Step |
Hyp |
Ref |
Expression |
1 |
|
dvnprodlem2.s |
|
2 |
|
dvnprodlem2.x |
|
3 |
|
dvnprodlem2.t |
|
4 |
|
dvnprodlem2.h |
|
5 |
|
dvnprodlem2.n |
|
6 |
|
dvnprodlem2.dvnh |
|
7 |
|
dvnprodlem2.c |
|
8 |
|
dvnprodlem2.r |
|
9 |
|
dvnprodlem2.z |
|
10 |
|
dvnprodlem2.ind |
|
11 |
|
dvnprodlem2.j |
|
12 |
|
dvnprodlem2.d |
|
13 |
|
nfv |
|
14 |
|
nfcv |
|
15 |
|
ssfi |
|
16 |
3 8 15
|
syl2anc |
|
17 |
16
|
adantr |
|
18 |
9
|
adantr |
|
19 |
9
|
eldifbd |
|
20 |
19
|
adantr |
|
21 |
|
simpl |
|
22 |
8
|
sselda |
|
23 |
21 22 4
|
syl2anc |
|
24 |
23
|
adantlr |
|
25 |
|
simplr |
|
26 |
24 25
|
ffvelrnd |
|
27 |
|
fveq2 |
|
28 |
27
|
fveq1d |
|
29 |
|
id |
|
30 |
|
eldifi |
|
31 |
9 30
|
syl |
|
32 |
|
simpr |
|
33 |
|
id |
|
34 |
|
eleq1 |
|
35 |
34
|
anbi2d |
|
36 |
27
|
feq1d |
|
37 |
35 36
|
imbi12d |
|
38 |
37 4
|
vtoclg |
|
39 |
32 33 38
|
sylc |
|
40 |
29 31 39
|
syl2anc |
|
41 |
40
|
adantr |
|
42 |
|
simpr |
|
43 |
41 42
|
ffvelrnd |
|
44 |
13 14 17 18 20 26 28 43
|
fprodsplitsn |
|
45 |
44
|
mpteq2dva |
|
46 |
45
|
oveq2d |
|
47 |
46
|
fveq1d |
|
48 |
13 17 26
|
fprodclf |
|
49 |
|
elfznn0 |
|
50 |
11 49
|
syl |
|
51 |
|
eqid |
|
52 |
|
eqid |
|
53 |
|
oveq2 |
|
54 |
|
rabeq |
|
55 |
53 54
|
syl |
|
56 |
|
sumeq1 |
|
57 |
56
|
eqeq1d |
|
58 |
57
|
rabbidv |
|
59 |
55 58
|
eqtrd |
|
60 |
59
|
mpteq2dv |
|
61 |
|
ssexg |
|
62 |
8 3 61
|
syl2anc |
|
63 |
|
elpwg |
|
64 |
62 63
|
syl |
|
65 |
8 64
|
mpbird |
|
66 |
65
|
adantr |
|
67 |
|
nn0ex |
|
68 |
67
|
mptex |
|
69 |
68
|
a1i |
|
70 |
7 60 66 69
|
fvmptd3 |
|
71 |
|
oveq2 |
|
72 |
71
|
oveq1d |
|
73 |
|
rabeq |
|
74 |
72 73
|
syl |
|
75 |
|
eqeq2 |
|
76 |
75
|
rabbidv |
|
77 |
74 76
|
eqtrd |
|
78 |
77
|
adantl |
|
79 |
|
elfznn0 |
|
80 |
79
|
adantl |
|
81 |
|
fzfid |
|
82 |
|
mapfi |
|
83 |
81 16 82
|
syl2anc |
|
84 |
83
|
adantr |
|
85 |
|
ssrab2 |
|
86 |
85
|
a1i |
|
87 |
84 86
|
ssexd |
|
88 |
70 78 80 87
|
fvmptd |
|
89 |
|
ssfi |
|
90 |
83 85 89
|
sylancl |
|
91 |
90
|
adantr |
|
92 |
88 91
|
eqeltrd |
|
93 |
92
|
adantr |
|
94 |
79
|
faccld |
|
95 |
94
|
nncnd |
|
96 |
95
|
ad2antlr |
|
97 |
16
|
adantr |
|
98 |
97
|
adantlr |
|
99 |
|
elfznn0 |
|
100 |
99
|
ssriv |
|
101 |
100
|
a1i |
|
102 |
|
simpr |
|
103 |
88
|
