Step |
Hyp |
Ref |
Expression |
1 |
|
bposlem7.1 |
|
2 |
|
bposlem7.2 |
|
3 |
|
6nn0 |
|
4 |
|
4nn |
|
5 |
3 4
|
decnncl |
|
6 |
|
fveq2 |
|
7 |
|
8cn |
|
8 |
7
|
sqvali |
|
9 |
|
8t8e64 |
|
10 |
8 9
|
eqtri |
|
11 |
10
|
fveq2i |
|
12 |
|
0re |
|
13 |
|
8re |
|
14 |
|
8pos |
|
15 |
12 13 14
|
ltleii |
|
16 |
13
|
sqrtsqi |
|
17 |
15 16
|
ax-mp |
|
18 |
11 17
|
eqtr3i |
|
19 |
6 18
|
eqtrdi |
|
20 |
19
|
fveq2d |
|
21 |
|
8nn |
|
22 |
|
nnrp |
|
23 |
|
fveq2 |
|
24 |
|
cu2 |
|
25 |
24
|
fveq2i |
|
26 |
|
2rp |
|
27 |
|
3z |
|
28 |
|
relogexp |
|
29 |
26 27 28
|
mp2an |
|
30 |
25 29
|
eqtr3i |
|
31 |
23 30
|
eqtrdi |
|
32 |
|
id |
|
33 |
31 32
|
oveq12d |
|
34 |
|
3cn |
|
35 |
|
2nn |
|
36 |
|
nnrp |
|
37 |
|
relogcl |
|
38 |
35 36 37
|
mp2b |
|
39 |
38
|
recni |
|
40 |
21
|
nnne0i |
|
41 |
34 39 7 40
|
div23i |
|
42 |
33 41
|
eqtrdi |
|
43 |
|
ovex |
|
44 |
42 2 43
|
fvmpt |
|
45 |
21 22 44
|
mp2b |
|
46 |
20 45
|
eqtrdi |
|
47 |
46
|
oveq2d |
|
48 |
|
sqrt2re |
|
49 |
48
|
recni |
|
50 |
34 7 40
|
divcli |
|
51 |
49 50 39
|
mulassi |
|
52 |
|
4cn |
|
53 |
49 52 49
|
mul12i |
|
54 |
|
2re |
|
55 |
|
0le2 |
|
56 |
|
remsqsqrt |
|
57 |
54 55 56
|
mp2an |
|
58 |
57
|
oveq2i |
|
59 |
|
4t2e8 |
|
60 |
53 58 59
|
3eqtri |
|
61 |
60
|
oveq2i |
|
62 |
52 49
|
mulcli |
|
63 |
|
nnrp |
|
64 |
4 63
|
ax-mp |
|
65 |
|
rpsqrtcl |
|
66 |
35 36 65
|
mp2b |
|
67 |
|
rpmulcl |
|
68 |
64 66 67
|
mp2an |
|
69 |
|
rpne0 |
|
70 |
68 69
|
ax-mp |
|
71 |
|
rpne0 |
|
72 |
26 65 71
|
mp2b |
|
73 |
|
divcan5 |
|
74 |
34 73
|
mp3an1 |
|
75 |
62 70 49 72 74
|
mp4an |
|
76 |
|
4ne0 |
|
77 |
|
divdiv1 |
|
78 |
34 77
|
mp3an1 |
|
79 |
52 76 49 72 78
|
mp4an |
|
80 |
75 79
|
eqtr4i |
|
81 |
49 34 7 40
|
divassi |
|
82 |
61 80 81
|
3eqtr3ri |
|
83 |
82
|
oveq1i |
|
84 |
51 83
|
eqtr3i |
|
85 |
47 84
|
eqtrdi |
|
86 |
|
oveq1 |
|
87 |
|
df-6 |
|
88 |
87
|
oveq2i |
|
89 |
|
2exp6 |
|
90 |
|
2cn |
|
91 |
|
5nn0 |
|
92 |
|
expp1 |
|
93 |
90 91 92
|
mp2an |
|
94 |
88 89 93
|
3eqtr3i |
|
95 |
94
|
oveq1i |
|
96 |
|
nnexpcl |
|
97 |
35 91 96
|
mp2an |
|
98 |
97
|
nncni |
|
99 |
|
2ne0 |
|
100 |
98 90 99
|
divcan4i |
|
101 |
95 100
|
eqtri |
|
102 |
86 101
|
eqtrdi |
|
103 |
102
|
fveq2d |
|
104 |
|
nnrp |
|
105 |
|
fveq2 |
|
106 |
|
5nn |
|
107 |
106
|
nnzi |
|
108 |
|
relogexp |
|
109 |
26 107 108
|
mp2an |
|
110 |
105 109
|
eqtrdi |
|
111 |
|
id |
|
112 |
110 111
|
oveq12d |
|
113 |
|
5cn |
|
114 |
97
|
nnne0i |
|
115 |
113 39 98 114
|
div23i |
|
116 |
112 115
|
eqtrdi |
|
117 |
|
ovex |
|
118 |
116 2 117
|
fvmpt |
|
119 |
97 104 118
|
mp2b |
|
120 |
103 119
|
eqtrdi |
|
121 |
120
|
oveq2d |
|
122 |
|
9cn |
|
123 |
122 52 76
|
divcli |
|
124 |
113 98 114
|
divcli |
|
125 |
123 124 39
|
mulassi |
|
126 |
121 125
|
eqtr4di |
|
127 |
85 126
|
