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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-pclN | Structured version Visualization version Unicode version |
Description: Projective subspace closure, which is the smallest projective subspace containing an arbitrary set of atoms. The subspace closure of the union of a set of projective subspaces is their supremum in . Related to an analogous definition of closure used in Lemma 3.1.4 of [PtakPulmannova] p. 68. (Note that this closure is not necessarily one of the closed projective subspaces of df-psubclN 35221.) (Contributed by NM, 7-Sep-2013.) |
Ref | Expression |
---|---|
df-pclN |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpclN 35173 | . 2 | |
2 | vk | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vx | . . . 4 | |
5 | 2 | cv 1482 | . . . . . 6 |
6 | catm 34550 | . . . . . 6 | |
7 | 5, 6 | cfv 5888 | . . . . 5 |
8 | 7 | cpw 4158 | . . . 4 |
9 | 4 | cv 1482 | . . . . . . 7 |
10 | vy | . . . . . . . 8 | |
11 | 10 | cv 1482 | . . . . . . 7 |
12 | 9, 11 | wss 3574 | . . . . . 6 |
13 | cpsubsp 34782 | . . . . . . 7 | |
14 | 5, 13 | cfv 5888 | . . . . . 6 |
15 | 12, 10, 14 | crab 2916 | . . . . 5 |
16 | 15 | cint 4475 | . . . 4 |
17 | 4, 8, 16 | cmpt 4729 | . . 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: pclfvalN 35175 |
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