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Mirrors > Home > ILE Home > Th. List > df-pc | Unicode version |
Description: Define the prime count function, which returns the largest exponent of a given prime (or other positive integer) that divides the number. For rational numbers, it returns negative values according to the power of a prime in the denominator. (Contributed by Mario Carneiro, 23-Feb-2014.) |
Ref | Expression |
---|---|
df-pc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpc 12231 | . 2 | |
2 | vp | . . 3 | |
3 | vr | . . 3 | |
4 | cprime 12054 | . . 3 | |
5 | cq 9571 | . . 3 | |
6 | 3 | cv 1347 | . . . . 5 |
7 | cc0 7767 | . . . . 5 | |
8 | 6, 7 | wceq 1348 | . . . 4 |
9 | cpnf 7944 | . . . 4 | |
10 | vx | . . . . . . . . . . 11 | |
11 | 10 | cv 1347 | . . . . . . . . . 10 |
12 | vy | . . . . . . . . . . 11 | |
13 | 12 | cv 1347 | . . . . . . . . . 10 |
14 | cdiv 8582 | . . . . . . . . . 10 | |
15 | 11, 13, 14 | co 5851 | . . . . . . . . 9 |
16 | 6, 15 | wceq 1348 | . . . . . . . 8 |
17 | vz | . . . . . . . . . 10 | |
18 | 17 | cv 1347 | . . . . . . . . 9 |
19 | 2 | cv 1347 | . . . . . . . . . . . . . 14 |
20 | vn | . . . . . . . . . . . . . . 15 | |
21 | 20 | cv 1347 | . . . . . . . . . . . . . 14 |
22 | cexp 10468 | . . . . . . . . . . . . . 14 | |
23 | 19, 21, 22 | co 5851 | . . . . . . . . . . . . 13 |
24 | cdvds 11742 | . . . . . . . . . . . . 13 | |
25 | 23, 11, 24 | wbr 3987 | . . . . . . . . . . . 12 |
26 | cn0 9128 | . . . . . . . . . . . 12 | |
27 | 25, 20, 26 | crab 2452 | . . . . . . . . . . 11 |
28 | cr 7766 | . . . . . . . . . . 11 | |
29 | clt 7947 | . . . . . . . . . . 11 | |
30 | 27, 28, 29 | csup 6957 | . . . . . . . . . 10 |
31 | 23, 13, 24 | wbr 3987 | . . . . . . . . . . . 12 |
32 | 31, 20, 26 | crab 2452 | . . . . . . . . . . 11 |
33 | 32, 28, 29 | csup 6957 | . . . . . . . . . 10 |
34 | cmin 8083 | . . . . . . . . . 10 | |
35 | 30, 33, 34 | co 5851 | . . . . . . . . 9 |
36 | 18, 35 | wceq 1348 | . . . . . . . 8 |
37 | 16, 36 | wa 103 | . . . . . . 7 |
38 | cn 8871 | . . . . . . 7 | |
39 | 37, 12, 38 | wrex 2449 | . . . . . 6 |
40 | cz 9205 | . . . . . 6 | |
41 | 39, 10, 40 | wrex 2449 | . . . . 5 |
42 | 41, 17 | cio 5156 | . . . 4 |
43 | 8, 9, 42 | cif 3525 | . . 3 |
44 | 2, 3, 4, 5, 43 | cmpo 5853 | . 2 |
45 | 1, 44 | wceq 1348 | 1 |
Colors of variables: wff set class |
This definition is referenced by: pcval 12243 pc0 12251 |
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