Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimir.i |
|
3 |
|
poimir.r |
|
4 |
|
poimir.1 |
|
5 |
|
poimirlem30.x |
|
6 |
|
poimirlem30.2 |
|
7 |
|
poimirlem30.3 |
|
8 |
|
poimirlem30.4 |
|
9 |
|
fzfi |
|
10 |
|
retop |
|
11 |
10
|
fconst6 |
|
12 |
|
pttop |
|
13 |
9 11 12
|
mp2an |
|
14 |
3 13
|
eqeltri |
|
15 |
|
ovex |
|
16 |
2 15
|
eqeltri |
|
17 |
|
elrest |
|
18 |
14 16 17
|
mp2an |
|
19 |
|
eqid |
|
20 |
3 19
|
ptrecube |
|
21 |
20
|
ex |
|
22 |
|
inss1 |
|
23 |
|
sseq1 |
|
24 |
22 23
|
mpbiri |
|
25 |
24
|
sseld |
|
26 |
|
ssrin |
|
27 |
|
sseq2 |
|
28 |
26 27
|
syl5ibr |
|
29 |
28
|
reximdv |
|
30 |
25 29
|
imim12d |
|
31 |
21 30
|
syl5com |
|
32 |
31
|
rexlimiv |
|
33 |
18 32
|
sylbi |
|
34 |
33
|
imp |
|
35 |
34
|
adantl |
|
36 |
|
resttop |
|
37 |
14 16 36
|
mp2an |
|
38 |
|
reex |
|
39 |
|
unitssre |
|
40 |
|
mapss |
|
41 |
38 39 40
|
mp2an |
|
42 |
2 41
|
eqsstri |
|
43 |
|
ovex |
|
44 |
|
uniretop |
|
45 |
3 44
|
ptuniconst |
|
46 |
43 10 45
|
mp2an |
|
47 |
46
|
restuni |
|
48 |
14 42 47
|
mp2an |
|
49 |
48
|
eltopss |
|
50 |
37 49
|
mpan |
|
51 |
50
|
sselda |
|
52 |
|
2rp |
|
53 |
|
rpdivcl |
|
54 |
52 53
|
mpan |
|
55 |
54
|
rpred |
|
56 |
|
ceicl |
|
57 |
55 56
|
syl |
|
58 |
|
0red |
|
59 |
57
|
zred |
|
60 |
54
|
rpgt0d |
|
61 |
|
ceige |
|
62 |
55 61
|
syl |
|
63 |
58 55 59 60 62
|
ltletrd |
|
64 |
|
elnnz |
|
65 |
57 63 64
|
sylanbrc |
|
66 |
|
fveq2 |
|
67 |
|
oveq2 |
|
68 |
67
|
oveq2d |
|
69 |
68
|
eleq2d |
|
70 |
69
|
ralbidv |
|
71 |
66 70
|
rexeqbidv |
|
72 |
71
|
rspcv |
|
73 |
65 72
|
syl |
|
74 |
73
|
adantl |
|
75 |
|
uznnssnn |
|
76 |
65 75
|
syl |
|
77 |
76
|
sseld |
|
78 |
77
|
adantl |
|
79 |
78
|
imdistani |
|
80 |
65
|
nnrpd |
|
81 |
54 80
|
lerecd |
|
82 |
62 81
|
mpbid |
|
83 |
|
rpcn |
|
84 |
|
rpne0 |
|
85 |
|
2cn |
|
86 |
|
2ne0 |
|
87 |
|
recdiv |
|
88 |
85 86 87
|
mpanl12 |
|
89 |
83 84 88
|
syl2anc |
|
90 |
82 89
|
breqtrd |
|
91 |
90
|
ad4antlr |
|
92 |
|
elmapi |
|
93 |
92 2
|
eleq2s |
|
94 |
93
|
ad4antlr |
|
95 |
94
|
ffvelrnda |
|
96 |
39 95
|
sseldi |
|
97 |
|
simp-4l |
|
98 |
|
simplr |
|
99 |
97 98
|
jca |
|
100 |
6
|
ffvelrnda |
|
101 |
|
xp1st |
|
102 |
|
elmapi |
|
103 |
100 101 102
|
3syl |
|
104 |
103
|
ffvelrnda |
|
105 |
104
|
nn0red |
|
106 |
|
simplr |
|
107 |
105 106
|
nndivred |
|
108 |
99 107
|
sylan |
|
109 |
96 108
|
resubcld |
|
110 |
109
|
recnd |
|
111 |
110
|
abscld |
|
112 |
65
|
nnrecred |
|
113 |
112
|
ad4antlr |
|
114 |
|
rphalfcl |
|
115 |
114
|
rpred |
|
116 |
115
|
ad4antlr |
|
117 |
|
ltletr |
|
118 |
111 113 116 117
|
syl3anc |
|
119 |
91 118
|
mpan2d |
|
120 |
79 119
|
sylanl1 |
|
121 |
|
simpl |
|
122 |
76
|
sselda |
|
123 |
121 122
