Step |
Hyp |
Ref |
Expression |
1 |
|
bpos.1 |
|
2 |
|
bpos.2 |
|
3 |
|
bpos.3 |
|
4 |
|
bpos.4 |
|
5 |
|
bpos.5 |
|
6 |
|
4nn |
|
7 |
|
5nn |
|
8 |
|
eluznn |
|
9 |
7 1 8
|
sylancr |
|
10 |
9
|
nnnn0d |
|
11 |
|
nnexpcl |
|
12 |
6 10 11
|
sylancr |
|
13 |
12
|
nnred |
|
14 |
13 9
|
nndivred |
|
15 |
|
fzctr |
|
16 |
10 15
|
syl |
|
17 |
|
bccl2 |
|
18 |
16 17
|
syl |
|
19 |
18
|
nnred |
|
20 |
|
2nn |
|
21 |
|
nnmulcl |
|
22 |
20 9 21
|
sylancr |
|
23 |
22
|
nnrpd |
|
24 |
22
|
nnred |
|
25 |
23
|
rpge0d |
|
26 |
24 25
|
resqrtcld |
|
27 |
|
3nn |
|
28 |
|
nndivre |
|
29 |
26 27 28
|
sylancl |
|
30 |
|
2re |
|
31 |
|
readdcl |
|
32 |
29 30 31
|
sylancl |
|
33 |
23 32
|
rpcxpcld |
|
34 |
33
|
rpred |
|
35 |
|
2rp |
|
36 |
|
nnmulcl |
|
37 |
6 9 36
|
sylancr |
|
38 |
37
|
nnred |
|
39 |
|
nndivre |
|
40 |
38 27 39
|
sylancl |
|
41 |
|
5re |
|
42 |
|
resubcl |
|
43 |
40 41 42
|
sylancl |
|
44 |
|
rpcxpcl |
|
45 |
35 43 44
|
sylancr |
|
46 |
45
|
rpred |
|
47 |
34 46
|
remulcld |
|
48 |
|
df-5 |
|
49 |
|
4z |
|
50 |
|
uzid |
|
51 |
|
peano2uz |
|
52 |
49 50 51
|
mp2b |
|
53 |
48 52
|
eqeltri |
|
54 |
|
eqid |
|
55 |
54
|
uztrn2 |
|
56 |
53 1 55
|
sylancr |
|
57 |
|
bclbnd |
|
58 |
56 57
|
syl |
|
59 |
|
id |
|
60 |
|
pccl |
|
61 |
59 18 60
|
syl2anr |
|
62 |
61
|
ralrimiva |
|
63 |
3 62
|
pcmptcl |
|
64 |
63
|
simprd |
|
65 |
1 2 3 4 5
|
bposlem4 |
|
66 |
|
elfzuz |
|
67 |
65 66
|
syl |
|
68 |
|
eluznn |
|
69 |
27 67 68
|
sylancr |
|
70 |
64 69
|
ffvelrnd |
|
71 |
70
|
nnred |
|
72 |
|
2z |
|
73 |
|
nndivre |
|
74 |
24 27 73
|
sylancl |
|
75 |
74
|
flcld |
|
76 |
4 75
|
eqeltrid |
|
77 |
|
zmulcl |
|
78 |
72 76 77
|
sylancr |
|
79 |
7
|
nnzi |
|
80 |
|
zsubcl |
|
81 |
78 79 80
|
sylancl |
|
82 |
81
|
zred |
|
83 |
|
rpcxpcl |
|
84 |
35 82 83
|
sylancr |
|
85 |
84
|
rpred |
|
86 |
71 85
|
remulcld |
|
87 |
1 2 3 4
|
bposlem3 |
|
88 |
|
elfzuz3 |
|
89 |
65 88
|
syl |
|
90 |
3 62 69 89
|
pcmptdvds |
|
91 |
70
|
nnzd |
|
92 |
70
|
nnne0d |
|
93 |
|
uztrn |
|
94 |
89 67 93
|
syl2anc |
|
95 |
|
eluznn |
|
96 |
27 94 95
|
sylancr |
|
97 |
64 96
|
ffvelrnd |
|
98 |
97
|
nnzd |
|
99 |
|
dvdsval2 |
|
100 |
91 92 98 99
|
syl3anc |
|
101 |
90 100
|
mpbid |
|
