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Mirrors > Home > MPE Home > Th. List > df-cfil | Unicode version |
Description: Define the set of Cauchy
filters on a metric space. A Cauchy filter is
a filter on the set such that for every ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
df-cfil |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccfil 19166 |
. 2
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2 | vd |
. . 3
![]() ![]() | |
3 | cxmt 16649 |
. . . . 5
![]() ![]() ![]() | |
4 | 3 | crn 4846 |
. . . 4
![]() ![]() ![]() ![]() |
5 | 4 | cuni 3983 |
. . 3
![]() ![]() ![]() ![]() ![]() |
6 | 2 | cv 1648 |
. . . . . . . 8
![]() ![]() |
7 | vy |
. . . . . . . . . 10
![]() ![]() | |
8 | 7 | cv 1648 |
. . . . . . . . 9
![]() ![]() |
9 | 8, 8 | cxp 4843 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
10 | 6, 9 | cima 4848 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | cc0 8954 |
. . . . . . . 8
![]() ![]() | |
12 | vx |
. . . . . . . . 9
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13 | 12 | cv 1648 |
. . . . . . . 8
![]() ![]() |
14 | cico 10882 |
. . . . . . . 8
![]() ![]() | |
15 | 11, 13, 14 | co 6048 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() |
16 | 10, 15 | wss 3288 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | vf |
. . . . . . 7
![]() ![]() | |
18 | 17 | cv 1648 |
. . . . . 6
![]() ![]() |
19 | 16, 7, 18 | wrex 2675 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | crp 10576 |
. . . . 5
![]() ![]() | |
21 | 19, 12, 20 | wral 2674 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 6 | cdm 4845 |
. . . . . 6
![]() ![]() ![]() |
23 | 22 | cdm 4845 |
. . . . 5
![]() ![]() ![]() ![]() |
24 | cfil 17838 |
. . . . 5
![]() ![]() | |
25 | 23, 24 | cfv 5421 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 21, 17, 25 | crab 2678 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 2, 5, 26 | cmpt 4234 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 1, 27 | wceq 1649 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: cfilfval 19178 cfili 19182 cfilfcls 19188 |
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