Proof of Theorem cdleme22eALTN
Step | Hyp | Ref
| Expression |
1 | | cdleme22eALT.n |
. . 3
|
2 | | simp11 1091 |
. . . . 5
|
3 | | hllat 34650 |
. . . . 5
|
4 | 2, 3 | syl 17 |
. . . 4
|
5 | | simp21l 1178 |
. . . . 5
|
6 | | simp22l 1180 |
. . . . 5
|
7 | | eqid 2622 |
. . . . . 6
|
8 | | cdleme22.j |
. . . . . 6
|
9 | | cdleme22.a |
. . . . . 6
|
10 | 7, 8, 9 | hlatjcl 34653 |
. . . . 5
|
11 | 2, 5, 6, 10 | syl3anc 1326 |
. . . 4
|
12 | | simp12 1092 |
. . . . . 6
|
13 | | simp3ll 1132 |
. . . . . . 7
|
14 | 13 | 3ad2ant3 1084 |
. . . . . 6
|
15 | | cdleme22.l |
. . . . . . 7
|
16 | | cdleme22.m |
. . . . . . 7
|
17 | | cdleme22.h |
. . . . . . 7
|
18 | | cdleme22eALT.u |
. . . . . . 7
|
19 | | cdleme22eALT.f |
. . . . . . 7
|
20 | 15, 8, 16, 9, 17, 18, 19, 7 | cdleme1b 35513 |
. . . . . 6
|
21 | 2, 12, 5, 6, 14, 20 | syl23anc 1333 |
. . . . 5
|
22 | | simp31 1097 |
. . . . . . 7
|
23 | 7, 8, 9 | hlatjcl 34653 |
. . . . . . 7
|
24 | 2, 22, 14, 23 | syl3anc 1326 |
. . . . . 6
|
25 | 7, 17 | lhpbase 35284 |
. . . . . . 7
|
26 | 12, 25 | syl 17 |
. . . . . 6
|
27 | 7, 16 | latmcl 17052 |
. . . . . 6
|
28 | 4, 24, 26, 27 | syl3anc 1326 |
. . . . 5
|
29 | 7, 8 | latjcl 17051 |
. . . . 5
|
30 | 4, 21, 28, 29 | syl3anc 1326 |
. . . 4
|
31 | 7, 15, 16 | latmle1 17076 |
. . . 4
|
32 | 4, 11, 30, 31 | syl3anc 1326 |
. . 3
|
33 | 1, 32 | syl5eqbr 4688 |
. 2
|
34 | | simp21 1094 |
. . . . 5
|
35 | | simp13 1093 |
. . . . 5
|
36 | | simp321 1211 |
. . . . . 6
|
37 | | simp322 1212 |
. . . . . 6
|
38 | 36, 37 | jca 554 |
. . . . 5
|
39 | | simp23 1096 |
. . . . 5
|
40 | | simp323 1213 |
. . . . 5
|
41 | 15, 8, 16, 9, 17, 18 | cdleme22a 35628 |
. . . . 5
|
42 | 2, 12, 34, 6, 35, 38, 39, 40, 41 | syl233anc 1355 |
. . . 4
|
43 | 42 | oveq2d 6666 |
. . 3
|
44 | | cdleme22eALT.o |
. . . . 5
|
45 | 44 | oveq1i 6660 |
. . . 4
|
46 | | simp21r 1179 |
. . . . . 6
|
47 | 15, 8, 16, 9, 17, 18 | cdleme0a 35498 |
. . . . . 6
|
48 | 2, 12, 5, 46, 6, 39, 47 | syl222anc 1342 |
. . . . 5
|
49 | | simp3rl 1134 |
. . . . . . . 8
|
50 | 49 | 3ad2ant3 1084 |
. . . . . . 7
|
51 | | cdleme22eALT.g |
. . . . . . . 8
|
52 | 15, 8, 16, 9, 17, 18, 51, 7 | cdleme1b 35513 |
. . . . . . 7
|
53 | 2, 12, 5, 6, 50, 52 | syl23anc 1333 |
. . . . . 6
|
54 | 7, 8, 9 | hlatjcl 34653 |
. . . . . . . 8
|
55 | 2, 35, 50, 54 | syl3anc 1326 |
. . . . . . 7
|
56 | 7, 16 | latmcl 17052 |
. . . . . . 7
|
57 | 4, 55, 26, 56 | syl3anc 1326 |
. . . . . 6
