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Mirrors > Home > MPE Home > Th. List > df-bc | Structured version Visualization version Unicode version |
Description: Define the binomial
coefficient operation. 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".
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Ref | Expression |
---|---|
df-bc |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbc 12519 |
. 2
![]() ![]() | |
2 | vn |
. . 3
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3 | vk |
. . 3
![]() ![]() | |
4 | cn0 10898 |
. . 3
![]() ![]() | |
5 | cz 10966 |
. . 3
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6 | 3 | cv 1454 |
. . . . 5
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7 | cc0 9565 |
. . . . . 6
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8 | 2 | cv 1454 |
. . . . . 6
![]() ![]() |
9 | cfz 11813 |
. . . . . 6
![]() ![]() | |
10 | 7, 8, 9 | co 6315 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
11 | 6, 10 | wcel 1898 |
. . . 4
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12 | cfa 12491 |
. . . . . 6
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13 | 8, 12 | cfv 5601 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
14 | cmin 9886 |
. . . . . . . 8
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15 | 8, 6, 14 | co 6315 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15, 12 | cfv 5601 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 6, 12 | cfv 5601 |
. . . . . 6
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18 | cmul 9570 |
. . . . . 6
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19 | 16, 17, 18 | co 6315 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | cdiv 10297 |
. . . . 5
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21 | 13, 19, 20 | co 6315 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 11, 21, 7 | cif 3893 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 2, 3, 4, 5, 22 | cmpt2 6317 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 1, 23 | wceq 1455 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
This definition is referenced by: bcval 12521 |
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