Step |
Hyp |
Ref |
Expression |
1 |
|
meascnbl.0 |
|
2 |
|
meascnbl.1 |
|
3 |
|
meascnbl.2 |
|
4 |
|
meascnbl.3 |
|
5 |
2
|
adantr |
|
6 |
|
measbase |
|
7 |
2 6
|
syl |
|
8 |
7
|
adantr |
|
9 |
3
|
ffvelrnda |
|
10 |
|
simpll |
|
11 |
|
fzossnn |
|
12 |
|
simpr |
|
13 |
11 12
|
sseldi |
|
14 |
3
|
ffvelrnda |
|
15 |
10 13 14
|
syl2anc |
|
16 |
15
|
ralrimiva |
|
17 |
|
sigaclfu2 |
|
18 |
8 16 17
|
syl2anc |
|
19 |
|
difelsiga |
|
20 |
8 9 18 19
|
syl3anc |
|
21 |
|
measvxrge0 |
|
22 |
5 20 21
|
syl2anc |
|
23 |
|
fveq2 |
|
24 |
|
oveq2 |
|
25 |
24
|
iuneq1d |
|
26 |
23 25
|
difeq12d |
|
27 |
26
|
fveq2d |
|
28 |
|
fveq2 |
|
29 |
|
oveq2 |
|
30 |
29
|
iuneq1d |
|
31 |
28 30
|
difeq12d |
|
32 |
31
|
fveq2d |
|
33 |
1 22 27 32
|
esumcvg2 |
|
34 |
|
measfrge0 |
|
35 |
2 34
|
syl |
|
36 |
|
fcompt |
|
37 |
35 3 36
|
syl2anc |
|
38 |
|
nfcv |
|
39 |
|
fveq2 |
|
40 |
|
simpr |
|
41 |
40
|
nnzd |
|
42 |
|
fzval3 |
|
43 |
41 42
|
syl |
|
44 |
43
|
olcd |
|
45 |
2
|
adantr |
|
46 |
|
simpll |
|
47 |
|
fzossnn |
|
48 |
43
|
eleq2d |
|
49 |
48
|
biimpa |
|
50 |
47 49
|
sseldi |
|
51 |
46 50 9
|
syl2anc |
|
52 |
38 39 44 45 51
|
measiuns |
|
53 |
3
|
ffnd |
|
54 |
53 4
|
iuninc |
|
55 |
54
|
fveq2d |
|
56 |
52 55
|
eqtr3d |
|
57 |
56
|
mpteq2dva |
|
58 |
37 57
|
eqtr4d |
|
59 |
9
|
ralrimiva |
|
60 |
|
dfiun2g |
|
61 |
59 60
|
syl |
|
62 |
|
fnrnfv |
|
63 |
53 62
|
syl |
|
64 |
63
|
unieqd |
|
65 |
61 64
|
eqtr4d |
|
66 |
65
|
fveq2d |
|
67 |
|
eqidd |
|
68 |
67
|
orcd |
|
69 |
38 39 68 2 9
|
measiuns |
|
70 |
66 69
|
eqtr3d |
|
71 |
33 58 70
|
3brtr4d |
|