oveq12d |
|
128 |
34 52 76
|
divcli |
|
129 |
128 49 72
|
divcli |
|
130 |
123 124
|
mulcli |
|
131 |
129 130 39
|
adddiri |
|
132 |
127 131
|
eqtr4di |
|
133 |
|
oveq2 |
|
134 |
133
|
fveq2d |
|
135 |
5
|
nnrei |
|
136 |
5
|
nngt0i |
|
137 |
12 135 136
|
ltleii |
|
138 |
54 135 55 137
|
sqrtmulii |
|
139 |
18
|
oveq2i |
|
140 |
138 139
|
eqtri |
|
141 |
134 140
|
eqtrdi |
|
142 |
141
|
oveq2d |
|
143 |
49 7
|
mulcli |
|
144 |
|
rpmulcl |
|
145 |
66 22 144
|
sylancr |
|
146 |
|
rpne0 |
|
147 |
21 145 146
|
mp2b |
|
148 |
|
divrec2 |
|
149 |
39 143 147 148
|
mp3an |
|
150 |
49 7
|
mulcomi |
|
151 |
150
|
oveq2i |
|
152 |
|
recdiv2 |
|
153 |
7 40 49 72 152
|
mp4an |
|
154 |
151 153
|
eqtr4i |
|
155 |
154
|
oveq1i |
|
156 |
149 155
|
eqtri |
|
157 |
142 156
|
eqtrdi |
|
158 |
132 157
|
oveq12d |
|
159 |
129 130
|
addcli |
|
160 |
7 40
|
reccli |
|
161 |
160 49 72
|
divcli |
|
162 |
159 161 39
|
adddiri |
|
163 |
158 162
|
eqtr4di |
|
164 |
|
ovex |
|
165 |
163 1 164
|
fvmpt |
|
166 |
5 165
|
ax-mp |
|
167 |
|
3re |
|
168 |
|
4re |
|
169 |
167 168 76
|
redivcli |
|
170 |
169 48 72
|
redivcli |
|
171 |
|
9re |
|
172 |
171 168 76
|
redivcli |
|
173 |
|
5re |
|
174 |
97
|
nnrei |
|
175 |
173 174 114
|
redivcli |
|
176 |
172 175
|
remulcli |
|
177 |
170 176
|
readdcli |
|
178 |
13 40
|
rereccli |
|
179 |
178 48 72
|
redivcli |
|
180 |
177 179
|
readdcli |
|
181 |
180 38
|
remulcli |
|
182 |
166 181
|
eqeltri |
|
183 |
129 130 161
|
add32i |
|
184 |
|
6cn |
|
185 |
|
ax-1cn |
|
186 |
184 185 7 40
|
divdiri |
|
187 |
|
df-7 |
|
188 |
187
|
oveq1i |
|
189 |
|
divcan5 |
|
190 |
34 189
|
mp3an1 |
|
191 |
52 76 90 99 190
|
mp4an |
|
192 |
|
3t2e6 |
|
193 |
34 90 192
|
mulcomli |
|
194 |
52 90 59
|
mulcomli |
|
195 |
193 194
|
oveq12i |
|
196 |
191 195
|
eqtr3i |
|
197 |
196
|
oveq1i |
|
198 |
186 188 197
|
3eqtr4ri |
|
199 |
198
|
oveq1i |
|
200 |
128 160 49 72
|
divdiri |
|
201 |
|
7cn |
|
202 |
201 7 49 40 72
|
divdiv32i |
|
203 |
199 200 202
|
3eqtr3i |
|
204 |
203
|
oveq1i |
|
205 |
183 204
|
eqtri |
|
206 |
|
4nn0 |
|
207 |
|
9nn0 |
|
208 |
|
0nn0 |
|
209 |
|
9lt10 |
|
210 |
|
4lt5 |
|
211 |
206 91 207 208 209 210
|
decltc |
|
212 |
|
7t7e49 |
|
213 |
57
|
oveq1i |
|
214 |
49 49 113 113
|
mul4i |
|
215 |
|
5t2e10 |
|
216 |
113 90 215
|
mulcomli |
|
217 |
216
|
oveq1i |
|
218 |
90 113 113
|
mulassi |
|
219 |
91
|
dec0u |
|
220 |
217 218 219
|
3eqtr3i |
|
221 |
213 214 220
|
3eqtr3i |
|
222 |
211 212 221
|
3brtr4i |
|
223 |
|
7re |
|
224 |
|
7pos |
|
225 |
12 223 224
|
ltleii |
|
226 |
|
nnrp |
|
227 |
106 226
|
ax-mp |
|
228 |
|
rpmulcl |
|
229 |
66 227 228
|
mp2an |
|
230 |
|
rpge0 |
|
231 |
229 230
|
ax-mp |
|
232 |
|
rpre |
|
233 |
229 232
|
ax-mp |
|
234 |
223 233
|
lt2msqi |
|
235 |
225 231 234
|
mp2an |
|
236 |
222 235
