Proof of Theorem cdlemk4
Step | Hyp | Ref
| Expression |
1 | | simp1l 1085 |
. . 3
|
2 | | simp1 1061 |
. . . 4
|
3 | | simp2l 1087 |
. . . 4
|
4 | | simp3l 1089 |
. . . 4
|
5 | | cdlemk.l |
. . . . 5
|
6 | | cdlemk.a |
. . . . 5
|
7 | | cdlemk.h |
. . . . 5
|
8 | | cdlemk.t |
. . . . 5
|
9 | 5, 6, 7, 8 | ltrnat 35426 |
. . . 4
|
10 | 2, 3, 4, 9 | syl3anc 1326 |
. . 3
|
11 | | simp2r 1088 |
. . . 4
|
12 | 5, 6, 7, 8 | ltrnat 35426 |
. . . 4
|
13 | 2, 11, 4, 12 | syl3anc 1326 |
. . 3
|
14 | | cdlemk.j |
. . . 4
|
15 | 5, 14, 6 | hlatlej1 34661 |
. . 3
|
16 | 1, 10, 13, 15 | syl3anc 1326 |
. 2
|
17 | | hllat 34650 |
. . . . . 6
|
18 | 1, 17 | syl 17 |
. . . . 5
|
19 | | cdlemk.b |
. . . . . . 7
|
20 | 19, 6 | atbase 34576 |
. . . . . 6
|
21 | 10, 20 | syl 17 |
. . . . 5
|
22 | 19, 6 | atbase 34576 |
. . . . . 6
|
23 | 13, 22 | syl 17 |
. . . . 5
|
24 | 19, 14 | latjcl 17051 |
. . . . 5
|
25 | 18, 21, 23, 24 | syl3anc 1326 |
. . . 4
|
26 | | simp1r 1086 |
. . . . 5
|
27 | 19, 7 | lhpbase 35284 |
. . . . 5
|
28 | 26, 27 | syl 17 |
. . . 4
|
29 | 5, 14, 6 | hlatlej2 34662 |
. . . . 5
|
30 | 1, 10, 13, 29 | syl3anc 1326 |
. . . 4
|
31 | | cdlemk.m |
. . . . 5
|
32 | 19, 5, 14, 31, 6 | atmod3i1 35150 |
. . . 4
|
33 | 1, 13, 25, 28, 30, 32 | syl131anc 1339 |
. . 3
|
34 | 7, 8 | ltrncnv 35432 |
. . . . . . . 8
|
35 | 2, 3, 34 | syl2anc 693 |
. . . . . . 7
|
36 | 7, 8 | ltrnco 36007 |
. . . . . . 7
|
37 | 2, 11, 35, 36 | syl3anc 1326 |
. . . . . 6
|
38 | 5, 6, 7, 8 | ltrnel 35425 |
. . . . . . 7
|
39 | 3, 38 | syld3an2 1373 |
. . . . . 6
|
40 | | cdlemk.r |
. . . . . . 7
|
41 | 5, 14, 31, 6, 7, 8,
40 | trlval2 35450 |
. . . . . 6
|
42 | 2, 37, 39, 41 | syl3anc 1326 |
. . . . 5
|
43 | 19, 7, 8 | ltrn1o 35410 |
. . . . . . . . . . . . . . 15
|
44 | 2, 3, 43 | syl2anc 693 |
. . . . . . . . . . . . . 14
|
45 | | f1ococnv1 6165 |
. . . . . . . . . . . . . 14
|
46 | 44, 45 | syl 17 |
. . . . . . . . . . . . 13
|
47 | 46 | coeq2d 5284 |
. . . . . . . . . . . 12
|
48 | 19, 7, 8 | ltrn1o 35410 |
. . . . . . . . . . . . . 14
|
49 | 2, 11, 48 | syl2anc 693 |
. . . . . . . . . . . . 13
|
50 | | f1of 6137 |
. . . . . . . . . . . . 13
|
51 | | fcoi1 6078 |
. . . . . . . . . . . . 13
|
52 | 49, 50, 51 | 3syl 18 |
. . . . . . . . . . . 12
|
53 | 47, 52 | eqtr2d 2657 |
. . . . . . . . . . 11
|
54 | | coass 5654 |
. . . . . . . . . . 11
|
55 | 53, 54 | syl6eqr 2674 |
. . . . . . . . . 10
|
56 | 55 | fveq1d 6193 |
. . . . . . . . 9
|
57 | 5, 6, 7, 8 | ltrncoval 35431 |
. . . . . . . . . 10
|
58 | 2, 37, 3, 4, 57 | syl121anc 1331 |
. . . . . . . . 9
|
59 | 56, 58 | eqtrd 2656 |
. . . . . . . 8
|
60 | 59 | oveq2d 6666 |
. . . . . . 7
|
61 | 60 | eqcomd 2628 |
. . . . . 6
|
62 | 61 | oveq1d 6665 |
. . . . 5
|
63 | 42, 62 | eqtrd 2656 |
. . . 4
|
64 | 63 | oveq2d 6666 |
. . 3
|
65 | 5, 6, 7, 8 | ltrnel 35425 |
. . . . . . 7
|
66 | 11, 65 | syld3an2 1373 |
. . . . . 6
|
67 | | eqid 2622 |
. . . . . . 7
|
68 | 5, 14, 67, 6, 7 | lhpjat2 35307 |
. . . . . 6
|
69 | 2, 66, 68 | syl2anc 693 |
. . . . 5
|
70 | 69 | oveq2d 6666 |
. . . 4
|
71 | | hlol 34648 |
. . . . . 6
|
72 | 1, 71 | syl 17 |
. . . . 5
|
73 | 19, 31, 67 | olm11 34514 |
. . . . 5
|
74 | 72, 25, 73 | syl2anc 693 |
. . . 4
|
75 | 70, 74 | eqtr2d 2657 |
. . 3
|
76 | 33, 64, 75 | 3eqtr4rd 2667 |
. 2
|
77 | 16, 76 | breqtrd 4679 |
1
|