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Mirrors > Home > ILE Home > Th. List > df-bc | Unicode version |
Description: Define the binomial
coefficient operation. For example,
(ex-bc 13764).
In the literature, this function is often written as a column vector of the two arguments, or with the arguments as subscripts before and after the letter "C". is read " choose ." Definition of binomial coefficient in [Gleason] p. 295. As suggested by Gleason, we define it to be 0 when does not hold. (Contributed by NM, 10-Jul-2005.) |
Ref | Expression |
---|---|
df-bc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbc 10681 | . 2 | |
2 | vn | . . 3 | |
3 | vk | . . 3 | |
4 | cn0 9135 | . . 3 | |
5 | cz 9212 | . . 3 | |
6 | 3 | cv 1347 | . . . . 5 |
7 | cc0 7774 | . . . . . 6 | |
8 | 2 | cv 1347 | . . . . . 6 |
9 | cfz 9965 | . . . . . 6 | |
10 | 7, 8, 9 | co 5853 | . . . . 5 |
11 | 6, 10 | wcel 2141 | . . . 4 |
12 | cfa 10659 | . . . . . 6 | |
13 | 8, 12 | cfv 5198 | . . . . 5 |
14 | cmin 8090 | . . . . . . . 8 | |
15 | 8, 6, 14 | co 5853 | . . . . . . 7 |
16 | 15, 12 | cfv 5198 | . . . . . 6 |
17 | 6, 12 | cfv 5198 | . . . . . 6 |
18 | cmul 7779 | . . . . . 6 | |
19 | 16, 17, 18 | co 5853 | . . . . 5 |
20 | cdiv 8589 | . . . . 5 | |
21 | 13, 19, 20 | co 5853 | . . . 4 |
22 | 11, 21, 7 | cif 3526 | . . 3 |
23 | 2, 3, 4, 5, 22 | cmpo 5855 | . 2 |
24 | 1, 23 | wceq 1348 | 1 |
Colors of variables: wff set class |
This definition is referenced by: bcval 10683 |
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