eleq2d |
|
104 |
103
|
adantr |
|
105 |
102 104
|
mpbid |
|
106 |
85
|
sseli |
|
107 |
105 106
|
syl |
|
108 |
|
elmapi |
|
109 |
107 108
|
syl |
|
110 |
109
|
adantr |
|
111 |
|
simpr |
|
112 |
110 111
|
ffvelrnd |
|
113 |
101 112
|
sseldd |
|
114 |
113
|
faccld |
|
115 |
114
|
nncnd |
|
116 |
98 115
|
fprodcl |
|
117 |
114
|
nnne0d |
|
118 |
98 115 117
|
fprodn0 |
|
119 |
96 116 118
|
divcld |
|
120 |
119
|
adantlr |
|
121 |
98
|
adantlr |
|
122 |
29
|
ad4antr |
|
123 |
122 22
|
sylancom |
|
124 |
|
elfzuz3 |
|
125 |
|
fzss2 |
|
126 |
124 125
|
syl |
|
127 |
126
|
adantl |
|
128 |
50
|
nn0zd |
|
129 |
5
|
nn0zd |
|
130 |
|
elfzle2 |
|
131 |
11 130
|
syl |
|
132 |
128 129 131
|
3jca |
|
133 |
|
eluz2 |
|
134 |
132 133
|
sylibr |
|
135 |
|
fzss2 |
|
136 |
134 135
|
syl |
|
137 |
136
|
adantr |
|
138 |
127 137
|
sstrd |
|
139 |
138
|
ad2antrr |
|
140 |
139 112
|
sseldd |
|
141 |
140
|
adantllr |
|
142 |
|
fvex |
|
143 |
|
eleq1 |
|
144 |
143
|
3anbi3d |
|
145 |
|
fveq2 |
|
146 |
145
|
feq1d |
|
147 |
144 146
|
imbi12d |
|
148 |
142 147 6
|
vtocl |
|
149 |
122 123 141 148
|
syl3anc |
|
150 |
|
simpllr |
|
151 |
149 150
|
ffvelrnd |
|
152 |
121 151
|
fprodcl |
|
153 |
120 152
|
mulcld |
|
154 |
93 153
|
fsumcl |
|
155 |
154
|
fmpttd |
|
156 |
10
|
adantr |
|
157 |
|
0zd |
|
158 |
129
|
adantr |
|
159 |
|
elfzelz |
|
160 |
159
|
adantl |
|
161 |
|
elfzle1 |
|
162 |
161
|
adantl |
|
163 |
160
|
zred |
|
164 |
50
|
nn0red |
|
165 |
164
|
adantr |
|
166 |
158
|
zred |
|
167 |
|
elfzle2 |
|
168 |
167
|
adantl |
|
169 |
131
|
adantr |
|
170 |
163 165 166 168 169
|
letrd |
|
171 |
157 158 160 162 170
|
elfzd |
|
172 |
|
rspa |
|
173 |
156 171 172
|
syl2anc |
|
174 |
173
|
feq1d |
|
175 |
155 174
|
mpbird |
|
176 |
31
|
adantr |
|
177 |
|
simpl |
|
178 |
177 176 171
|
3jca |
|
179 |
34
|
3anbi2d |
|
180 |
27
|
oveq2d |
|
181 |
180
|
fveq1d |
|
182 |
181
|
feq1d |
|
183 |
179 182
|
imbi12d |
|
184 |
|
eleq1 |
|
185 |
184
|
3anbi3d |
|
186 |
|
fveq2 |
|
187 |
186
|
feq1d |
|
188 |
185 187
|
imbi12d |
|
189 |
188 6
|
chvarvv |
|
190 |
183 189
|
vtoclg |
|
191 |
176 178 190
|
sylc |
|
192 |
40
|
feqmptd |
|
193 |
192
|
eqcomd |
|
194 |
193
|
oveq2d |
|
195 |
194
|
fveq1d |
|
196 |
195
|
adantr |
|
