Description: Closure theorem for the "distance to nearest integer" function. (Contributed by Asger C. Ipsen, 4-Apr-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | dnicld1.1 | |
|
Assertion | dnicld1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dnicld1.1 | |
|
2 | halfre | |
|
3 | 2 | a1i | |
4 | 1 3 | jca | |
5 | readdcl | |
|
6 | 4 5 | syl | |
7 | reflcl | |
|
8 | 6 7 | syl | |
9 | 8 | recnd | |
10 | 1 | recnd | |
11 | 9 10 | subcld | |
12 | 11 | abscld | |