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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-lplanes | Structured version Visualization version Unicode version |
Description: Define the set of all "lattice planes" (lattice elements which cover a line) in a Hilbert lattice , in other words all elements of height 3 (or lattice dimension 3 or projective dimension 2). (Contributed by NM, 16-Jun-2012.) |
Ref | Expression |
---|---|
df-lplanes |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clpl 34778 | . 2 | |
2 | vk | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vp | . . . . . . 7 | |
5 | 4 | cv 1482 | . . . . . 6 |
6 | vx | . . . . . . 7 | |
7 | 6 | cv 1482 | . . . . . 6 |
8 | 2 | cv 1482 | . . . . . . 7 |
9 | ccvr 34549 | . . . . . . 7 | |
10 | 8, 9 | cfv 5888 | . . . . . 6 |
11 | 5, 7, 10 | wbr 4653 | . . . . 5 |
12 | clln 34777 | . . . . . 6 | |
13 | 8, 12 | cfv 5888 | . . . . 5 |
14 | 11, 4, 13 | wrex 2913 | . . . 4 |
15 | cbs 15857 | . . . . 5 | |
16 | 8, 15 | cfv 5888 | . . . 4 |
17 | 14, 6, 16 | crab 2916 | . . 3 |
18 | 2, 3, 17 | cmpt 4729 | . 2 |
19 | 1, 18 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: lplnset 34815 |
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