Step |
Hyp |
Ref |
Expression |
1 |
|
djaj.k |
|
2 |
|
djaj.h |
|
3 |
|
djaj.i |
|
4 |
|
djaj.j |
|
5 |
|
hllat |
|
6 |
5
|
ad2antrr |
|
7 |
|
hlop |
|
8 |
7
|
ad2antrr |
|
9 |
|
eqid |
|
10 |
9 2 3
|
diadmclN |
|
11 |
10
|
adantrr |
|
12 |
|
eqid |
|
13 |
9 12
|
opoccl |
|
14 |
8 11 13
|
syl2anc |
|
15 |
9 2
|
lhpbase |
|
16 |
15
|
ad2antlr |
|
17 |
9 12
|
opoccl |
|
18 |
8 16 17
|
syl2anc |
|
19 |
9 1
|
latjcl |
|
20 |
6 14 18 19
|
syl3anc |
|
21 |
|
eqid |
|
22 |
9 21
|
latmcl |
|
23 |
6 20 16 22
|
syl3anc |
|
24 |
9 2 3
|
diadmclN |
|
25 |
24
|
adantrl |
|
26 |
9 12
|
opoccl |
|
27 |
8 25 26
|
syl2anc |
|
28 |
9 1
|
latjcl |
|
29 |
6 27 18 28
|
syl3anc |
|
30 |
9 21
|
latmcl |
|
31 |
6 29 16 30
|
syl3anc |
|
32 |
9 21
|
latmcl |
|
33 |
6 23 31 32
|
syl3anc |
|
34 |
|
eqid |
|
35 |
9 34 21
|
latmle2 |
|
36 |
6 23 31 35
|
syl3anc |
|
37 |
9 34 21
|
latmle2 |
|
38 |
6 29 16 37
|
syl3anc |
|
39 |
9 34 6 33 31 16 36 38
|
lattrd |
|
40 |
9 34 2 3
|
diaeldm |
|
41 |
40
|
adantr |
|
42 |
33 39 41
|
mpbir2and |
|
43 |
|
eqid |
|
44 |
|
eqid |
|
45 |
1 21 12 2 43 3 44
|
diaocN |
|
46 |
42 45
|
syldan |
|
47 |
|
hloml |
|
48 |
47
|
ad2antrr |
|
49 |
9 1
|
latjcl |
|
50 |
6 11 25 49
|
syl3anc |
|
51 |
34 2 3
|
diadmleN |
|
52 |
51
|
adantrr |
|
53 |
34 2 3
|
diadmleN |
|
54 |
53
|
adantrl |
|
55 |
9 34 1
|
latjle12 |
|
56 |
6 11 25 16 55
|
syl13anc |
|
57 |
52 54 56
|
mpbi2and |
|
58 |
9 34 1 21 12
|
omlspjN |
|
59 |
48 50 16 57 58
|
syl121anc |
|
60 |
9 1
|
latjidm |
|
61 |
6 18 60
|
syl2anc |
|
62 |
61
|
oveq2d |
|
63 |
9 1
|
latjass |
|
64 |
6 50 18 18 63
|
syl13anc |
|
65 |
|
hlol |
|
66 |
65
|
ad2antrr |
|
67 |
9 1 21 12
|
oldmm2 |
|
68 |
66 50 16 67
|
syl3anc |
|
69 |
9 1 21 12
|
oldmj1 |
|
70 |
66 11 25 69
|
syl3anc |
|
71 |
9 34 21
|
latleeqm1 |
|
72 |
6 11 16 71
|
syl3anc |
|
73 |
52 72
|
mpbid |
|
74 |
73
|
fveq2d |
|
75 |
9 1 21 12
|
oldmm1 |
|
76 |
66 11 16 75
|
syl3anc |
|
77 |
74 76
|
eqtr3d |
|
78 |
9 34 21
|
latleeqm1 |
|
79 |
6 25 16 78
|
syl3anc |
|
80 |
54 79
|
mpbid |
|
81 |
80
|
fveq2d |
|
82 |
9 1 21 12
|
oldmm1 |
|
83 |
66 25 16 82
|
syl3anc |
|
84 |
81 83
|
eqtr3d |
|
85 |
77 84
|
oveq12d |
|
86 |
70 85
|
eqtrd |
|
87 |
86
|
oveq1d |
|
88 |
9 21
|
latmmdir |
|
89 |
66 20 29 16 88
|
syl13anc |
|
90 |
87 89
|
eqtrd |
|
91 |
90
|
fveq2d |
|
92 |
68 91
|
eqtr3d |
|
93 |
92
|
oveq1d |
|
94 |
64 93
|
eqtr3d |
|
95 |
62 94
|
eqtr3d |
|
96 |
95
|
oveq1d |
|
97 |
59 96
|
eqtr3d |
|
98 |
97
|
fveq2d |
|
99 |
|
simpl |
|
100 |
2 3
|
diaclN |
|
101 |
100
|
adantrr |
|
102 |
2 43 3
|
diaelrnN |
|
103 |
101 102
|
syldan |
|
104 |
2 3
|
diaclN |
|
105 |
104
|
adantrl |
|
106 |
2 43 3
|
diaelrnN |
|
107 |
105 106
|
syldan |
|
108 |
2 43 3 44 4
|
djavalN |
|
109 |
99 103 107 108
|
syl12anc |
|
110 |
9 34 21
|
latmle2 |
|
111 |
6 20 16 110
|
syl3anc |
|
112 |
9 34 2 3
|
diaeldm |
|
113 |
112
|
adantr |
|
114 |
23 111 113
|
mpbir2and |
|
115 |
9 34 2 3
|
diaeldm |
|
116 |
115
|
adantr |
|
117 |
31 38 116
|
mpbir2and |
|
118 |
21 2 3
|
diameetN |
|
119 |
99 114 117 118
|
syl12anc |
|
120 |
1 21 12 2 43 3 44
|
diaocN |
|
121 |
120
|
adantrr |
|
122 |
1 21 12 2 43 3 44
|
diaocN |
|
123 |
122
|
adantrl |
|
124 |
121 123
|
ineq12d |
|
125 |
119 124
|
eqtrd |
|
126 |
125
|
fveq2d |
|
127 |
109 126
|
eqtr4d |
|
128 |
46 98 127
|
3eqtr4d |
|