Description: "Less than or equal to" in terms of meet. (Contributed by NM, 7-Nov-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | latmle.b | |
|
latmle.l | |
||
latmle.m | |
||
Assertion | latleeqm1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | latmle.b | |
|
2 | latmle.l | |
|
3 | latmle.m | |
|
4 | 1 2 | latref | |
5 | 4 | 3adant3 | |
6 | 5 | biantrurd | |
7 | simp1 | |
|
8 | simp2 | |
|
9 | simp3 | |
|
10 | 1 2 3 | latlem12 | |
11 | 7 8 8 9 10 | syl13anc | |
12 | 6 11 | bitrd | |
13 | 1 2 3 | latmle1 | |
14 | 13 | biantrurd | |
15 | 12 14 | bitrd | |
16 | latpos | |
|
17 | 16 | 3ad2ant1 | |
18 | 1 3 | latmcl | |
19 | 1 2 | posasymb | |
20 | 17 18 8 19 | syl3anc | |
21 | 15 20 | bitrd | |