh1dim |
|
13 |
|
eqid |
|
14 |
1 13 7
|
lcdlmod |
|
15 |
14
|
3ad2ant1 |
|
16 |
|
eqid |
|
17 |
|
eqid |
|
18 |
7
|
3ad2ant1 |
|
19 |
8
|
3ad2ant1 |
|
20 |
1 2 3 4 13 16 17 6 18 19
|
hgmapdcl |
|
21 |
1 2 3 4 13 16 17 6 7 9
|
hgmapdcl |
|
22 |
21
|
3ad2ant1 |
|
23 |
|
eqid |
|
24 |
|
eqid |
|
25 |
|
simp2 |
|
26 |
1 2 10 13 23 24 18 25
|
hdmapcl |
|
27 |
|
eqid |
|
28 |
|
eqid |
|
29 |
|
eqid |
|
30 |
23 27 16 28 17 29
|
lmodvsdir |
|
31 |
15 20 22 26 30
|
syl13anc |
|
32 |
1 2 7
|
dvhlmod |
|
33 |
32
|
3ad2ant1 |
|
34 |
9
|
3ad2ant1 |
|
35 |
|
eqid |
|
36 |
|
eqid |
|
37 |
10 35 3 36 4 5
|
lmodvsdir |
|
38 |
33 19 34 25 37
|
syl13anc |
|
39 |
38
|
fveq2d |
|
40 |
10 3 36 4
|
lmodvscl |
|
41 |
33 19 25 40
|
syl3anc |
|
42 |
10 3 36 4
|
lmodvscl |
|
43 |
33 34 25 42
|
syl3anc |
|
44 |
1 2 10 35 13 27 24 18 41 43
|
hdmapadd |
|
45 |
1 2 10 36 3 4 13 28 24 6 18 25 19
|
hgmapvs |
|
46 |
1 2 10 36 3 4 13 28 24 6 18 25 34
|
hgmapvs |
|
47 |
45 46
|
oveq12d |
|
48 |
39 44 47
|
3eqtrrd |
|
49 |
3 4 5
|
lmodacl |
|
50 |
32 8 9 49
|
syl3anc |
|
51 |
50
|
3ad2ant1 |
|
52 |
1 2 10 36 3 4 13 28 24 6 18 25 51
|
hgmapvs |
|
53 |
31 48 52
|
3eqtrrd |
|
54 |
|
eqid |
|
55 |
1 13 7
|
lcdlvec |
|
56 |
55
|
3ad2ant1 |
|
57 |
1 2 3 4 13 16 17 6 7 50
|
hgmapdcl |
|
58 |
57
|
3ad2ant1 |
|
59 |
1 2 3 4 13 16 17 6 7 8
|
hgmapdcl |
|
60 |
16 17 29
|
lmodacl |
|
61 |
14 59 21 60
|
syl3anc |
|
62 |
61
|
3ad2ant1 |
|
63 |
|
simp3 |
|
64 |
1 2 10 11 13 54 24 18 25
|
hdmapeq0 |
|
65 |
64
|
necon3bid |
|
66 |
63 65
|
mpbird |
|
67 |
23 28 16 17 54 56 58 62 26 66
|
lvecvscan2 |
|
68 |
53 67
|
mpbid |
|
69 |
68
|
rexlimdv3a |
|
70 |
12 69
|
mpd |
|
71 |
1 2 3 5 13 16 29 7
|
lcdsadd |
|
72 |
71
|
oveqd |
|
73 |
70 72
|
eqtrd |
|