Step |
Hyp |
Ref |
Expression |
1 |
|
basel.n |
|
2 |
|
basel.p |
|
3 |
|
basel.t |
|
4 |
1
|
basellem1 |
|
5 |
|
tanrpcl |
|
6 |
4 5
|
syl |
|
7 |
|
2z |
|
8 |
|
znegcl |
|
9 |
7 8
|
ax-mp |
|
10 |
|
rpexpcl |
|
11 |
6 9 10
|
sylancl |
|
12 |
11
|
rpcnd |
|
13 |
1 2
|
basellem3 |
|
14 |
4 13
|
syldan |
|
15 |
|
elfzelz |
|
16 |
15
|
adantl |
|
17 |
16
|
zred |
|
18 |
|
pire |
|
19 |
|
remulcl |
|
20 |
17 18 19
|
sylancl |
|
21 |
20
|
recnd |
|
22 |
|
2nn |
|
23 |
|
nnmulcl |
|
24 |
22 23
|
mpan |
|
25 |
24
|
peano2nnd |
|
26 |
1 25
|
eqeltrid |
|
27 |
26
|
adantr |
|
28 |
27
|
nncnd |
|
29 |
27
|
nnne0d |
|
30 |
21 28 29
|
divcan2d |
|
31 |
30
|
fveq2d |
|
32 |
|
sinkpi |
|
33 |
16 32
|
syl |
|
34 |
31 33
|
eqtrd |
|
35 |
34
|
oveq1d |
|
36 |
20 27
|
nndivred |
|
37 |
36
|
resincld |
|
38 |
37
|
recnd |
|
39 |
27
|
nnnn0d |
|
40 |
38 39
|
expcld |
|
41 |
|
sincosq1sgn |
|
42 |
4 41
|
syl |
|
43 |
42
|
simpld |
|
44 |
43
|
gt0ne0d |
|
45 |
27
|
nnzd |
|
46 |
38 44 45
|
expne0d |
|
47 |
40 46
|
div0d |
|
48 |
14 35 47
|
3eqtrd |
|
49 |
1 2
|
basellem2 |
|
50 |
49
|
simp1d |
|
51 |
|
plyf |
|
52 |
|
ffn |
|
53 |
50 51 52
|
3syl |
|
54 |
53
|
adantr |
|
55 |
|
fniniseg |
|
56 |
54 55
|
syl |
|
57 |
12 48 56
|
mpbir2and |
|
58 |
57 3
|
fmptd |
|
59 |
|
fveq2 |
|
60 |
|
fveq2 |
|
61 |
|
fveq2 |
|
62 |
15
|
zred |
|
63 |
62
|
ssriv |
|
64 |
11
|
rpred |
|
65 |
64 3
|
fmptd |
|
66 |
65
|
ffvelrnda |
|
67 |
|
simplr |
|
68 |
63
|
sseli |
|
69 |
68
|
ad2antrl |
|
70 |
63
|
sseli |
|
71 |
70
|
ad2antll |
|
72 |
18
|
a1i |
|
73 |
|
pipos |
|
74 |
73
|
a1i |
|
75 |
|
ltmul1 |
|
76 |
69 71 72 74 75
|
syl112anc |
|
77 |
67 76
|
mpbid |
|
78 |
|
remulcl |
|
79 |
69 18 78
|
sylancl |
|
80 |
|
remulcl |
|
81 |
71 18 80
|
sylancl |
|
82 |
26
|
ad2antrr |
|
83 |
82
|
nnred |
|
84 |
82
|
nngt0d |
|
85 |
|
ltdiv1 |
|
86 |
79 81 83 84 85
|
syl112anc |
|
87 |
77 86
|
mpbid |
|
88 |
|
neghalfpirx |
|
89 |
|
pirp |
|
90 |
|
rphalfcl |
|
91 |
|
rpge0 |
|
92 |
89 90 91
|
mp2b |
|
93 |
|
halfpire |
|
94 |
|
le0neg2 |
|
95 |
93 94
|
ax-mp |
|
96 |