|
58 | 7, 8 | latjcl 17051 |
. . . . . 6
|
59 | 4, 53, 57, 58 | syl3anc 1326 |
. . . . 5
|
60 | 15, 8, 16, 9, 17, 18 | cdlemeulpq 35507 |
. . . . . 6
|
61 | 2, 12, 5, 6, 60 | syl22anc 1327 |
. . . . 5
|
62 | 7, 15, 8, 16, 9 | atmod2i1 35147 |
. . . . 5
|
63 | 2, 48, 11, 59, 61, 62 | syl131anc 1339 |
. . . 4
|
64 | 45, 63 | syl5req 2669 |
. . 3
|
65 | 42 | oveq2d 6666 |
. . . . . 6
|
66 | 40, 65 | eqtr3d 2658 |
. . . . 5
|
67 | 7, 8, 9 | hlatjcl 34653 |
. . . . . . . 8
|
68 | 2, 35, 48, 67 | syl3anc 1326 |
. . . . . . 7
|
69 | 7, 9 | atbase 34576 |
. . . . . . . 8
|
70 | 50, 69 | syl 17 |
. . . . . . 7
|
71 | 7, 15, 8 | latlej1 17060 |
. . . . . . 7
|
72 | 4, 68, 70, 71 | syl3anc 1326 |
. . . . . 6
|
73 | 8, 9 | hlatj32 34658 |
. . . . . . . 8
|
74 | 2, 35, 48, 50, 73 | syl13anc 1328 |
. . . . . . 7
|
75 | 7, 9 | atbase 34576 |
. . . . . . . . . 10
|
76 | 48, 75 | syl 17 |
. . . . . . . . 9
|
77 | 7, 8 | latj32 17097 |
. . . . . . . . 9
|
78 | 4, 70, 76, 57, 77 | syl13anc 1328 |
. . . . . . . 8
|
79 | 7, 8 | latj32 17097 |
. . . . . . . . . 10
|
80 | 4, 53, 57, 76, 79 | syl13anc 1328 |
. . . . . . . . 9
|
81 | 7, 8, 9 | hlatjcl 34653 |
. . . . . . . . . . . . . . . . . . 19
|
82 | 2, 5, 50, 81 | syl3anc 1326 |
. . . . . . . . . . . . . . . . . 18
|
83 | 15, 8, 9 | hlatlej1 34661 |
. . . . . . . . . . . . . . . . . . 19
|
84 | 2, 5, 50, 83 | syl3anc 1326 |
. . . . . . . . . . . . . . . . . 18
|
85 | 7, 15, 8, 16, 9 | atmod3i1 35150 |
. . . . . . . . . . . . . . . . . 18
|
86 | 2, 5, 82, 26, 84, 85 | syl131anc 1339 |
. . . . . . . . . . . . . . . . 17
|
87 | | eqid 2622 |
. . . . . . . . . . . . . . . . . . . 20
|
88 | 15, 8, 87, 9, 17 | lhpjat2 35307 |
. . . . . . . . . . . . . . . . . . 19
|
89 | 2, 12, 34, 88 | syl21anc 1325 |
. . . . . . . . . . . . . . . . . 18
|
90 | 89 | oveq2d 6666 |
. . . . . . . . . . . . . . . . 17
|
91 | | hlol 34648 |
. . . . . . . . . . . . . . . . . . 19
|
92 | 2, 91 | syl 17 |
. . . . . . . . . . . . . . . . . 18
|
93 | 7, 16, 87 | olm11 34514 |
. . . . . . . . . . . . . . . . . 18
|
94 | 92, 82, 93 | syl2anc 693 |
. . . . . . . . . . . . . . . . 17
|
95 | 86, 90, 94 | 3eqtrd 2660 |
. . . . . . . . . . . . . . . 16
|
96 | 95 | oveq1d 6665 |
. . . . . . . . . . . . . . 15
|
97 | 18 | oveq2i 6661 |
. . . . . . . . . . . . . . . . . . 19
|
98 | 15, 8, 9 | hlatlej2 34662 |
. . . . . . . . . . . . . . . . . . . . 21
|
99 | 2, 5, 6, 98 | syl3anc 1326 |
