Description: A bound on the harmonic series, as compared to the natural logarithm. (Contributed by Mario Carneiro, 9-Apr-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | harmonicbnd | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 | |
|
2 | 1 | sumeq1d | |
3 | fveq2 | |
|
4 | 2 3 | oveq12d | |
5 | 4 | eleq1d | |
6 | eqid | |
|
7 | eqid | |
|
8 | eqid | |
|
9 | oveq2 | |
|
10 | 9 | oveq2d | |
11 | 10 | fveq2d | |
12 | 9 11 | oveq12d | |
13 | 12 | cbvmptv | |
14 | 6 7 8 13 | emcllem7 | |
15 | 14 | simp2i | |
16 | 6 | fmpt | |
17 | 15 16 | mpbir | |
18 | 5 17 | vtoclri | |