Description: If A is simply normal, then the function F of relative density of B in the digit string converges to 1 / R , i.e. the set of occurrences of B in the digit string has natural density 1 / R . (Contributed by Mario Carneiro, 6-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | snml.s | |
|
snml.f | |
||
Assertion | snmlflim | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snml.s | |
|
2 | snml.f | |
|
3 | 1 | snmlval | |
4 | 3 | simp3bi | |
5 | eqeq2 | |
|
6 | 5 | rabbidv | |
7 | 6 | fveq2d | |
8 | 7 | oveq1d | |
9 | 8 | mpteq2dv | |
10 | 9 2 | eqtr4di | |
11 | 10 | breq1d | |
12 | 11 | rspccva | |
13 | 4 12 | sylan | |