Step |
Hyp |
Ref |
Expression |
1 |
|
rpcn |
|
2 |
1
|
sqcld |
|
3 |
|
rpre |
|
4 |
3
|
renegcld |
|
5 |
|
iccssre |
|
6 |
4 3 5
|
syl2anc |
|
7 |
|
ax-resscn |
|
8 |
6 7
|
sstrdi |
|
9 |
|
ssid |
|
10 |
9
|
a1i |
|
11 |
|
cncfmptc |
|
12 |
2 8 10 11
|
syl3anc |
|
13 |
|
eqid |
|
14 |
13
|
addcn |
|
15 |
14
|
a1i |
|
16 |
8
|
sselda |
|
17 |
1
|
adantr |
|
18 |
|
rpne0 |
|
19 |
18
|
adantr |
|
20 |
16 17 19
|
divcld |
|
21 |
|
asinval |
|
22 |
20 21
|
syl |
|
23 |
|
ax-icn |
|
24 |
23
|
a1i |
|
25 |
24 20
|
mulcld |
|
26 |
|
1cnd |
|
27 |
20
|
sqcld |
|
28 |
26 27
|
subcld |
|
29 |
28
|
sqrtcld |
|
30 |
25 29
|
addcld |
|
31 |
|
0lt1 |
|
32 |
|
simp3 |
|
33 |
32
|
oveq1d |
|
34 |
1 18
|
div0d |
|
35 |
34
|
3ad2ant1 |
|
36 |
33 35
|
eqtrd |
|
37 |
36
|
oveq2d |
|
38 |
|
it0e0 |
|
39 |
37 38
|
eqtrdi |
|
40 |
36
|
oveq1d |
|
41 |
40
|
oveq2d |
|
42 |
41
|
fveq2d |
|
43 |
|
sq0 |
|
44 |
43
|
oveq2i |
|
45 |
|
1m0e1 |
|
46 |
44 45
|
eqtri |
|
47 |
46
|
fveq2i |
|
48 |
|
sqrt1 |
|
49 |
47 48
|
eqtri |
|
50 |
42 49
|
eqtrdi |
|
51 |
39 50
|
oveq12d |
|
52 |
|
0p1e1 |
|
53 |
51 52
|
eqtrdi |
|
54 |
53
|
breq2d |
|
55 |
|
0red |
|
56 |
|
1red |
|
57 |
53 56
|
eqeltrd |
|
58 |
55 57
|
ltnled |
|
59 |
54 58
|
bitr3d |
|
60 |
31 59
|
mpbii |
|
61 |
60
|
3expa |
|
62 |
61
|
olcd |
|
63 |
|
inelr |
|
64 |
25 29
|
pncand |
|
65 |
64
|
3adant3 |
|
66 |
65
|
oveq1d |
|
67 |
23
|
a1i |
|
68 |
20
|
3adant3 |
|
69 |
1
|
3ad2ant1 |
|
70 |
16
|
3adant3 |
|
71 |
|
simp3 |
|
72 |
69 70 71
|
divcld |
|
73 |
67 68 72
|
mulassd |
|
74 |
66 73
|
eqtrd |
|
75 |
18
|
3ad2ant1 |
|
76 |
70 69 71 75
|
divcan6d |
|
77 |
76
|
oveq2d |
|
78 |
67
|
mulid1d |
|
79 |
74 77 78
|
3eqtrrd |
|
80 |
79
|
adantr |
|
81 |
|
simpr |
|
82 |
|
1red |
|
83 |
6
|
sselda |
|
84 |
3
|
adantr |
|
85 |
83 84 19
|
redivcld |
|
86 |
85
|
resqcld |
|
87 |
82 86
|
resubcld |
|
88 |
|
elicc2 |
|
89 |
4 3 88
|
syl2anc |
|
90 |
|
1red |
|
91 |
|
simpr |
|
92 |
3
|
adantr |
|
93 |
18
|
adantr |
|
94 |
91 92 93
|
redivcld |
|
95 |
94
|
resqcld |
|
96 |
90 95
|
subge0d |
|
97 |
|
recn |
|
98 |
97
|
adantl |
|
99 |
1
|
adantr |
|
100 |
98 99 93
|