. . . . . . . . . . . . . . . . . . . 20
|
100 | 7, 15, 8, 16, 9 | atmod3i1 35150 |
. . . . . . . . . . . . . . . . . . . 20
|
101 | 2, 6, 11, 26, 99, 100 | syl131anc 1339 |
. . . . . . . . . . . . . . . . . . 19
|
102 | 97, 101 | syl5eq 2668 |
. . . . . . . . . . . . . . . . . 18
|
103 | | simp22 1095 |
. . . . . . . . . . . . . . . . . . . 20
|
104 | 15, 8, 87, 9, 17 | lhpjat2 35307 |
. . . . . . . . . . . . . . . . . . . 20
|
105 | 2, 12, 103, 104 | syl21anc 1325 |
. . . . . . . . . . . . . . . . . . 19
|
106 | 105 | oveq2d 6666 |
. . . . . . . . . . . . . . . . . 18
|
107 | 7, 16, 87 | olm11 34514 |
. . . . . . . . . . . . . . . . . . 19
|
108 | 92, 11, 107 | syl2anc 693 |
. . . . . . . . . . . . . . . . . 18
|
109 | 102, 106,
108 | 3eqtrd 2660 |
. . . . . . . . . . . . . . . . 17
|
110 | 109 | oveq1d 6665 |
. . . . . . . . . . . . . . . 16
|
111 | 7, 9 | atbase 34576 |
. . . . . . . . . . . . . . . . . 18
|
112 | 5, 111 | syl 17 |
. . . . . . . . . . . . . . . . 17
|
113 | 7, 16 | latmcl 17052 |
. . . . . . . . . . . . . . . . . 18
|
114 | 4, 82, 26, 113 | syl3anc 1326 |
. . . . . . . . . . . . . . . . 17
|
115 | 7, 9 | atbase 34576 |
. . . . . . . . . . . . . . . . . 18
|
116 | 6, 115 | syl 17 |
. . . . . . . . . . . . . . . . 17
|
117 | 7, 8 | latj32 17097 |
. . . . . . . . . . . . . . . . 17
|
118 | 4, 112, 114, 116, 117 | syl13anc 1328 |
. . . . . . . . . . . . . . . 16
|
119 | 110, 118 | eqtr4d 2659 |
. . . . . . . . . . . . . . 15
|
120 | 8, 9 | hlatj32 34658 |
. . . . . . . . . . . . . . . 16
|
121 | 2, 5, 6, 50, 120 | syl13anc 1328 |
. . . . . . . . . . . . . . 15
|
122 | 96, 119, 121 | 3eqtr4rd 2667 |
. . . . . . . . . . . . . 14
|
123 | 7, 8 | latj32 17097 |
. . . . . . . . . . . . . . 15
|
124 | 4, 116, 76, 114, 123 | syl13anc 1328 |
. . . . . . . . . . . . . 14
|
125 | 122, 124 | eqtrd 2656 |
. . . . . . . . . . . . 13
|
126 | 125 | oveq2d 6666 |
. . . . . . . . . . . 12
|
127 | 7, 8 | latjcl 17051 |
. . . . . . . . . . . . . 14
|
128 | 4, 11, 70, 127 | syl3anc 1326 |
. . . . . . . . . . . . 13
|
129 | 7, 15, 8 | latlej2 17061 |
. . . . . . . . . . . . . 14
|
130 | 4, 11, 70, 129 | syl3anc 1326 |
. . . . . . . . . . . . 13
|
131 | 7, 15, 8, 16, 9 | atmod1i1 35143 |
. . . . . . . . . . . . 13
|
132 | 2, 50, 76, 128, 130, 131 | syl131anc 1339 |
. . . . . . . . . . . 12
|
133 | 51 | oveq1i 6660 |
. . . . . . . . . . . . 13
|
134 | 7, 8, 9 | hlatjcl 34653 |
. . . . . . . . . . . . . . 15
