Description: Two ways to express " A divides B " for positive integers. (Contributed by NM, 3-Feb-2004) (Proof shortened by Mario Carneiro, 16-May-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | nndiv | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | risset | |
|
2 | eqcom | |
|
3 | nncn | |
|
4 | 3 | ad2antlr | |
5 | nncn | |
|
6 | 5 | ad2antrr | |
7 | nncn | |
|
8 | 7 | adantl | |
9 | nnne0 | |
|
10 | 9 | ad2antrr | |
11 | 4 6 8 10 | divmuld | |
12 | 2 11 | bitrid | |
13 | 12 | rexbidva | |
14 | 1 13 | bitr2id | |