sqdivd |
|
101 |
100
|
breq1d |
|
102 |
|
resqcl |
|
103 |
102
|
adantl |
|
104 |
3
|
resqcld |
|
105 |
|
rpgt0 |
|
106 |
|
0red |
|
107 |
|
0le0 |
|
108 |
107
|
a1i |
|
109 |
|
rpge0 |
|
110 |
106 3 108 109
|
lt2sqd |
|
111 |
43
|
a1i |
|
112 |
111
|
breq1d |
|
113 |
110 112
|
bitrd |
|
114 |
105 113
|
mpbid |
|
115 |
104 114
|
elrpd |
|
116 |
115
|
adantr |
|
117 |
103 90 116
|
ledivmuld |
|
118 |
|
absresq |
|
119 |
118
|
eqcomd |
|
120 |
2
|
mulid1d |
|
121 |
119 120
|
breqan12rd |
|
122 |
97
|
abscld |
|
123 |
122
|
adantl |
|
124 |
97
|
absge0d |
|
125 |
124
|
adantl |
|
126 |
109
|
adantr |
|
127 |
123 92 125 126
|
le2sqd |
|
128 |
91 92
|
absled |
|
129 |
121 127 128
|
3bitr2d |
|
130 |
117 129
|
bitrd |
|
131 |
96 101 130
|
3bitrrd |
|
132 |
131
|
biimpd |
|
133 |
132
|
exp4b |
|
134 |
133
|
3impd |
|
135 |
89 134
|
sylbid |
|
136 |
135
|
imp |
|
137 |
87 136
|
resqrtcld |
|
138 |
137
|
3adant3 |
|
139 |
138
|
adantr |
|
140 |
81 139
|
resubcld |
|
141 |
3
|
3ad2ant1 |
|
142 |
83
|
3adant3 |
|
143 |
141 142 71
|
redivcld |
|
144 |
143
|
adantr |
|
145 |
140 144
|
remulcld |
|
146 |
80 145
|
eqeltrd |
|
147 |
146
|
ex |
|
148 |
147
|
3expa |
|
149 |
63 148
|
mtoi |
|
150 |
149
|
orcd |
|
151 |
62 150
|
pm2.61dane |
|
152 |
|
ianor |
|
153 |
151 152
|
sylibr |
|
154 |
|
mnfxr |
|
155 |
|
0re |
|
156 |
|
elioc2 |
|
157 |
154 155 156
|
mp2an |
|
158 |
|
3simpb |
|
159 |
157 158
|
sylbi |
|
160 |
153 159
|
nsyl |
|
161 |
30 160
|
eldifd |
|
162 |
|
fvres |
|
163 |
161 162
|
syl |
|
164 |
163
|
oveq2d |
|
165 |
22 164
|
eqtr4d |
|
166 |
165
|
mpteq2dva |
|
167 |
|
negicn |
|
168 |
167
|
a1i |
|
169 |
|
cncfmptc |
|
170 |
168 8 10 169
|
syl3anc |
|
171 |
13
|
cnfldtopon |
|
172 |
171
|
a1i |
|
173 |
|
resttopon |
|
174 |
172 8 173
|
syl2anc |
|
175 |
161
|
fmpttd |
|
176 |
|
difssd |
|
177 |
16 17 19
|
divrec2d |
|
178 |
177
|
oveq2d |
|
179 |
1 18
|
reccld |
|
180 |
179
|
adantr |
|
181 |
24 180 16
|
mulassd |
|
182 |
178 181
|
eqtr4d |
|
183 |
182
|
mpteq2dva |
|
184 |
23
|
a1i |
|
185 |
184 179
|
mulcld |
|
186 |
|
cncfmptc |
|
187 |
185 8 10 186
|
syl3anc |
|
188 |
|
cncfmptid |
