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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-lhyp | Structured version Visualization version Unicode version |
Description: Define the set of lattice hyperplanes, which are all lattice elements covered by 1 (i.e. all co-atoms). We call them "hyperplanes" instead of "co-atoms" in analogy with projective geometry hyperplanes. (Contributed by NM, 11-May-2012.) |
Ref | Expression |
---|---|
df-lhyp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clh 35270 | . 2 | |
2 | vk | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vx | . . . . . 6 | |
5 | 4 | cv 1482 | . . . . 5 |
6 | 2 | cv 1482 | . . . . . 6 |
7 | cp1 17038 | . . . . . 6 | |
8 | 6, 7 | cfv 5888 | . . . . 5 |
9 | ccvr 34549 | . . . . . 6 | |
10 | 6, 9 | cfv 5888 | . . . . 5 |
11 | 5, 8, 10 | wbr 4653 | . . . 4 |
12 | cbs 15857 | . . . . 5 | |
13 | 6, 12 | cfv 5888 | . . . 4 |
14 | 11, 4, 13 | crab 2916 | . . 3 |
15 | 2, 3, 14 | cmpt 4729 | . 2 |
16 | 1, 15 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: lhpset 35281 |
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