Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > trlval2 | Structured version Visualization version Unicode version |
Description: The value of the trace of a lattice translation, given any atom not under the fiducial co-atom . Note: this requires only the weaker assumption ; we use for convenience. (Contributed by NM, 20-May-2012.) |
Ref | Expression |
---|---|
trlval2.l | |
trlval2.j | |
trlval2.m | |
trlval2.a | |
trlval2.h | |
trlval2.t | |
trlval2.r |
Ref | Expression |
---|---|
trlval2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hllat 34650 | . . 3 | |
2 | 1 | anim1i 592 | . 2 |
3 | eqid 2622 | . . . . 5 | |
4 | trlval2.l | . . . . 5 | |
5 | trlval2.j | . . . . 5 | |
6 | trlval2.m | . . . . 5 | |
7 | trlval2.a | . . . . 5 | |
8 | trlval2.h | . . . . 5 | |
9 | trlval2.t | . . . . 5 | |
10 | trlval2.r | . . . . 5 | |
11 | 3, 4, 5, 6, 7, 8, 9, 10 | trlval 35449 | . . . 4 |
12 | 11 | 3adant3 1081 | . . 3 |
13 | simp1l 1085 | . . . . 5 | |
14 | simp3l 1089 | . . . . . . 7 | |
15 | 3, 7 | atbase 34576 | . . . . . . 7 |
16 | 14, 15 | syl 17 | . . . . . 6 |
17 | 3, 8, 9 | ltrncl 35411 | . . . . . . 7 |
18 | 16, 17 | syld3an3 1371 | . . . . . 6 |
19 | 3, 5 | latjcl 17051 | . . . . . 6 |
20 | 13, 16, 18, 19 | syl3anc 1326 | . . . . 5 |
21 | simp1r 1086 | . . . . . 6 | |
22 | 3, 8 | lhpbase 35284 | . . . . . 6 |
23 | 21, 22 | syl 17 | . . . . 5 |
24 | 3, 6 | latmcl 17052 | . . . . 5 |
25 | 13, 20, 23, 24 | syl3anc 1326 | . . . 4 |
26 | simpl3l 1116 | . . . . . 6 | |
27 | simpl3r 1117 | . . . . . 6 | |
28 | breq1 4656 | . . . . . . . . . 10 | |
29 | 28 | notbid 308 | . . . . . . . . 9 |
30 | id 22 | . . . . . . . . . . . 12 | |
31 | fveq2 6191 | . . . . . . . . . . . 12 | |
32 | 30, 31 | oveq12d 6668 | . . . . . . . . . . 11 |
33 | 32 | oveq1d 6665 | . . . . . . . . . 10 |
34 | 33 | eqeq2d 2632 | . . . . . . . . 9 |
35 | 29, 34 | imbi12d 334 | . . . . . . . 8 |
36 | 35 | rspcv 3305 | . . . . . . 7 |
37 | 36 | com23 86 | . . . . . 6 |
38 | 26, 27, 37 | sylc 65 | . . . . 5 |
39 | simp11 1091 | . . . . . . . . . . 11 | |
40 | simp12 1092 | . . . . . . . . . . 11 | |
41 | simp13l 1176 | . . . . . . . . . . 11 | |
42 | simp13r 1177 | . . . . . . . . . . 11 | |
43 | simp3 1063 | . . . . . . . . . . 11 | |
44 | simp2 1062 | . . . . . . . . . . 11 | |
45 | 4, 5, 6, 7, 8, 9 | ltrnu 35407 | . . . . . . . . . . 11 |
46 | 39, 40, 41, 42, 43, 44, 45 | syl222anc 1342 | . . . . . . . . . 10 |
47 | eqeq2 2633 | . . . . . . . . . . 11 | |
48 | 47 | biimpd 219 | . . . . . . . . . 10 |
49 | 46, 48 | syl 17 | . . . . . . . . 9 |
50 | 49 | 3exp 1264 | . . . . . . . 8 |
51 | 50 | com24 95 | . . . . . . 7 |
52 | 51 | ralrimdv 2968 | . . . . . 6 |
53 | 52 | adantr 481 | . . . . 5 |
54 | 38, 53 | impbid 202 | . . . 4 |
55 | 25, 54 | riota5 6637 | . . 3 |
56 | 12, 55 | eqtrd 2656 | . 2 |
57 | 2, 56 | syl3an1 1359 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 wral 2912 class class class wbr 4653 cfv 5888 crio 6610 (class class class)co 6650 cbs 15857 cple 15948 cjn 16944 cmee 16945 clat 17045 catm 34550 chlt 34637 clh 35270 cltrn 35387 ctrl 35445 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-map 7859 df-lub 16974 df-glb 16975 df-join 16976 df-meet 16977 df-lat 17046 df-ats 34554 df-atl 34585 df-cvlat 34609 df-hlat 34638 df-lhyp 35274 df-laut 35275 df-ldil 35390 df-ltrn 35391 df-trl 35446 |
This theorem is referenced by: trlcl 35451 trlcnv 35452 trljat1 35453 trljat2 35454 trlat 35456 trl0 35457 trlle 35471 trlval3 35474 trlval5 35476 cdlemd6 35490 cdlemf 35851 cdlemg4a 35896 cdlemg4b1 35897 cdlemg4b2 35898 cdlemg4 35905 cdlemg11b 35930 cdlemg13a 35939 cdlemg13 35940 cdlemg17a 35949 cdlemg17dN 35951 cdlemg17e 35953 cdlemg17f 35954 trlcoabs2N 36010 trlcolem 36014 cdlemg42 36017 cdlemg43 36018 cdlemi1 36106 cdlemk4 36122 cdlemk39 36204 dia2dimlem1 36353 dia2dimlem2 36354 dia2dimlem3 36355 cdlemm10N 36407 cdlemn2 36484 cdlemn10 36495 dihjatcclem3 36709 |
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