Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-mapd | Structured version Visualization version Unicode version |
Description: Extend class notation with a one-to-one onto (mapd1o 36937), order-preserving (mapdord 36927) map, called a projectivity (definition of projectivity in [Baer] p. 40), from subspaces of vector space H to those subspaces of the dual space having functionals with closed kernels. (Contributed by NM, 25-Jan-2015.) |
Ref | Expression |
---|---|
df-mapd | mapd LFnl LKer LKer LKer |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmpd 36913 | . 2 mapd | |
2 | vk | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vw | . . . 4 | |
5 | 2 | cv 1482 | . . . . 5 |
6 | clh 35270 | . . . . 5 | |
7 | 5, 6 | cfv 5888 | . . . 4 |
8 | vs | . . . . 5 | |
9 | 4 | cv 1482 | . . . . . . 7 |
10 | cdvh 36367 | . . . . . . . 8 | |
11 | 5, 10 | cfv 5888 | . . . . . . 7 |
12 | 9, 11 | cfv 5888 | . . . . . 6 |
13 | clss 18932 | . . . . . 6 | |
14 | 12, 13 | cfv 5888 | . . . . 5 |
15 | vf | . . . . . . . . . . . 12 | |
16 | 15 | cv 1482 | . . . . . . . . . . 11 |
17 | clk 34372 | . . . . . . . . . . . 12 LKer | |
18 | 12, 17 | cfv 5888 | . . . . . . . . . . 11 LKer |
19 | 16, 18 | cfv 5888 | . . . . . . . . . 10 LKer |
20 | coch 36636 | . . . . . . . . . . . 12 | |
21 | 5, 20 | cfv 5888 | . . . . . . . . . . 11 |
22 | 9, 21 | cfv 5888 | . . . . . . . . . 10 |
23 | 19, 22 | cfv 5888 | . . . . . . . . 9 LKer |
24 | 23, 22 | cfv 5888 | . . . . . . . 8 LKer |
25 | 24, 19 | wceq 1483 | . . . . . . 7 LKer LKer |
26 | 8 | cv 1482 | . . . . . . . 8 |
27 | 23, 26 | wss 3574 | . . . . . . 7 LKer |
28 | 25, 27 | wa 384 | . . . . . 6 LKer LKer LKer |
29 | clfn 34344 | . . . . . . 7 LFnl | |
30 | 12, 29 | cfv 5888 | . . . . . 6 LFnl |
31 | 28, 15, 30 | crab 2916 | . . . . 5 LFnl LKer LKer LKer |
32 | 8, 14, 31 | cmpt 4729 | . . . 4 LFnl LKer LKer LKer |
33 | 4, 7, 32 | cmpt 4729 | . . 3 LFnl LKer LKer LKer |
34 | 2, 3, 33 | cmpt 4729 | . 2 LFnl LKer LKer LKer |
35 | 1, 34 | wceq 1483 | 1 mapd LFnl LKer LKer LKer |
Colors of variables: wff setvar class |
This definition is referenced by: mapdffval 36915 |
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