102 |
101
|
zred |
|
103 |
69
|
nnred |
|
104 |
76
|
zred |
|
105 |
|
eluzle |
|
106 |
89 105
|
syl |
|
107 |
|
efchtdvds |
|
108 |
103 104 106 107
|
syl3anc |
|
109 |
|
efchtcl |
|
110 |
103 109
|
syl |
|
111 |
110
|
nnzd |
|
112 |
110
|
nnne0d |
|
113 |
|
efchtcl |
|
114 |
104 113
|
syl |
|
115 |
114
|
nnzd |
|
116 |
|
dvdsval2 |
|
117 |
111 112 115 116
|
syl3anc |
|
118 |
108 117
|
mpbid |
|
119 |
118
|
zred |
|
120 |
|
prmz |
|
121 |
|
fllt |
|
122 |
26 120 121
|
syl2an |
|
123 |
5
|
breq1i |
|
124 |
122 123
|
bitr4di |
|
125 |
120
|
zred |
|
126 |
|
ltnle |
|
127 |
103 125 126
|
syl2an |
|
128 |
124 127
|
bitrd |
|
129 |
|
bposlem1 |
|
130 |
9 129
|
sylan |
|
131 |
125
|
adantl |
|
132 |
|
id |
|
133 |
|
pccl |
|
134 |
132 18 133
|
syl2anr |
|
135 |
131 134
|
reexpcld |
|
136 |
24
|
adantr |
|
137 |
131
|
resqcld |
|
138 |
|
lelttr |
|
139 |
135 136 137 138
|
syl3anc |
|
140 |
130 139
|
mpand |
|
141 |
|
resqrtth |
|
142 |
24 25 141
|
syl2anc |
|
143 |
142
|
breq1d |
|
144 |
143
|
adantr |
|
145 |
134
|
nn0zd |
|
146 |
72
|
a1i |
|
147 |
|
prmgt1 |
|
148 |
147
|
adantl |
|
149 |
131 145 146 148
|
ltexp2d |
|
150 |
140 144 149
|
3imtr4d |
|
151 |
|
df-2 |
|
152 |
151
|
breq2i |
|
153 |
150 152
|
syl6ib |
|
154 |
26
|
adantr |
|
155 |
24 25
|
sqrtge0d |
|
156 |
155
|
adantr |
|
157 |
|
prmnn |
|
158 |
157
|
nnrpd |
|
159 |
158
|
rpge0d |
|
160 |
159
|
adantl |
|
161 |
154 131 156 160
|
lt2sqd |
|
162 |
|
1z |
|
163 |
|
zleltp1 |
|
164 |
145 162 163
|
sylancl |
|
165 |
153 161 164
|
3imtr4d |
|
166 |
128 165
|
sylbird |
|
167 |
166
|
imp |
|
168 |
167
|
adantrl |
|
169 |
|
iftrue |
|
170 |
169
|
adantl |
|
171 |
|
iftrue |
|
172 |
171
|
adantl |
|
173 |
168 170 172
|
3brtr4d |
|
174 |
|
0le0 |
|
175 |
|
iffalse |
|
176 |
|
iffalse |
|
177 |
175 176
|
breq12d |
|
178 |
174 177
|
mpbiri |
|
179 |
178
|
adantl |
|
180 |
173 179
|
pm2.61dan |
|
181 |
62
|
adantr |
|
182 |
69
|
adantr |
|
183 |
|
simpr |
|
184 |
|
oveq1 |
|
185 |
89
|
adantr |
|
186 |
3 181 182 183 184 185
|
pcmpt2 |
|
187 |
|
eqid |
|
188 |
187
|
prmorcht |
|
189 |
96 188
|
syl |
|
190 |
187
|
prmorcht |
|
191 |
69 190
|
syl |
|
192 |
189 191
|
oveq12d |
|
193 |
192
|
adantr |
|
194 |
