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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-lcv | Structured version Visualization version Unicode version |
Description: Define the covering relation for subspaces of a left vector space. Similar to Definition 3.2.18 of [PtakPulmannova] p. 68. Ptak/Pulmannova's notation L is read " covers " or " is covered by " , and it means that is larger than and there is nothing in between. See lcvbr 34308 for binary relation. (df-cv 29138 analog.) (Contributed by NM, 7-Jan-2015.) |
Ref | Expression |
---|---|
df-lcv | L |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clcv 34305 | . 2 L | |
2 | vw | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vt | . . . . . . . 8 | |
5 | 4 | cv 1482 | . . . . . . 7 |
6 | 2 | cv 1482 | . . . . . . . 8 |
7 | clss 18932 | . . . . . . . 8 | |
8 | 6, 7 | cfv 5888 | . . . . . . 7 |
9 | 5, 8 | wcel 1990 | . . . . . 6 |
10 | vu | . . . . . . . 8 | |
11 | 10 | cv 1482 | . . . . . . 7 |
12 | 11, 8 | wcel 1990 | . . . . . 6 |
13 | 9, 12 | wa 384 | . . . . 5 |
14 | 5, 11 | wpss 3575 | . . . . . 6 |
15 | vs | . . . . . . . . . . 11 | |
16 | 15 | cv 1482 | . . . . . . . . . 10 |
17 | 5, 16 | wpss 3575 | . . . . . . . . 9 |
18 | 16, 11 | wpss 3575 | . . . . . . . . 9 |
19 | 17, 18 | wa 384 | . . . . . . . 8 |
20 | 19, 15, 8 | wrex 2913 | . . . . . . 7 |
21 | 20 | wn 3 | . . . . . 6 |
22 | 14, 21 | wa 384 | . . . . 5 |
23 | 13, 22 | wa 384 | . . . 4 |
24 | 23, 4, 10 | copab 4712 | . . 3 |
25 | 2, 3, 24 | cmpt 4729 | . 2 |
26 | 1, 25 | wceq 1483 | 1 L |
Colors of variables: wff setvar class |
This definition is referenced by: lcvfbr 34307 |
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