Step |
Hyp |
Ref |
Expression |
1 |
|
wallispilem2.1 |
|
2 |
|
0nn0 |
|
3 |
|
oveq2 |
|
4 |
3
|
adantr |
|
5 |
|
ioosscn |
|
6 |
5
|
sseli |
|
7 |
6
|
sincld |
|
8 |
7
|
adantl |
|
9 |
8
|
exp0d |
|
10 |
4 9
|
eqtrd |
|
11 |
10
|
itgeq2dv |
|
12 |
|
ioombl |
|
13 |
|
0re |
|
14 |
|
pire |
|
15 |
|
ioovolcl |
|
16 |
13 14 15
|
mp2an |
|
17 |
|
ax-1cn |
|
18 |
|
itgconst |
|
19 |
12 16 17 18
|
mp3an |
|
20 |
16
|
recni |
|
21 |
20
|
mulid2i |
|
22 |
|
pipos |
|
23 |
13 14 22
|
ltleii |
|
24 |
|
volioo |
|
25 |
13 14 23 24
|
mp3an |
|
26 |
14
|
recni |
|
27 |
26
|
subid1i |
|
28 |
25 27
|
eqtri |
|
29 |
21 28
|
eqtri |
|
30 |
19 29
|
eqtri |
|
31 |
11 30
|
eqtrdi |
|
32 |
14
|
elexi |
|
33 |
31 1 32
|
fvmpt |
|
34 |
2 33
|
ax-mp |
|
35 |
|
1nn0 |
|
36 |
|
simpl |
|
37 |
36
|
oveq2d |
|
38 |
7
|
adantl |
|
39 |
38
|
exp1d |
|
40 |
37 39
|
eqtrd |
|
41 |
40
|
itgeq2dv |
|
42 |
|
itgex |
|
43 |
41 1 42
|
fvmpt |
|
44 |
35 43
|
ax-mp |
|
45 |
|
itgsin0pi |
|
46 |
44 45
|
eqtri |
|
47 |
|
id |
|
48 |
1 47
|
itgsinexp |
|
49 |
34 46 48
|
3pm3.2i |
|