Description: From ovolun , it suffices to show that the measure of x is at least the sum of the measures of x i^i A and x \ A . (Contributed by Mario Carneiro, 15-Jun-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | ismbl2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ismbl | |
|
2 | elpwi | |
|
3 | inundif | |
|
4 | 3 | fveq2i | |
5 | inss1 | |
|
6 | simprl | |
|
7 | 5 6 | sstrid | |
8 | ovolsscl | |
|
9 | 5 8 | mp3an1 | |
10 | 9 | adantl | |
11 | difss | |
|
12 | 11 6 | sstrid | |
13 | ovolsscl | |
|
14 | 11 13 | mp3an1 | |
15 | 14 | adantl | |
16 | ovolun | |
|
17 | 7 10 12 15 16 | syl22anc | |
18 | 4 17 | eqbrtrrid | |
19 | simprr | |
|
20 | 10 15 | readdcld | |
21 | 19 20 | letri3d | |
22 | 18 21 | mpbirand | |
23 | 22 | expr | |
24 | 23 | pm5.74d | |
25 | 2 24 | sylan2 | |
26 | 25 | ralbidva | |
27 | 26 | pm5.32i | |
28 | 1 27 | bitri | |