193
|
oveq2d |
|
195 |
|
nncn |
|
196 |
195
|
exp1d |
|
197 |
196
|
ifeq1d |
|
198 |
197
|
mpteq2ia |
|
199 |
198
|
eqcomi |
|
200 |
|
1nn0 |
|
201 |
200
|
a1i |
|
202 |
201
|
ralrimiva |
|
203 |
202
|
adantr |
|
204 |
|
eqidd |
|
205 |
199 203 182 183 204 185
|
pcmpt2 |
|
206 |
194 205
|
eqtrd |
|
207 |
180 186 206
|
3brtr4d |
|
208 |
207
|
ralrimiva |
|
209 |
|
pc2dvds |
|
210 |
101 118 209
|
syl2anc |
|
211 |
208 210
|
mpbird |
|
212 |
114
|
nnred |
|
213 |
110
|
nnred |
|
214 |
114
|
nngt0d |
|
215 |
110
|
nngt0d |
|
216 |
212 213 214 215
|
divgt0d |
|
217 |
|
elnnz |
|
218 |
118 216 217
|
sylanbrc |
|
219 |
|
dvdsle |
|
220 |
101 218 219
|
syl2anc |
|
221 |
211 220
|
mpd |
|
222 |
|
nndivre |
|
223 |
212 6 222
|
sylancl |
|
224 |
|
4re |
|
225 |
224
|
a1i |
|
226 |
|
6re |
|
227 |
226
|
a1i |
|
228 |
|
4lt6 |
|
229 |
228
|
a1i |
|
230 |
|
cht3 |
|
231 |
230
|
fveq2i |
|
232 |
|
6pos |
|
233 |
226 232
|
elrpii |
|
234 |
|
reeflog |
|
235 |
233 234
|
ax-mp |
|
236 |
231 235
|
eqtri |
|
237 |
|
3re |
|
238 |
237
|
a1i |
|
239 |
|
eluzle |
|
240 |
67 239
|
syl |
|
241 |
|
chtwordi |
|
242 |
238 103 240 241
|
syl3anc |
|
243 |
|
chtcl |
|
244 |
237 243
|
ax-mp |
|
245 |
|
chtcl |
|
246 |
103 245
|
syl |
|
247 |
|
efle |
|
248 |
244 246 247
|
sylancr |
|
249 |
242 248
|
mpbid |
|
250 |
236 249
|
eqbrtrrid |
|
251 |
225 227 213 229 250
|
ltletrd |
|
252 |
|
4pos |
|
253 |
252
|
a1i |
|
254 |
|
ltdiv2 |
|
255 |
225 253 213 215 212 214 254
|
syl222anc |
|
256 |
251 255
|
mpbid |
|
257 |
30
|
a1i |
|
258 |
|
2lt3 |
|
259 |
258
|
a1i |
|
260 |
238 103 104 240 106
|
letrd |
|
261 |
257 238 104 259 260
|
ltletrd |
|
262 |
|
chtub |
|
263 |
104 261 262
|
syl2anc |
|
264 |
|
chtcl |
|
265 |
104 264
|
syl |
|
266 |
|
relogcl |
|
267 |
35 266
|
ax-mp |
|
268 |
|
3z |
|
269 |
|
zsubcl |
|
270 |
78 268 269
|
sylancl |
|
271 |
270
|
zred |
|
272 |
|
remulcl |
|
273 |
267 271 272
|
sylancr |
|
274 |
|
eflt |
|
275 |
265 273 274
|
syl2anc |
|
276 |
263 275
|
mpbid |
|
277 |
|
reexplog |
|
278 |
35 270 277
|
sylancr |
|
279 |
270
|
zcnd |
|
280 |
267
|
recni |
|
281 |
|
mulcom |
|
282 |
279 280 281
|
sylancl |
|
283 |
282
|
fveq2d |
|
284 |
278 283
|
eqtrd |
|
285 |