|
anim12i |
|
124 |
123
|
anassrs |
|
125 |
|
1re |
|
126 |
|
snssi |
|
127 |
125 126
|
ax-mp |
|
128 |
|
0re |
|
129 |
|
snssi |
|
130 |
128 129
|
ax-mp |
|
131 |
127 130
|
unssi |
|
132 |
|
1ex |
|
133 |
132
|
fconst |
|
134 |
|
c0ex |
|
135 |
134
|
fconst |
|
136 |
133 135
|
pm3.2i |
|
137 |
|
xp2nd |
|
138 |
100 137
|
syl |
|
139 |
|
fvex |
|
140 |
|
f1oeq1 |
|
141 |
139 140
|
elab |
|
142 |
138 141
|
sylib |
|
143 |
|
dff1o3 |
|
144 |
143
|
simprbi |
|
145 |
|
imain |
|
146 |
142 144 145
|
3syl |
|
147 |
|
elfznn0 |
|
148 |
147
|
nn0red |
|
149 |
148
|
ltp1d |
|
150 |
|
fzdisj |
|
151 |
149 150
|
syl |
|
152 |
151
|
imaeq2d |
|
153 |
|
ima0 |
|
154 |
152 153
|
eqtrdi |
|
155 |
146 154
|
sylan9req |
|
156 |
|
fun |
|
157 |
136 155 156
|
sylancr |
|
158 |
|
imaundi |
|
159 |
|
nn0p1nn |
|
160 |
147 159
|
syl |
|
161 |
|
nnuz |
|
162 |
160 161
|
eleqtrdi |
|
163 |
|
elfzuz3 |
|
164 |
|
fzsplit2 |
|
165 |
162 163 164
|
syl2anc |
|
166 |
165
|
imaeq2d |
|
167 |
|
f1ofo |
|
168 |
|
foima |
|
169 |
142 167 168
|
3syl |
|
170 |
166 169
|
sylan9req |
|
171 |
170
|
ancoms |
|
172 |
158 171
|
syl5eqr |
|
173 |
172
|
feq2d |
|
174 |
157 173
|
mpbid |
|
175 |
174
|
ffvelrnda |
|
176 |
131 175
|
sseldi |
|
177 |
|
simpllr |
|
178 |
176 177
|
nndivred |
|
179 |
178
|
recnd |
|
180 |
179
|
absnegd |
|
181 |
124 180
|
sylanl1 |
|
182 |
124 175
|
sylanl1 |
|
183 |
|
elun |
|
184 |
182 183
|
sylib |
|
185 |
|
nnrecre |
|
186 |
|
nnrp |
|
187 |
186
|
rpreccld |
|
188 |
187
|
rpge0d |
|
189 |
185 188
|
absidd |
|
190 |
122 189
|
syl |
|
191 |
122
|
nnrecred |
|
192 |
112
|
adantr |
|
193 |
115
|
adantr |
|
194 |
|
eluzle |
|
195 |
194
|
adantl |
|
196 |
65
|
adantr |
|
197 |
196
|
nnrpd |
|
198 |
122
|
nnrpd |
|
199 |
197 198
|
lerecd |
|
200 |
195 199
|
mpbid |
|
201 |
90
|
adantr |
|
202 |
191 192 193 200 201
|
letrd |
|
203 |
190 202
|
eqbrtrd |
|
204 |
|
elsni |
|
205 |
204
|
fvoveq1d |
|
206 |
205
|
breq1d |
|
207 |
203 206
|
syl5ibrcom |
|
208 |
114
|
rpge0d |
|
209 |
|
nncn |
|
210 |
|
nnne0 |
|
211 |
209 210
|
div0d |
|
212 |
211
|
abs00bd |
|
213 |
212
|
breq1d |
|
214 |
213
|
biimparc |
|
215 |
208 214
|
sylan |
|
216 |
122 215
|
syldan |
|
217 |
|
elsni |
|
218 |
217
|
fvoveq1d |
|
219 |
218
|
breq1d |
|
220 |
216 219
|
syl5ibrcom |
|
221 |
207 220
|
jaod |
|
222 |
221
|
adantll |
|
223 |
222
|
ad2antrr |
|
224 |
184 223
|
mpd |
|
225 |
181 224
|
eqbrtrd |
|
226 |
79 111
|
sylanl1 |
|
227 |
|
simpll |
|
228 |
227
|
anim1i |
|
229 |
178
|
renegcld |
|
230 |
228 229
|
sylanl1 |
|
231 |
230
|
recnd |
|
232 |
231
|
abscld |
|
233 |
79 232
|
sylanl1 |
|
234 |
115 115
|
jca |
|
235 |
234
|
ad4antlr |
|
236 |
|
ltleadd |
|
237 |