|
135 | 2, 50, 48, 134 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
136 | 7, 8 | latjcl 17051 |
. . . . . . . . . . . . . . 15
|
137 | 4, 116, 114, 136 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
138 | 15, 8, 9 | hlatlej2 34662 |
. . . . . . . . . . . . . . 15
|
139 | 2, 50, 48, 138 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
140 | 7, 15, 8, 16, 9 | atmod2i1 35147 |
. . . . . . . . . . . . . 14
|
141 | 2, 48, 135, 137, 139, 140 | syl131anc 1339 |
. . . . . . . . . . . . 13
|
142 | 133, 141 | syl5eq 2668 |
. . . . . . . . . . . 12
|
143 | 126, 132,
142 | 3eqtr4rd 2667 |
. . . . . . . . . . 11
|
144 | 7, 15, 8 | latlej1 17060 |
. . . . . . . . . . . . . . 15
|
145 | 4, 11, 70, 144 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
146 | 7, 15, 4, 76, 11, 128, 61, 145 | lattrd 17058 |
. . . . . . . . . . . . 13
|
147 | 7, 15, 16 | latleeqm1 17079 |
. . . . . . . . . . . . . 14
|
148 | 4, 76, 128, 147 | syl3anc 1326 |
. . . . . . . . . . . . 13
|
149 | 146, 148 | mpbid 222 |
. . . . . . . . . . . 12
|
150 | 149 | oveq2d 6666 |
. . . . . . . . . . 11
|
151 | 143, 150 | eqtrd 2656 |
. . . . . . . . . 10
|
152 | 151 | oveq1d 6665 |
. . . . . . . . 9
|
153 | 80, 152 | eqtrd 2656 |
. . . . . . . 8
|
154 | 15, 8, 9 | hlatlej2 34662 |
. . . . . . . . . . . 12
|
155 | 2, 35, 50, 154 | syl3anc 1326 |
. . . . . . . . . . 11
|
156 | 7, 15, 8, 16, 9 | atmod3i1 35150 |
. . . . . . . . . . 11
|
157 | 2, 50, 55, 26, 155, 156 | syl131anc 1339 |
. . . . . . . . . 10
|
158 | | simp33r 1189 |
. . . . . . . . . . . 12
|
159 | 15, 8, 87, 9, 17 | lhpjat2 35307 |
. . . . . . . . . . . 12
|
160 | 2, 12, 158, 159 | syl21anc 1325 |
. . . . . . . . . . 11
|
161 | 160 | oveq2d 6666 |
. . . . . . . . . 10
|
162 | 7, 16, 87 | olm11 34514 |
. . . . . . . . . . 11
|
163 | 92, 55, 162 | syl2anc 693 |
. . . . . . . . . 10
|
164 | 157, 161,
163 | 3eqtrrd 2661 |
. . . . . . . . 9
|
165 | 164 | oveq1d 6665 |
. . . . . . . 8
|
166 | 78, 153, 165 | 3eqtr4rd 2667 |
. . . . . . 7
|
167 | 74, 166 | eqtrd 2656 |
. . . . . 6
|
168 | 72, 167 | breqtrd 4679 |
. . . . 5
|
169 | 66, 168 | eqbrtrd 4675 |
. . . 4
|
170 | 7, 8 | latjcl 17051 |
. . . . . 6
|
171 | 4, 59, 76, 170 | syl3anc 1326 |
. . . . 5
|
172 | 7, 15, 16 | latleeqm1 17079 |
. . . . 5
|
173 | 4, 11, 171, 172 | syl3anc 1326 |
. . . 4
|
174 | 169, 173 | mpbid 222 |
. . 3
|
175 | 43, 64, 174 | 3eqtr2rd 2663 |
. 2
|
176 | 33, 175 | breqtrd 4679 |
1
|