|
mpbir |
|
237 |
|
rpgt0 |
|
238 |
26 65 237
|
mp2b |
|
239 |
|
ltdivmul |
|
240 |
223 173 239
|
mp3an12 |
|
241 |
48 238 240
|
mp2an |
|
242 |
236 241
|
mpbir |
|
243 |
223 48 72
|
redivcli |
|
244 |
243 173 13 14
|
ltdiv1ii |
|
245 |
242 244
|
mpbi |
|
246 |
|
divsubdir |
|
247 |
7 34 246
|
mp3an12 |
|
248 |
7 40 247
|
mp2an |
|
249 |
|
5p3e8 |
|
250 |
249
|
oveq1i |
|
251 |
113 34
|
pncan3oi |
|
252 |
250 251
|
eqtr3i |
|
253 |
252
|
oveq1i |
|
254 |
7 40
|
dividi |
|
255 |
254
|
oveq1i |
|
256 |
248 253 255
|
3eqtr3ri |
|
257 |
|
5lt8 |
|
258 |
13 173
|
remulcli |
|
259 |
173 13 258
|
ltadd2i |
|
260 |
257 259
|
mpbi |
|
261 |
|
df-9 |
|
262 |
261
|
oveq1i |
|
263 |
7 185 113
|
adddiri |
|
264 |
113
|
mulid2i |
|
265 |
264
|
oveq2i |
|
266 |
262 263 265
|
3eqtri |
|
267 |
87
|
oveq2i |
|
268 |
7 113 185
|
adddii |
|
269 |
7
|
mulid1i |
|
270 |
269
|
oveq2i |
|
271 |
267 268 270
|
3eqtri |
|
272 |
260 266 271
|
3brtr4i |
|
273 |
171 173
|
remulcli |
|
274 |
|
6re |
|
275 |
13 274
|
remulcli |
|
276 |
168 174
|
remulcli |
|
277 |
4 97
|
nnmulcli |
|
278 |
277
|
nngt0i |
|
279 |
273 275 276 278
|
ltdiv1ii |
|
280 |
272 279
|
mpbi |
|
281 |
122 52 113 98 76 114
|
divmuldivi |
|
282 |
|
nnexpcl |
|
283 |
35 206 282
|
mp2an |
|
284 |
283
|
nncni |
|
285 |
283
|
nnne0i |
|
286 |
|
divcan5 |
|
287 |
34 286
|
mp3an1 |
|
288 |
7 40 284 285 287
|
mp4an |
|
289 |
|
df-4 |
|
290 |
289
|
oveq2i |
|
291 |
|
3nn0 |
|
292 |
|
expp1 |
|
293 |
90 291 292
|
mp2an |
|
294 |
24
|
oveq1i |
|
295 |
290 293 294
|
3eqtri |
|
296 |
295
|
oveq1i |
|
297 |
7 90 34
|
mulassi |
|
298 |
193
|
oveq2i |
|
299 |
296 297 298
|
3eqtri |
|
300 |
|
4p3e7 |
|
301 |
|
5p2e7 |
|
302 |
113 90
|
addcomi |
|
303 |
300 301 302
|
3eqtr2i |
|
304 |
303
|
oveq2i |
|
305 |
|
expadd |
|
306 |
90 206 291 305
|
mp3an |
|
307 |
|
2nn0 |
|
308 |
|
expadd |
|
309 |
90 307 91 308
|
mp3an |
|
310 |
304 306 309
|
3eqtr3i |
|
311 |
24
|
oveq2i |
|
312 |
|
sq2 |
|
313 |
312
|
oveq1i |
|
314 |
310 311 313
|
3eqtr3i |
|
315 |
299 314
|
oveq12i |
|
316 |
288 315
|
eqtr3i |
|
317 |
280 281 316
|
3brtr4i |
|
318 |
167 13 40
|
redivcli |
|
319 |
|
1re |
|
320 |
|
ltsub2 |
|
321 |
176 318 319 320
|
mp3an |
|
322 |
317 321
|
mpbi |
|
323 |
256 322
|
eqbrtrri |
|
324 |
243 13 40
|
redivcli |
|
325 |
173 13 40
|
redivcli |
|
326 |
319 176
|
resubcli |
|
327 |
324 325 326
|
lttri |
|
328 |
245 323 327
|
mp2an |
|
329 |
324 176 319
|
ltaddsubi |
|
330 |
328 329
|
mpbir |
|
331 |
205 330
|
eqbrtri |
|
332 |
|
1lt2 |
|
333 |
|
rplogcl |
|
334 |
54 332 333
|
mp2an |
|
335 |
|
rpgt0 |
|
336 |
334 335
|
ax-mp |
|
337 |
180 319 38 336
|
ltmul1ii |
|
338 |
331 337
|
mpbi |
|
339 |
39
|
mulid2i |
|
340 |
339
|
eqcomi |
|
341 |
338 166 340
|
3brtr4i |
|
342 |
182 341
|
pm3.2i |
|