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Mirrors > Home > ILE Home > Th. List > df-ihash | Unicode version |
Description: Define the set size
function ♯, which gives the cardinality of a
finite set as a member of ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() Note that we use the sharp sign (♯) for this function and we use the different character octothorpe (#) for the apartness relation (see df-ap 8538). We adopt the former notation from Corollary 8.2.4 of [AczelRathjen], p. 80 (although that work only defines it for finite sets).
This definition (in terms of |
Ref | Expression |
---|---|
df-ihash |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chash 10754 |
. 2
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2 | vx |
. . . . . 6
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3 | cz 9252 |
. . . . . 6
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4 | 2 | cv 1352 |
. . . . . . 7
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5 | c1 7811 |
. . . . . . 7
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6 | caddc 7813 |
. . . . . . 7
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7 | 4, 5, 6 | co 5874 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() |
8 | 2, 3, 7 | cmpt 4064 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | cc0 7810 |
. . . . 5
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10 | 8, 9 | cfrec 6390 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | com 4589 |
. . . . . 6
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12 | cpnf 7988 |
. . . . . 6
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13 | 11, 12 | cop 3595 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
14 | 13 | csn 3592 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 10, 14 | cun 3127 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | cvv 2737 |
. . . 4
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17 | vy |
. . . . . . . 8
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18 | 17 | cv 1352 |
. . . . . . 7
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19 | cdom 6738 |
. . . . . . 7
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20 | 18, 4, 19 | wbr 4003 |
. . . . . 6
![]() ![]() ![]() ![]() |
21 | 11 | csn 3592 |
. . . . . . 7
![]() ![]() ![]() ![]() |
22 | 11, 21 | cun 3127 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 20, 17, 22 | crab 2459 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23 | cuni 3809 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 2, 16, 24 | cmpt 4064 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 15, 25 | ccom 4630 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 1, 26 | wceq 1353 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: hashinfom 10757 hashennn 10759 |
Copyright terms: Public domain | W3C validator |