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Mirrors > Home > ILE Home > Th. List > df-mod | Unicode version |
Description: Define the modulo (remainder) operation. See modqval 10250 for its value. For example, and . As with df-fl 10196 we define this for first and second arguments which are real and positive real, respectively, even though many theorems will need to be more restricted (for example, specify rational arguments). (Contributed by NM, 10-Nov-2008.) |
Ref | Expression |
---|---|
df-mod |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmo 10248 | . 2 | |
2 | vx | . . 3 | |
3 | vy | . . 3 | |
4 | cr 7744 | . . 3 | |
5 | crp 9581 | . . 3 | |
6 | 2 | cv 1341 | . . . 4 |
7 | 3 | cv 1341 | . . . . 5 |
8 | cdiv 8560 | . . . . . . 7 | |
9 | 6, 7, 8 | co 5837 | . . . . . 6 |
10 | cfl 10194 | . . . . . 6 | |
11 | 9, 10 | cfv 5183 | . . . . 5 |
12 | cmul 7750 | . . . . 5 | |
13 | 7, 11, 12 | co 5837 | . . . 4 |
14 | cmin 8061 | . . . 4 | |
15 | 6, 13, 14 | co 5837 | . . 3 |
16 | 2, 3, 4, 5, 15 | cmpo 5839 | . 2 |
17 | 1, 16 | wceq 1342 | 1 |
Colors of variables: wff set class |
This definition is referenced by: modqval 10250 |
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