Description: Subtraction property of the modulo operation. (Contributed by Mario Carneiro, 9-Sep-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | modadd12d.1 | |
|
modadd12d.2 | |
||
modadd12d.3 | |
||
modadd12d.4 | |
||
modadd12d.5 | |
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modadd12d.6 | |
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modadd12d.7 | |
||
Assertion | modsub12d | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | modadd12d.1 | |
|
2 | modadd12d.2 | |
|
3 | modadd12d.3 | |
|
4 | modadd12d.4 | |
|
5 | modadd12d.5 | |
|
6 | modadd12d.6 | |
|
7 | modadd12d.7 | |
|
8 | 3 | renegcld | |
9 | 4 | renegcld | |
10 | 3 4 5 7 | modnegd | |
11 | 1 2 8 9 5 6 10 | modadd12d | |
12 | 1 | recnd | |
13 | 3 | recnd | |
14 | 12 13 | negsubd | |
15 | 14 | oveq1d | |
16 | 2 | recnd | |
17 | 4 | recnd | |
18 | 16 17 | negsubd | |
19 | 18 | oveq1d | |
20 | 11 15 19 | 3eqtr3d | |