Step |
Hyp |
Ref |
Expression |
1 |
|
cosord.1 |
|
2 |
|
cosord.2 |
|
3 |
|
cosord.3 |
|
4 |
|
0re |
|
5 |
|
pire |
|
6 |
4 5
|
elicc2i |
|
7 |
2 6
|
sylib |
|
8 |
7
|
simp1d |
|
9 |
8
|
recnd |
|
10 |
4 5
|
elicc2i |
|
11 |
1 10
|
sylib |
|
12 |
11
|
simp1d |
|
13 |
12
|
recnd |
|
14 |
|
subcos |
|
15 |
9 13 14
|
syl2anc |
|
16 |
|
2rp |
|
17 |
8 12
|
readdcld |
|
18 |
17
|
rehalfcld |
|
19 |
18
|
resincld |
|
20 |
4
|
a1i |
|
21 |
11
|
simp2d |
|
22 |
20 12 8 21 3
|
lelttrd |
|
23 |
8 12 22 21
|
addgtge0d |
|
24 |
|
2re |
|
25 |
|
2pos |
|
26 |
|
divgt0 |
|
27 |
24 25 26
|
mpanr12 |
|
28 |
17 23 27
|
syl2anc |
|
29 |
5
|
a1i |
|
30 |
12 8 8 3
|
ltadd2dd |
|
31 |
9
|
2timesd |
|
32 |
30 31
|
breqtrrd |
|
33 |
24
|
a1i |
|
34 |
25
|
a1i |
|
35 |
|
ltdivmul |
|
36 |
17 8 33 34 35
|
syl112anc |
|
37 |
32 36
|
mpbird |
|
38 |
7
|
simp3d |
|
39 |
18 8 29 37 38
|
ltletrd |
|
40 |
|
0xr |
|
41 |
5
|
rexri |
|
42 |
|
elioo2 |
|
43 |
40 41 42
|
mp2an |
|
44 |
18 28 39 43
|
syl3anbrc |
|
45 |
|
sinq12gt0 |
|
46 |
44 45
|
syl |
|
47 |
19 46
|
elrpd |
|
48 |
8 12
|
resubcld |
|
49 |
48
|
rehalfcld |
|
50 |
49
|
resincld |
|
51 |
12 8
|
posdifd |
|
52 |
3 51
|
mpbid |
|
53 |
|
divgt0 |
|
54 |
24 25 53
|
mpanr12 |
|
55 |
48 52 54
|
syl2anc |
|
56 |
|
rehalfcl |
|
57 |
5 56
|
mp1i |
|
58 |
8 12
|
subge02d |
|
59 |
21 58
|
mpbid |
|
60 |
48 8 29 59 38
|
letrd |
|
61 |
|
lediv1 |
|
62 |
48 29 33 34 61
|
syl112anc |
|
63 |
60 62
|
mpbid |
|
64 |
|
pirp |
|
65 |
|
rphalflt |
|
66 |
64 65
|
mp1i |
|
67 |
49 57 29 63 66
|
lelttrd |
|
68 |
|
elioo2 |
|
69 |
40 41 68
|
mp2an |
|
70 |
49 55 67 69
|
syl3anbrc |
|
71 |
|
sinq12gt0 |
|
72 |
70 71
|
syl |
|
73 |
50 72
|
elrpd |
|
74 |
47 73
|
rpmulcld |
|
75 |
|
rpmulcl |
|
76 |
16 74 75
|
sylancr |
|
77 |
15 76
|
eqeltrd |
|
78 |
8
|
recoscld |
|
79 |
12
|
recoscld |
|
80 |
|
difrp |
|
81 |
78 79 80
|
syl2anc |
|
82 |
77 81
|
mpbird |
|