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Definition df-pc 14361
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.)
Assertion
Ref Expression
df-pc
Distinct variable group:   , , , , ,

Detailed syntax breakdown of Definition df-pc
StepHypRef Expression
1 cpc 14360 . 2
2 vp . . 3
3 vr . . 3
4 cprime 14217 . . 3
5 cq 11211 . . 3
63cv 1394 . . . . 5
7 cc0 9513 . . . . 5
86, 7wceq 1395 . . . 4
9 cpnf 9646 . . . 4
10 vx . . . . . . . . . . 11
1110cv 1394 . . . . . . . . . 10
12 vy . . . . . . . . . . 11
1312cv 1394 . . . . . . . . . 10
14 cdiv 10231 . . . . . . . . . 10
1511, 13, 14co 6296 . . . . . . . . 9
166, 15wceq 1395 . . . . . . . 8
17 vz . . . . . . . . . 10
1817cv 1394 . . . . . . . . 9
192cv 1394 . . . . . . . . . . . . . 14
20 vn . . . . . . . . . . . . . . 15
2120cv 1394 . . . . . . . . . . . . . 14
22 cexp 12166 . . . . . . . . . . . . . 14
2319, 21, 22co 6296 . . . . . . . . . . . . 13
24 cdvds 13986 . . . . . . . . . . . . 13
2523, 11, 24wbr 4452 . . . . . . . . . . . 12
26 cn0 10820 . . . . . . . . . . . 12
2725, 20, 26crab 2811 . . . . . . . . . . 11
28 cr 9512 . . . . . . . . . . 11
29 clt 9649 . . . . . . . . . . 11
3027, 28, 29csup 7920 . . . . . . . . . 10
3123, 13, 24wbr 4452 . . . . . . . . . . . 12
3231, 20, 26crab 2811 . . . . . . . . . . 11
3332, 28, 29csup 7920 . . . . . . . . . 10
34 cmin 9828 . . . . . . . . . 10
3530, 33, 34co 6296 . . . . . . . . 9
3618, 35wceq 1395 . . . . . . . 8
3716, 36wa 369 . . . . . . 7
38 cn 10561 . . . . . . 7
3937, 12, 38wrex 2808 . . . . . 6
40 cz 10889 . . . . . 6
4139, 10, 40wrex 2808 . . . . 5
4241, 17cio 5554 . . . 4
438, 9, 42cif 3941 . . 3
442, 3, 4, 5, 43cmpt2 6298 . 2
451, 44wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  pcval  14368  pc0  14378
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