226 233 235 236
|
syl21anc |
|
238 |
225 237
|
mpan2d |
|
239 |
110 231
|
abstrid |
|
240 |
109 230
|
readdcld |
|
241 |
240
|
recnd |
|
242 |
241
|
abscld |
|
243 |
111 232
|
readdcld |
|
244 |
115 115
|
readdcld |
|
245 |
244
|
ad4antlr |
|
246 |
|
lelttr |
|
247 |
242 243 245 246
|
syl3anc |
|
248 |
239 247
|
mpand |
|
249 |
79 248
|
sylanl1 |
|
250 |
120 238 249
|
3syld |
|
251 |
105
|
adantlr |
|
252 |
251 176
|
readdcld |
|
253 |
252 177
|
nndivred |
|
254 |
124 253
|
sylanl1 |
|
255 |
250 254
|
jctild |
|
256 |
255
|
adantld |
|
257 |
79
|
adantr |
|
258 |
93
|
ad3antlr |
|
259 |
258
|
ffvelrnda |
|
260 |
39 259
|
sseldi |
|
261 |
80
|
rpreccld |
|
262 |
261
|
rpxrd |
|
263 |
262
|
ad3antlr |
|
264 |
19
|
rexmet |
|
265 |
|
elbl |
|
266 |
264 265
|
mp3an1 |
|
267 |
260 263 266
|
syl2anc |
|
268 |
|
elmapfn |
|
269 |
100 101 268
|
3syl |
|
270 |
|
vex |
|
271 |
|
fnconstg |
|
272 |
270 271
|
mp1i |
|
273 |
|
fzfid |
|
274 |
|
inidm |
|
275 |
|
eqidd |
|
276 |
270
|
fvconst2 |
|
277 |
276
|
adantl |
|
278 |
269 272 273 273 274 275 277
|
ofval |
|
279 |
278
|
oveq2d |
|
280 |
227 279
|
sylanl1 |
|
281 |
227 107
|
sylanl1 |
|
282 |
19
|
remetdval |
|
283 |
260 281 282
|
syl2anc |
|
284 |
280 283
|
eqtrd |
|
285 |
284
|
breq1d |
|
286 |
285
|
anbi2d |
|
287 |
267 286
|
bitrd |
|
288 |
257 287
|
sylan |
|
289 |
|
rpxr |
|
290 |
289
|
ad4antlr |
|
291 |
|
elbl |
|
292 |
264 291
|
mp3an1 |
|
293 |
96 290 292
|
syl2anc |
|
294 |
|
elun |
|
295 |
|
fzofzp1 |
|
296 |
|
elsni |
|
297 |
296
|
oveq2d |
|
298 |
297
|
eleq1d |
|
299 |
295 298
|
syl5ibrcom |
|
300 |
|
elfzonn0 |
|
301 |
300
|
nn0cnd |
|
302 |
301
|
addid1d |
|
303 |
|
elfzofz |
|
304 |
302 303
|
eqeltrd |
|
305 |
|
elsni |
|
306 |
305
|
oveq2d |
|
307 |
306
|
eleq1d |
|
308 |
304 307
|
syl5ibrcom |
|
309 |
299 308
|
jaod |
|
310 |
294 309
|
syl5bi |
|
311 |
310
|
imp |
|
312 |
311
|
adantl |
|
313 |
|
dffn3 |
|
314 |
269 313
|
sylib |
|
315 |
314 7
|
fssd |
|
316 |
315
|
adantr |
|
317 |
|
fzfid |
|
318 |
312 316 174 317 317 274
|
off |
|
319 |
318
|
ffnd |
|
320 |
270 271
|
mp1i |
|
321 |
269
|
adantr |
|
322 |
174
|
ffnd |
|
323 |
|
eqidd |
|
324 |
|
eqidd |
|
325 |
321 322 317 317 274 323 324
|
ofval |
|
326 |
276
|
adantl |
|
327 |
319 320 317 317 274 325 326
|
ofval |
|
328 |
327
|
eleq1d |
|
329 |
228 328
|
sylanl1 |
|
330 |
327
|
adantl3r |
|
331 |
330
|
oveq2d |
|
332 |
93
|
ad3antlr |
|
333 |
332
|
ffvelrnda |
|
334 |
39 333
|
sseldi |
|
335 |
253
|
adantl3r |
|
336 |
19
|
remetdval |
|
337 |
334 335 336
|
syl2anc |
|
338 |
251
|
recnd |
|
339 |
176
|
recnd |
|
340 |
209
|
ad3antlr |
|
341 |
210
|
ad3antlr |
|
342 |
338 339 340 341
|
divdird |
|
343 |
107