|
189 |
8 10 188
|
syl2anc |
|
190 |
187 189
|
mulcncf |
|
191 |
183 190
|
eqeltrd |
|
192 |
17 29
|
mulcld |
|
193 |
192 17 19
|
divrec2d |
|
194 |
29 17 19
|
divcan3d |
|
195 |
104
|
adantr |
|
196 |
3
|
sqge0d |
|
197 |
196
|
adantr |
|
198 |
195 197 87 136
|
sqrtmuld |
|
199 |
2
|
adantr |
|
200 |
199 26 27
|
subdid |
|
201 |
199
|
mulid1d |
|
202 |
16 17 19
|
sqdivd |
|
203 |
202
|
oveq2d |
|
204 |
16
|
sqcld |
|
205 |
|
sqne0 |
|
206 |
1 205
|
syl |
|
207 |
18 206
|
mpbird |
|
208 |
207
|
adantr |
|
209 |
204 199 208
|
divcan2d |
|
210 |
203 209
|
eqtrd |
|
211 |
201 210
|
oveq12d |
|
212 |
200 211
|
eqtrd |
|
213 |
212
|
fveq2d |
|
214 |
109
|
adantr |
|
215 |
84 214
|
sqrtsqd |
|
216 |
215
|
oveq1d |
|
217 |
198 213 216
|
3eqtr3rd |
|
218 |
217
|
oveq2d |
|
219 |
193 194 218
|
3eqtr3d |
|
220 |
219
|
mpteq2dva |
|
221 |
|
cncfmptc |
|
222 |
179 8 10 221
|
syl3anc |
|
223 |
|
areacirclem2 |
|
224 |
3 109 223
|
syl2anc |
|
225 |
222 224
|
mulcncf |
|
226 |
220 225
|
eqeltrd |
|
227 |
13 15 191 226
|
cncfmpt2f |
|
228 |
|
cncffvrn |
|
229 |
176 227 228
|
syl2anc |
|
230 |
175 229
|
mpbird |
|
231 |
|
eqid |
|
232 |
|
eqid |
|
233 |
13 231 232
|
cncfcn |
|
234 |
8 176 233
|
syl2anc |
|
235 |
230 234
|
eleqtrd |
|
236 |
|
eqid |
|
237 |
236
|
logcn |
|
238 |
|
difss |
|
239 |
|
eqid |
|
240 |
13 232 239
|
cncfcn |
|
241 |
238 9 240
|
mp2an |
|
242 |
237 241
|
eleqtri |
|
243 |
242
|
a1i |
|
244 |
174 235 243
|
cnmpt11f |
|
245 |
13 231 239
|
cncfcn |
|
246 |
8 10 245
|
syl2anc |
|
247 |
244 246
|
eleqtrrd |
|
248 |
170 247
|
mulcncf |
|
249 |
166 248
|
eqeltrd |
|
250 |
219
|
oveq2d |
|
251 |
199 204
|
subcld |
|
252 |
251
|
sqrtcld |
|
253 |
20 180 252
|
mulassd |
|
254 |
16 17 19
|
divrecd |
|
255 |
254
|
oveq1d |
|
256 |
16 180 180
|
mulassd |
|
257 |
255 256
|
eqtrd |
|
258 |
257
|
oveq1d |
|
259 |
250 253 258
|
3eqtr2d |
|
260 |
259
|
mpteq2dva |
|
261 |
179 179
|
mulcld |
|
262 |
|
cncfmptc |
|
263 |
261 8 10 262
|
syl3anc |
|
264 |
189 263
|
mulcncf |
|
265 |
264 224
|
mulcncf |
|
266 |
260 265
|
eqeltrd |
|
267 |
13 15 249 266
|
cncfmpt2f |
|
268 |
12 267
|
mulcncf |
|