197 |
196
|
feq1d |
|
198 |
191 197
|
mpbird |
|
199 |
|
fveq2 |
|
200 |
199
|
prodeq2ad |
|
201 |
200
|
cbvmptv |
|
202 |
201
|
oveq2i |
|
203 |
202
|
fveq1i |
|
204 |
203
|
mpteq2i |
|
205 |
|
fveq2 |
|
206 |
205
|
cbvmptv |
|
207 |
206
|
oveq2i |
|
208 |
207
|
fveq1i |
|
209 |
208
|
mpteq2i |
|
210 |
1 2 48 43 50 51 52 175 198 204 209
|
dvnmul |
|
211 |
203
|
a1i |
|
212 |
10
|
r19.21bi |
|
213 |
177 171 212
|
syl2anc |
|
214 |
211 213
|
eqtrd |
|
215 |
214
|
mpteq2dva |
|
216 |
|
mptexg |
|
217 |
2 216
|
syl |
|
218 |
217
|
adantr |
|
219 |
215 218
|
fvmpt2d |
|
220 |
219
|
adantlr |
|
221 |
220
|
fveq1d |
|
222 |
42
|
adantr |
|
223 |
154
|
an32s |
|
224 |
|
eqid |
|
225 |
224
|
fvmpt2 |
|
226 |
222 223 225
|
syl2anc |
|
227 |
221 226
|
eqtrd |
|
228 |
|
fveq2 |
|
229 |
228
|
cbvmptv |
|
230 |
229
|
a1i |
|
231 |
207 194
|
syl5eq |
|
232 |
231
|
fveq1d |
|
233 |
232
|
mpteq2dv |
|
234 |
230 233
|
eqtrd |
|
235 |
234
|
adantr |
|
236 |
|
fveq2 |
|
237 |
236
|
adantl |
|
238 |
|
0zd |
|
239 |
|
elfzel2 |
|
240 |
239 159
|
zsubcld |
|
241 |
238 239 240
|
3jca |
|
242 |
239
|
zred |
|
243 |
79
|
nn0red |
|
244 |
242 243
|
subge0d |
|
245 |
167 244
|
mpbird |
|
246 |
242 243
|
subge02d |
|
247 |
161 246
|
mpbid |
|
248 |
241 245 247
|
jca32 |
|
249 |
248
|
adantl |
|
250 |
|
elfz2 |
|
251 |
249 250
|
sylibr |
|
252 |
|
fvex |
|
253 |
252
|
a1i |
|
254 |
235 237 251 253
|
fvmptd |
|
255 |
254
|
adantlr |
|
256 |
255
|
fveq1d |
|
257 |
227 256
|
oveq12d |
|
258 |
257
|
oveq2d |
|
259 |
92
|
adantlr |
|
260 |
|
ovex |
|
261 |
|
eleq1 |
|
262 |
261
|
anbi2d |
|
263 |
236
|
feq1d |
|
264 |
262 263
|
imbi12d |
|
265 |
|
eleq1 |
|
266 |
265
|
anbi2d |
|
267 |
|
fveq2 |
|
268 |
267
|
feq1d |
|
269 |
266 268
|
imbi12d |
|
270 |
269 191
|
chvarvv |
|
271 |
260 264 270
|
vtocl |
|
272 |
177 251 271
|
syl2anc |
|
273 |
272
|
adantlr |
|
274 |
273 222
|
ffvelrnd |
|
275 |
|
anass |
|
276 |
|
ancom |
|
277 |
276
|
anbi2i |
|
278 |
|
anass |
|
279 |
278
|
bicomi |
|
280 |
277 279
|
bitri |
|
281 |
275 280
|
bitri |
|
282 |
281
|
anbi1i |
|
283 |
282
|
imbi1i |
|
284 |
153 283
|
mpbi |
|
285 |
259 274 284
|
fsummulc1 |
|
286 |
285
|
oveq2d |
|
287 |
177 50
|
syl |
|
288 |
287 160
|
bccld |
|
289 |
288
|