276 284
|
breqtrrd |
|
286 |
|
3p2e5 |
|
287 |
286
|
oveq1i |
|
288 |
|
3cn |
|
289 |
|
2cn |
|
290 |
288 289
|
pncan3oi |
|
291 |
287 290
|
eqtr3i |
|
292 |
291
|
oveq2i |
|
293 |
78
|
zcnd |
|
294 |
|
5cn |
|
295 |
|
subsub |
|
296 |
294 289 295
|
mp3an23 |
|
297 |
293 296
|
syl |
|
298 |
292 297
|
syl5eqr |
|
299 |
298
|
oveq2d |
|
300 |
|
2ne0 |
|
301 |
|
cxpexpz |
|
302 |
289 300 270 301
|
mp3an12i |
|
303 |
81
|
zcnd |
|
304 |
|
2cnne0 |
|
305 |
|
cxpadd |
|
306 |
304 289 305
|
mp3an13 |
|
307 |
303 306
|
syl |
|
308 |
299 302 307
|
3eqtr3d |
|
309 |
|
2nn0 |
|
310 |
|
cxpexp |
|
311 |
289 309 310
|
mp2an |
|
312 |
|
sq2 |
|
313 |
311 312
|
eqtri |
|
314 |
313
|
oveq2i |
|
315 |
308 314
|
eqtrdi |
|
316 |
285 315
|
breqtrd |
|
317 |
224 252
|
pm3.2i |
|
318 |
317
|
a1i |
|
319 |
|
ltdivmul2 |
|
320 |
212 85 318 319
|
syl3anc |
|
321 |
316 320
|
mpbird |
|
322 |
119 223 85 256 321
|
lttrd |
|
323 |
102 119 85 221 322
|
lelttrd |
|
324 |
97
|
nnred |
|
325 |
|
nnre |
|
326 |
|
nngt0 |
|
327 |
325 326
|
jca |
|
328 |
70 327
|
syl |
|
329 |
|
ltdivmul |
|
330 |
324 85 328 329
|
syl3anc |
|
331 |
323 330
|
mpbid |
|
332 |
87 331
|
eqbrtrrd |
|
333 |
34 85
|
remulcld |
|
334 |
1 2 3 4 5
|
bposlem5 |
|
335 |
71 34 84
|
lemul1d |
|
336 |
334 335
|
mpbid |
|
337 |
78
|
zred |
|
338 |
41
|
a1i |
|
339 |
|
flle |
|
340 |
74 339
|
syl |
|
341 |
4 340
|
eqbrtrid |
|
342 |
|
2pos |
|
343 |
30 342
|
pm3.2i |
|
344 |
343
|
a1i |
|
345 |
|
lemul2 |
|
346 |
104 74 344 345
|
syl3anc |
|
347 |
341 346
|
mpbid |
|
348 |
22
|
nncnd |
|
349 |
|
3ne0 |
|
350 |
288 349
|
pm3.2i |
|
351 |
|
divass |
|
352 |
289 350 351
|
mp3an13 |
|
353 |
348 352
|
syl |
|
354 |
|
2t2e4 |
|
355 |
354
|
oveq1i |
|
356 |
9
|
nncnd |
|
357 |
|
mulass |
|
358 |
289 289 356 357
|
mp3an12i |
|
359 |
355 358
|
syl5reqr |
|
360 |
359
|
oveq1d |
|
361 |
353 360
|
eqtr3d |
|
362 |
347 361
|
breqtrd |
|
363 |
337 40 338 362
|
lesub1dd |
|
364 |
|
1lt2 |
|
365 |
364
|
a1i |
|
366 |
257 365 82 43
|
cxpled |
|
367 |
363 366
|
mpbid |
|
368 |
85 46 33
|
lemul2d |
|
369 |
367 368
|
mpbid |
|
370 |
86 333 47 336 369
|
letrd |
|
371 |
19 86 47 332 370
|
ltletrd |
|
372 |
14 19 47 58 371
|
lttrd |
|