|
recnd |
|
344 |
343
|
adantlr |
|
345 |
344 179
|
subnegd |
|
346 |
342 345
|
eqtr4d |
|
347 |
346
|
oveq2d |
|
348 |
347
|
adantl3r |
|
349 |
334
|
recnd |
|
350 |
107
|
adantllr |
|
351 |
350
|
adantlr |
|
352 |
351
|
recnd |
|
353 |
179
|
adantl3r |
|
354 |
353
|
negcld |
|
355 |
349 352 354
|
subsubd |
|
356 |
348 355
|
eqtrd |
|
357 |
356
|
fveq2d |
|
358 |
331 337 357
|
3eqtrd |
|
359 |
358
|
adantl3r |
|
360 |
83
|
2halvesd |
|
361 |
360
|
eqcomd |
|
362 |
361
|
ad4antlr |
|
363 |
359 362
|
breq12d |
|
364 |
329 363
|
anbi12d |
|
365 |
293 364
|
bitrd |
|
366 |
79 365
|
sylanl1 |
|
367 |
256 288 366
|
3imtr4d |
|
368 |
367
|
ralimdva |
|
369 |
|
simplr |
|
370 |
|
elfznn0 |
|
371 |
370
|
nn0red |
|
372 |
|
nndivre |
|
373 |
371 372
|
sylan |
|
374 |
|
elfzle1 |
|
375 |
371 374
|
jca |
|
376 |
186
|
rpregt0d |
|
377 |
|
divge0 |
|
378 |
375 376 377
|
syl2an |
|
379 |
|
elfzle2 |
|
380 |
379
|
adantr |
|
381 |
371
|
adantr |
|
382 |
|
1red |
|
383 |
186
|
adantl |
|
384 |
381 382 383
|
ledivmuld |
|
385 |
209
|
mulid1d |
|
386 |
385
|
breq2d |
|
387 |
386
|
adantl |
|
388 |
384 387
|
bitrd |
|
389 |
380 388
|
mpbird |
|
390 |
|
elicc01 |
|
391 |
373 378 389 390
|
syl3anbrc |
|
392 |
391
|
ancoms |
|
393 |
|
elsni |
|
394 |
393
|
oveq2d |
|
395 |
394
|
eleq1d |
|
396 |
392 395
|
syl5ibrcom |
|
397 |
396
|
impr |
|
398 |
369 397
|
sylan |
|
399 |
270
|
fconst |
|
400 |
399
|
a1i |
|
401 |
398 318 400 317 317 274
|
off |
|
402 |
401
|
ffnd |
|
403 |
124 402
|
sylan |
|
404 |
368 403
|
jctild |
|
405 |
2
|
eleq2i |
|
406 |
|
ovex |
|
407 |
406 43
|
elmap |
|
408 |
405 407
|
bitri |
|
409 |
401 408
|
sylibr |
|
410 |
124 409
|
sylan |
|
411 |
404 410
|
jctird |
|
412 |
|
elin |
|
413 |
|
ovex |
|
414 |
413
|
elixp |
|
415 |
414
|
anbi1i |
|
416 |
412 415
|
bitri |
|
417 |
411 416
|
syl6ibr |
|
418 |
|
ssel |
|
419 |
418
|
com12 |
|
420 |
417 419
|
syl6 |
|
421 |
420
|
impd |
|
422 |
421
|
ralrimdva |
|
423 |
422
|
expd |
|
424 |
8
|
3exp2 |
|
425 |
424
|
imp43 |
|
426 |
|
r19.29 |
|
427 |
|
fveq2 |
|
428 |
427
|
fveq1d |
|
429 |
428 5
|
eqtr4di |
|
430 |
429
|
breq2d |
|
431 |
430
|
rspcev |
|
432 |
431
|
rexlimivw |
|
433 |
426 432
|
syl |
|
434 |
433
|
expcom |
|
435 |
425 434
|
syl |
|
436 |
435
|
ralrimdvva |
|
437 |
122 436
|
sylan2 |
|
438 |
437
|
anassrs |
|
439 |
438
|
adantllr |
|
440 |
423 439
|
syl6d |
|
441 |
440
|
rexlimdva |
|
442 |
74 441
|
syld |
|
443 |
442
|
com23 |
|
444 |
443
|
impr |
|
445 |
51 444
|
sylanl2 |
|
446 |
35 445
|
rexlimddv |
|
447 |
446
|
expr |
|
448 |
447
|
com23 |
|
449 |
|
r19.21v |
|
450 |
448 449
|
syl6ibr |
|
451 |
450
|
ralrimdva |
|
452 |
|
ralcom |
|
453 |
451 452
|
syl6ib |
|