nn0cnd |
|
290 |
289
|
adantlr |
|
291 |
274
|
adantr |
|
292 |
284 291
|
mulcld |
|
293 |
259 290 292
|
fsummulc2 |
|
294 |
258 286 293
|
3eqtrd |
|
295 |
294
|
sumeq2dv |
|
296 |
|
vex |
|
297 |
|
vex |
|
298 |
296 297
|
op1std |
|
299 |
298
|
oveq2d |
|
300 |
298
|
fveq2d |
|
301 |
296 297
|
op2ndd |
|
302 |
301
|
fveq1d |
|
303 |
302
|
fveq2d |
|
304 |
303
|
prodeq2ad |
|
305 |
300 304
|
oveq12d |
|
306 |
302
|
fveq2d |
|
307 |
306
|
fveq1d |
|
308 |
307
|
prodeq2ad |
|
309 |
305 308
|
oveq12d |
|
310 |
298
|
oveq2d |
|
311 |
310
|
fveq2d |
|
312 |
311
|
fveq1d |
|
313 |
309 312
|
oveq12d |
|
314 |
299 313
|
oveq12d |
|
315 |
|
fzfid |
|
316 |
290
|
adantrr |
|
317 |
292
|
anasss |
|
318 |
316 317
|
mulcld |
|
319 |
314 315 259 318
|
fsum2d |
|
320 |
|
ovex |
|
321 |
297
|
resex |
|
322 |
320 321
|
op1std |
|
323 |
322
|
oveq2d |
|
324 |
322
|
fveq2d |
|
325 |
320 321
|
op2ndd |
|
326 |
325
|
fveq1d |
|
327 |
326
|
fveq2d |
|
328 |
327
|
prodeq2ad |
|
329 |
324 328
|
oveq12d |
|
330 |
326
|
fveq2d |
|
331 |
330
|
fveq1d |
|
332 |
331
|
prodeq2ad |
|
333 |
329 332
|
oveq12d |
|
334 |
322
|
oveq2d |
|
335 |
334
|
fveq2d |
|
336 |
335
|
fveq1d |
|
337 |
333 336
|
oveq12d |
|
338 |
323 337
|
oveq12d |
|
339 |
|
oveq2 |
|
340 |
|
rabeq |
|
341 |
339 340
|
syl |
|
342 |
|
sumeq1 |
|
343 |
342
|
eqeq1d |
|
344 |
343
|
rabbidv |
|
345 |
341 344
|
eqtrd |
|
346 |
345
|
mpteq2dv |
|
347 |
31
|
snssd |
|
348 |
8 347
|
unssd |
|
349 |
3 348
|
ssexd |
|
350 |
|
elpwg |
|
351 |
349 350
|
syl |
|
352 |
348 351
|
mpbird |
|
353 |
67
|
mptex |
|
354 |
353
|
a1i |
|
355 |
7 346 352 354
|
fvmptd3 |
|
356 |
|
oveq2 |
|
357 |
356
|
oveq1d |
|
358 |
|
rabeq |
|
359 |
357 358
|
syl |
|
360 |
|
eqeq2 |
|
361 |
360
|
rabbidv |
|
362 |
359 361
|
eqtrd |
|
363 |
362
|
adantl |
|
364 |
|
ovex |
|
365 |
364
|
rabex |
|
366 |
365
|
a1i |
|
367 |
355 363 50 366
|
fvmptd |
|
368 |
|
fzfid |
|
369 |
|
snfi |
|
370 |
369
|
a1i |
|
371 |
|
unfi |
|
372 |
16 370 371
|
syl2anc |
|
373 |
|
mapfi |
|
374 |
368 372 373
|
syl2anc |
|
375 |
|
ssrab2 |
|
376 |
375
|
a1i |
|
377 |
|
ssfi |
|
378 |
374 376 377
|
syl2anc |
|
379 |
367 378
|
eqeltrd |
|
380 |
379
|
adantr |
|
381 |
7 50 12 3 31 19 348
|
dvnprodlem1 |
|
382 |
