Step |
Hyp |
Ref |
Expression |
1 |
|
tru |
|
2 |
|
fveq2 |
|
3 |
|
fveq2 |
|
4 |
|
fveq2 |
|
5 |
|
ioossre |
|
6 |
|
elioore |
|
7 |
6
|
recnd |
|
8 |
6
|
rered |
|
9 |
|
id |
|
10 |
8 9
|
eqeltrd |
|
11 |
|
cosne0 |
|
12 |
7 10 11
|
syl2anc |
|
13 |
6 12
|
retancld |
|
14 |
13
|
adantl |
|
15 |
6
|
3ad2ant1 |
|
16 |
15
|
adantr |
|
17 |
16
|
recnd |
|
18 |
17
|
negnegd |
|
19 |
18
|
fveq2d |
|
20 |
17
|
negcld |
|
21 |
|
cosneg |
|
22 |
17 21
|
syl |
|
23 |
|
simpl1 |
|
24 |
23 12
|
syl |
|
25 |
22 24
|
eqnetrd |
|
26 |
|
tanneg |
|
27 |
20 25 26
|
syl2anc |
|
28 |
19 27
|
eqtr3d |
|
29 |
15
|
adantr |
|
30 |
29
|
renegcld |
|
31 |
25
|
adantrr |
|
32 |
30 31
|
retancld |
|
33 |
32
|
renegcld |
|
34 |
|
0red |
|
35 |
|
simp2 |
|
36 |
5 35
|
sselid |
|
37 |
36
|
adantr |
|
38 |
|
simpl2 |
|
39 |
|
elioore |
|
40 |
39
|
recnd |
|
41 |
39
|
rered |
|
42 |
|
id |
|
43 |
41 42
|
eqeltrd |
|
44 |
|
cosne0 |
|
45 |
40 43 44
|
syl2anc |
|
46 |
38 45
|
syl |
|
47 |
37 46
|
retancld |
|
48 |
|
simprl |
|
49 |
29
|
lt0neg1d |
|
50 |
48 49
|
mpbid |
|
51 |
|
simpl1 |
|
52 |
|
eliooord |
|
53 |
51 52
|
syl |
|
54 |
53
|
simpld |
|
55 |
|
halfpire |
|
56 |
|
ltnegcon1 |
|
57 |
55 29 56
|
sylancr |
|
58 |
54 57
|
mpbid |
|
59 |
|
0xr |
|
60 |
55
|
rexri |
|
61 |
|
elioo2 |
|
62 |
59 60 61
|
mp2an |
|
63 |
30 50 58 62
|
syl3anbrc |
|
64 |
|
tanrpcl |
|
65 |
63 64
|
syl |
|
66 |
65
|
rpgt0d |
|
67 |
32
|
lt0neg2d |
|
68 |
66 67
|
mpbid |
|
69 |
|
simprr |
|
70 |
|
eliooord |
|
71 |
38 70
|
syl |
|
72 |
71
|
simprd |
|
73 |
|
elioo2 |
|
74 |
59 60 73
|
mp2an |
|
75 |
37 69 72 74
|
syl3anbrc |
|
76 |
|
tanrpcl |
|
77 |
75 76
|
syl |
|
78 |
77
|
rpgt0d |
|
79 |
33 34 47 68 78
|
lttrd |
|
80 |
79
|
anassrs |
|
81 |
|
simpl3 |
|
82 |
15
|
adantr |
|
83 |
36
|
adantr |
|
84 |
82 83
|
ltnegd |
|
85 |
81 84
|
mpbid |
|
86 |
83
|
renegcld |
|
87 |
|
simpr |
|
88 |
83
|
le0neg1d |
|
89 |
87 88
|
mpbid |
|
90 |
|
simpl2 |
|
91 |
90 70
|
syl |
|
92 |
91
|
simpld |
|
93 |
|
ltnegcon1 |
|
94 |
55 83 93
|
sylancr |
|
95 |
92 94
|
mpbid |
|
96 |
|
0re |
|
97 |
|
elico2 |
|
98 |
96 60 97
|
mp2an |
|
99 |
86 89 95 98
|
syl3anbrc |
|
100 |
82
|
renegcld |
|
101 |
|
simp3 |
|
102 |
|
0red |
|
103 |
|
ltletr |
|
104 |
15 36 102 103
|
syl3anc |
|
105 |
101 104
|
mpand |
|
106 |
105
|
imp |
|
107 |
|
ltle |
|
108 |
82 96 107
|
sylancl |
|
109 |
106 108
|
mpd |
|
110 |
82
|
le0neg1d |
|
111 |
109 110
|
mpbid |
|
112 |
|
simpl1 |
|
113 |
112 52
|
syl |
|
114 |
113
|
simpld |
|
115 |
55 82 56
|
sylancr |
|
116 |
114 115
|
mpbid |
|
117 |
|
elico2 |
|
118 |
96 60 117
|
mp2an |
|
119 |
100 111 116 118
|
syl3anbrc |
|
120 |
|
tanord1 |
|
121 |
99 119 120
|
syl2anc |
|
122 |
85 121
|
mpbid |
|
123 |
83
|
recnd |
|
124 |
|
cosneg |
|
125 |
123 124
|
syl |
|
126 |
90 45
|
syl |
|
127 |
125 126
|
eqnetrd |
|
128 |
86 127
|
retancld |
|
129 |
106 25
|
syldan |
|
130 |
100 129
|
retancld |
|
131 |
128 130
|
ltnegd |
|
132 |
122 131
|
mpbid |
|
133 |
123
|
negnegd |
|
134 |
133
|
fveq2d |
|
135 |
123
|
negcld |
|
136 |
|
tanneg |
|
137 |
135 127 136
|
syl2anc |
|
138 |
134 137
|
eqtr3d |
|
139 |
132 138
|
breqtrrd |
|
140 |
139
|
adantlr |
|
141 |
|
0red |
|
142 |
|
simpl2 |
|
143 |
5 142
|
sselid |
|
144 |
80 140 141 143
|
ltlecasei |
|
145 |
28 144
|
eqbrtrd |
|
146 |
|
simpl3 |
|
147 |
15
|
adantr |
|
148 |
|
simpr |
|
149 |
|
simpl1 |
|
150 |
149 52
|
syl |
|
151 |
150
|
simprd |
|
152 |
|
elico2 |
|
153 |
96 60 152
|
mp2an |
|
154 |
147 148 151 153
|
syl3anbrc |
|
155 |
|
simpl2 |
|
156 |
5 155
|
sselid |
|
157 |
|
0red |
|
158 |
147 156 146
|
ltled |
|
159 |
157 147 156 148 158
|
letrd |
|
160 |
155 70
|
syl |
|
161 |
160
|
simprd |
|
162 |
|
elico2 |
|
163 |
96 60 162
|
mp2an |
|
164 |
156 159 161 163
|
syl3anbrc |
|
165 |
|
tanord1 |
|
166 |
154 164 165
|
syl2anc |
|
167 |
146 166
|
mpbid |
|
168 |
145 167 15 102
|
ltlecasei |
|
169 |
168
|
3expia |
|
170 |
169
|
adantl |
|
171 |
2 3 4 5 14 170
|
ltord1 |
|
172 |
1 171
|
mpan |
|