Step |
Hyp |
Ref |
Expression |
1 |
|
measiuns.0 |
|
2 |
|
measiuns.1 |
|
3 |
|
measiuns.2 |
|
4 |
|
measiuns.3 |
|
5 |
|
measiuns.4 |
|
6 |
1 2 3
|
iundisjcnt |
|
7 |
6
|
fveq2d |
|
8 |
|
measbase |
|
9 |
4 8
|
syl |
|
10 |
9
|
adantr |
|
11 |
|
simpll |
|
12 |
|
fzossnn |
|
13 |
|
simpr |
|
14 |
12 13
|
sseqtrrid |
|
15 |
|
simplr |
|
16 |
|
simpr |
|
17 |
15 16
|
eleqtrd |
|
18 |
|
elfzouz2 |
|
19 |
|
fzoss2 |
|
20 |
17 18 19
|
3syl |
|
21 |
20 16
|
sseqtrrd |
|
22 |
3
|
adantr |
|
23 |
14 21 22
|
mpjaodan |
|
24 |
23
|
sselda |
|
25 |
5
|
sbimi |
|
26 |
|
sban |
|
27 |
|
sbv |
|
28 |
|
clelsb3 |
|
29 |
27 28
|
anbi12i |
|
30 |
26 29
|
bitri |
|
31 |
|
sbsbc |
|
32 |
|
sbcel1g |
|
33 |
32
|
elv |
|
34 |
|
nfcv |
|
35 |
34 1 2
|
cbvcsbw |
|
36 |
|
csbid |
|
37 |
35 36
|
eqtri |
|
38 |
37
|
eleq1i |
|
39 |
31 33 38
|
3bitri |
|
40 |
25 30 39
|
3imtr3i |
|
41 |
11 24 40
|
syl2anc |
|
42 |
41
|
ralrimiva |
|
43 |
|
sigaclfu2 |
|
44 |
10 42 43
|
syl2anc |
|
45 |
|
difelsiga |
|
46 |
10 5 44 45
|
syl3anc |
|
47 |
46
|
ralrimiva |
|
48 |
|
eqimss |
|
49 |
|
fzossnn |
|
50 |
|
sseq1 |
|
51 |
49 50
|
mpbiri |
|
52 |
48 51
|
jaoi |
|
53 |
3 52
|
syl |
|
54 |
|
nnct |
|
55 |
|
ssct |
|
56 |
53 54 55
|
sylancl |
|
57 |
1 2 3
|
iundisj2cnt |
|
58 |
|
measvuni |
|
59 |
4 47 56 57 58
|
syl112anc |
|
60 |
7 59
|
eqtrd |
|