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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-lines | Structured version Visualization version Unicode version |
Description: Define set of all projective lines for a Hilbert lattice (actually in any set at all, for simplicity). The join of two distinct atoms equals a line. Definition of lines in item 1 of [Holland95] p. 222. (Contributed by NM, 19-Sep-2011.) |
Ref | Expression |
---|---|
df-lines |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clines 34780 | . 2 | |
2 | vk | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vq | . . . . . . . . 9 | |
5 | 4 | cv 1482 | . . . . . . . 8 |
6 | vr | . . . . . . . . 9 | |
7 | 6 | cv 1482 | . . . . . . . 8 |
8 | 5, 7 | wne 2794 | . . . . . . 7 |
9 | vs | . . . . . . . . 9 | |
10 | 9 | cv 1482 | . . . . . . . 8 |
11 | vp | . . . . . . . . . . 11 | |
12 | 11 | cv 1482 | . . . . . . . . . 10 |
13 | 2 | cv 1482 | . . . . . . . . . . . 12 |
14 | cjn 16944 | . . . . . . . . . . . 12 | |
15 | 13, 14 | cfv 5888 | . . . . . . . . . . 11 |
16 | 5, 7, 15 | co 6650 | . . . . . . . . . 10 |
17 | cple 15948 | . . . . . . . . . . 11 | |
18 | 13, 17 | cfv 5888 | . . . . . . . . . 10 |
19 | 12, 16, 18 | wbr 4653 | . . . . . . . . 9 |
20 | catm 34550 | . . . . . . . . . 10 | |
21 | 13, 20 | cfv 5888 | . . . . . . . . 9 |
22 | 19, 11, 21 | crab 2916 | . . . . . . . 8 |
23 | 10, 22 | wceq 1483 | . . . . . . 7 |
24 | 8, 23 | wa 384 | . . . . . 6 |
25 | 24, 6, 21 | wrex 2913 | . . . . 5 |
26 | 25, 4, 21 | wrex 2913 | . . . 4 |
27 | 26, 9 | cab 2608 | . . 3 |
28 | 2, 3, 27 | cmpt 4729 | . 2 |
29 | 1, 28 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: lineset 35024 |
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