92 95
|
mpbi |
|
97 |
|
iooss1 |
|
98 |
88 96 97
|
mp2an |
|
99 |
1
|
basellem1 |
|
100 |
99
|
ad2ant2r |
|
101 |
98 100
|
sseldi |
|
102 |
1
|
basellem1 |
|
103 |
102
|
ad2ant2rl |
|
104 |
98 103
|
sseldi |
|
105 |
|
tanord |
|
106 |
101 104 105
|
syl2anc |
|
107 |
87 106
|
mpbid |
|
108 |
|
tanrpcl |
|
109 |
100 108
|
syl |
|
110 |
|
tanrpcl |
|
111 |
103 110
|
syl |
|
112 |
|
rprege0 |
|
113 |
|
rprege0 |
|
114 |
|
lt2sq |
|
115 |
112 113 114
|
syl2an |
|
116 |
109 111 115
|
syl2anc |
|
117 |
107 116
|
mpbid |
|
118 |
|
rpexpcl |
|
119 |
109 7 118
|
sylancl |
|
120 |
|
rpexpcl |
|
121 |
111 7 120
|
sylancl |
|
122 |
119 121
|
ltrecd |
|
123 |
117 122
|
mpbid |
|
124 |
|
oveq1 |
|
125 |
124
|
fvoveq1d |
|
126 |
125
|
oveq1d |
|
127 |
|
ovex |
|
128 |
126 3 127
|
fvmpt |
|
129 |
128
|
ad2antll |
|
130 |
111
|
rpcnd |
|
131 |
|
2nn0 |
|
132 |
|
expneg |
|
133 |
130 131 132
|
sylancl |
|
134 |
129 133
|
eqtrd |
|
135 |
|
oveq1 |
|
136 |
135
|
fvoveq1d |
|
137 |
136
|
oveq1d |
|
138 |
|
ovex |
|
139 |
137 3 138
|
fvmpt |
|
140 |
139
|
ad2antrl |
|
141 |
109
|
rpcnd |
|
142 |
|
expneg |
|
143 |
141 131 142
|
sylancl |
|
144 |
140 143
|
eqtrd |
|
145 |
123 134 144
|
3brtr4d |
|
146 |
145
|
an32s |
|
147 |
146
|
ex |
|
148 |
59 60 61 63 66 147
|
eqord2 |
|
149 |
148
|
biimprd |
|
150 |
149
|
ralrimivva |
|
151 |
|
dff13 |
|
152 |
58 150 151
|
sylanbrc |
|
153 |
49
|
simp2d |
|
154 |
|
nnne0 |
|
155 |
153 154
|
eqnetrd |
|
156 |
|
fveq2 |
|
157 |
|
dgr0 |
|
158 |
156 157
|
eqtrdi |
|
159 |
158
|
necon3i |
|
160 |
155 159
|
syl |
|
161 |
|
eqid |
|
162 |
161
|
fta1 |
|
163 |
50 160 162
|
syl2anc |
|
164 |
163
|
simpld |
|
165 |
|
f1domg |
|
166 |
164 152 165
|
sylc |
|
167 |
163
|
simprd |
|
168 |
|
nnnn0 |
|
169 |
|
hashfz1 |
|
170 |
168 169
|
syl |
|
171 |
153 170
|
eqtr4d |
|
172 |
167 171
|
breqtrd |
|
173 |
|
fzfid |
|
174 |
|
hashdom |
|
175 |
164 173 174
|
syl2anc |
|
176 |
172 175
|
mpbid |
|
177 |
|
sbth |
|
178 |
166 176 177
|
syl2anc |
|
179 |
|
f1finf1o |
|
180 |
178 164 179
|
syl2anc |
|
181 |
152 180
|
mpbid |
|