Step |
Hyp |
Ref |
Expression |
1 |
|
halfpire |
|
2 |
|
elioore |
|
3 |
|
resubcl |
|
4 |
1 2 3
|
sylancr |
|
5 |
|
neghalfpirx |
|
6 |
1
|
rexri |
|
7 |
|
elioo2 |
|
8 |
5 6 7
|
mp2an |
|
9 |
8
|
simp3bi |
|
10 |
|
posdif |
|
11 |
2 1 10
|
sylancl |
|
12 |
9 11
|
mpbid |
|
13 |
|
picn |
|
14 |
|
halfcl |
|
15 |
13 14
|
ax-mp |
|
16 |
15
|
negcli |
|
17 |
13 15
|
negsubi |
|
18 |
|
pidiv2halves |
|
19 |
13 15 15 18
|
subaddrii |
|
20 |
17 19
|
eqtri |
|
21 |
15 13 16 20
|
subaddrii |
|
22 |
8
|
simp2bi |
|
23 |
21 22
|
eqbrtrid |
|
24 |
|
pire |
|
25 |
|
ltsub23 |
|
26 |
1 24 25
|
mp3an13 |
|
27 |
2 26
|
syl |
|
28 |
23 27
|
mpbird |
|
29 |
|
0xr |
|
30 |
24
|
rexri |
|
31 |
|
elioo2 |
|
32 |
29 30 31
|
mp2an |
|
33 |
4 12 28 32
|
syl3anbrc |
|
34 |
|
sinq12gt0 |
|
35 |
33 34
|
syl |
|
36 |
2
|
recnd |
|
37 |
|
sinhalfpim |
|
38 |
36 37
|
syl |
|
39 |
35 38
|
breqtrd |
|