Description: Closure for a decimal fraction with no decimal expansion in the positive real numbers. (Contributed by Thierry Arnoux, 25-Dec-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | rpdp2cl2.a | |- A e. NN |
|
Assertion | rpdp2cl2 | |- _ A 0 e. RR+ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpdp2cl2.a | |- A e. NN |
|
2 | 1 | nnnn0i | |- A e. NN0 |
3 | 2 | dp20u | |- _ A 0 = A |
4 | nnrp | |- ( A e. NN -> A e. RR+ ) |
|
5 | 1 4 | ax-mp | |- A e. RR+ |
6 | 3 5 | eqeltri | |- _ A 0 e. RR+ |