Step |
Hyp |
Ref |
Expression |
1 |
|
dia2dimlem2.l |
|
2 |
|
dia2dimlem2.j |
|
3 |
|
dia2dimlem2.m |
|
4 |
|
dia2dimlem2.a |
|
5 |
|
dia2dimlem2.h |
|
6 |
|
dia2dimlem2.t |
|
7 |
|
dia2dimlem2.r |
|
8 |
|
dia2dimlem2.q |
|
9 |
|
dia2dimlem2.k |
|
10 |
|
dia2dimlem2.u |
|
11 |
|
dia2dimlem2.v |
|
12 |
|
dia2dimlem2.p |
|
13 |
|
dia2dimlem2.f |
|
14 |
|
dia2dimlem2.rf |
|
15 |
|
dia2dimlem2.rv |
|
16 |
|
dia2dimlem2.g |
|
17 |
|
dia2dimlem2.gv |
|
18 |
9
|
simpld |
|
19 |
18
|
hllatd |
|
20 |
12
|
simpld |
|
21 |
|
eqid |
|
22 |
21 4
|
atbase |
|
23 |
20 22
|
syl |
|
24 |
10
|
simpld |
|
25 |
21 4
|
atbase |
|
26 |
24 25
|
syl |
|
27 |
21 1 2
|
latlej2 |
|
28 |
19 23 26 27
|
syl3anc |
|
29 |
21 2 4
|
hlatjcl |
|
30 |
18 20 24 29
|
syl3anc |
|
31 |
21 1 3
|
latleeqm2 |
|
32 |
19 26 30 31
|
syl3anc |
|
33 |
28 32
|
mpbid |
|
34 |
1 4 5 6 7
|
trlat |
|
35 |
9 12 13 34
|
syl3anc |
|
36 |
11
|
simpld |
|
37 |
1 2 4
|
hlatexch2 |
|
38 |
18 35 24 36 15 37
|
syl131anc |
|
39 |
14 38
|
mpd |
|
40 |
13
|
simpld |
|
41 |
1 2 3 4 5 6 7
|
trlval2 |
|
42 |
9 40 12 41
|
syl3anc |
|
43 |
42
|
oveq1d |
|
44 |
1 4 5 6
|
ltrnel |
|
45 |
9 40 12 44
|
syl3anc |
|
46 |
45
|
simpld |
|
47 |
21 2 4
|
hlatjcl |
|
48 |
18 20 46 47
|
syl3anc |
|
49 |
9
|
simprd |
|
50 |
21 5
|
lhpbase |
|
51 |
49 50
|
syl |
|
52 |
11
|
simprd |
|
53 |
21 1 2 3 4
|
atmod4i1 |
|
54 |
18 36 48 51 52 53
|
syl131anc |
|
55 |
2 4
|
hlatjass |
|
56 |
18 20 46 36 55
|
syl13anc |
|
57 |
56
|
oveq1d |
|
58 |
54 57
|
eqtrd |
|
59 |
43 58
|
eqtrd |
|
60 |
39 59
|
breqtrd |
|
61 |
21 2 4
|
hlatjcl |
|
62 |
18 46 36 61
|
syl3anc |
|
63 |
21 2
|
latjcl |
|
64 |
19 23 62 63
|
syl3anc |
|
65 |
21 3
|
latmcl |
|
66 |
19 64 51 65
|
syl3anc |
|
67 |
21 1 3
|
latmlem2 |
|
68 |
19 26 66 30 67
|
syl13anc |
|
69 |
60 68
|
mpd |
|
70 |
33 69
|
eqbrtrrd |
|
71 |
1 2 3 4 5 6 7
|
trlval2 |
|
72 |
9 16 12 71
|
syl3anc |
|
73 |
17 8
|
eqtrdi |
|
74 |
73
|
oveq2d |
|
75 |
74
|
oveq1d |
|
76 |
1 2 4
|
hlatlej1 |
|
77 |
18 20 24 76
|
syl3anc |
|
78 |
21 1 2 3 4
|
atmod3i1 |
|
79 |
18 20 30 62 77 78
|
syl131anc |
|
80 |
79
|
oveq1d |
|
81 |
|
hlol |
|
82 |
18 81
|
syl |
|
83 |
21 3
|
latmassOLD |
|
84 |
82 30 64 51 83
|
syl13anc |
|
85 |
80 84
|
eqtrd |
|
86 |
75 85
|
eqtrd |
|
87 |
72 86
|
eqtrd |
|
88 |
87
|
eqcomd |
|
89 |
70 88
|
breqtrd |
|
90 |
|
hlatl |
|
91 |
18 90
|
syl |
|
92 |
|
hlop |
|
93 |
18 92
|
syl |
|
94 |
|
eqid |
|
95 |
|
eqid |
|
96 |
94 95 4
|
0ltat |
|
97 |
93 24 96
|
syl2anc |
|
98 |
|
hlpos |
|
99 |
18 98
|
syl |
|
100 |
21 94
|
op0cl |
|
101 |
93 100
|
syl |
|
102 |
21 5 6 7
|
trlcl |
|
103 |
9 16 102
|
syl2anc |
|
104 |
21 1 95
|
pltletr |
|
105 |
99 101 26 103 104
|
syl13anc |
|
106 |
97 89 105
|
mp2and |
|
107 |
21 95 94
|
opltn0 |
|
108 |
93 103 107
|
syl2anc |
|
109 |
106 108
|
mpbid |
|
110 |
109
|
neneqd |
|
111 |
94 4 5 6 7
|
trlator0 |
|
112 |
9 16 111
|
syl2anc |
|
113 |
112
|
orcomd |
|
114 |
113
|
ord |
|
115 |
110 114
|
mpd |
|
116 |
1 4
|
atcmp |
|
117 |
91 24 115 116
|
syl3anc |
|
118 |
89 117
|
mpbid |
|
119 |
118
|
eqcomd |
|