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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 , and assigns all infinite sets the
value .
For example, ♯ .
Note that we use the sharp sign (♯) for this function and we use the different character octothorpe (#) for the apartness relation (see df-ap 8471). 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 and ) is not taken directly from the literature, but for finite sets should be equivalent to the conventional definition that the size of a finite set is the unique natural number which is equinumerous to the given set. (Contributed by Jim Kingdon, 19-Feb-2022.) |
Ref | Expression |
---|---|
df-ihash | ♯ frec |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chash 10677 | . 2 ♯ | |
2 | vx | . . . . . 6 | |
3 | cz 9182 | . . . . . 6 | |
4 | 2 | cv 1341 | . . . . . . 7 |
5 | c1 7745 | . . . . . . 7 | |
6 | caddc 7747 | . . . . . . 7 | |
7 | 4, 5, 6 | co 5836 | . . . . . 6 |
8 | 2, 3, 7 | cmpt 4037 | . . . . 5 |
9 | cc0 7744 | . . . . 5 | |
10 | 8, 9 | cfrec 6349 | . . . 4 frec |
11 | com 4561 | . . . . . 6 | |
12 | cpnf 7921 | . . . . . 6 | |
13 | 11, 12 | cop 3573 | . . . . 5 |
14 | 13 | csn 3570 | . . . 4 |
15 | 10, 14 | cun 3109 | . . 3 frec |
16 | cvv 2721 | . . . 4 | |
17 | vy | . . . . . . . 8 | |
18 | 17 | cv 1341 | . . . . . . 7 |
19 | cdom 6696 | . . . . . . 7 | |
20 | 18, 4, 19 | wbr 3976 | . . . . . 6 |
21 | 11 | csn 3570 | . . . . . . 7 |
22 | 11, 21 | cun 3109 | . . . . . 6 |
23 | 20, 17, 22 | crab 2446 | . . . . 5 |
24 | 23 | cuni 3783 | . . . 4 |
25 | 2, 16, 24 | cmpt 4037 | . . 3 |
26 | 15, 25 | ccom 4602 | . 2 frec |
27 | 1, 26 | wceq 1342 | 1 ♯ frec |
Colors of variables: wff set class |
This definition is referenced by: hashinfom 10680 hashennn 10682 |
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