381
|
adantr |
|
383 |
|
simpr |
|
384 |
|
opex |
|
385 |
384
|
a1i |
|
386 |
12
|
fvmpt2 |
|
387 |
383 385 386
|
syl2anc |
|
388 |
387
|
adantlr |
|
389 |
50
|
adantr |
|
390 |
|
eliun |
|
391 |
390
|
biimpi |
|
392 |
391
|
adantl |
|
393 |
|
nfv |
|
394 |
|
nfcv |
|
395 |
|
nfiu1 |
|
396 |
394 395
|
nfel |
|
397 |
393 396
|
nfan |
|
398 |
|
nfv |
|
399 |
|
xp1st |
|
400 |
|
elsni |
|
401 |
399 400
|
syl |
|
402 |
401
|
adantl |
|
403 |
|
simpl |
|
404 |
402 403
|
eqeltrd |
|
405 |
404
|
ex |
|
406 |
405
|
a1i |
|
407 |
397 398 406
|
rexlimd |
|
408 |
392 407
|
mpd |
|
409 |
|
elfzelz |
|
410 |
408 409
|
syl |
|
411 |
389 410
|
bccld |
|
412 |
411
|
nn0cnd |
|
413 |
412
|
adantlr |
|
414 |
|
elfznn0 |
|
415 |
408 414
|
syl |
|
416 |
415
|
faccld |
|
417 |
416
|
nncnd |
|
418 |
417
|
adantlr |
|
419 |
16
|
adantr |
|
420 |
|
nfv |
|
421 |
88 86
|
eqsstrd |
|
422 |
|
ovex |
|
423 |
422
|
a1i |
|
424 |
|
mapss |
|
425 |
423 126 424
|
syl2anc |
|
426 |
425
|
adantl |
|
427 |
421 426
|
sstrd |
|
428 |
427
|
3adant3 |
|
429 |
|
xp2nd |
|
430 |
429
|
3ad2ant3 |
|
431 |
428 430
|
sseldd |
|
432 |
|
elmapi |
|
433 |
431 432
|
syl |
|
434 |
433
|
3exp |
|
435 |
434
|
adantr |
|
436 |
397 420 435
|
rexlimd |
|
437 |
392 436
|
mpd |
|
438 |
437
|
ffvelrnda |
|
439 |
|
elfznn0 |
|
440 |
439
|
faccld |
|
441 |
440
|
nncnd |
|
442 |
438 441
|
syl |
|
443 |
419 442
|
fprodcl |
|
444 |
443
|
adantlr |
|
445 |
438 440
|
syl |
|
446 |
|
nnne0 |
|
447 |
445 446
|
syl |
|
448 |
419 442 447
|
fprodn0 |
|
449 |
448
|
adantlr |
|
450 |
418 444 449
|
divcld |
|
451 |
17
|
adantr |
|
452 |
|
simpll |
|
453 |
452 22
|
sylancom |
|
454 |
452 136
|
syl |
|
455 |
454 438
|
sseldd |
|
456 |
452 453 455
|
3jca |
|
457 |
|
eleq1 |
|
458 |
457
|
3anbi3d |
|
459 |
|
fveq2 |
|
460 |
459
|
feq1d |
|
461 |
458 460
|
imbi12d |
|
462 |
461 6
|
vtoclg |
|
463 |
438 456 462
|
sylc |
|
464 |
463
|
adantllr |
|
465 |
25
|
adantlr |
|
466 |
464 465
|
ffvelrnd |
|
467 |
451 466
|
fprodcl |
|
468 |
450 467
|
mulcld |
|
469 |
|
nfv |
|
470 |
|
simp1 |
|
471 |
404
|
3adant1 |
|
472 |
|
fznn0sub2 |
|
473 |
472
|
adantl |
|
474 |
470 471 473
|
syl2anc |
|
475 |
474
|
3exp |
|
476 |
475
|
adantr |
|
477 |
397 469 476
|
rexlimd |
|
478 |
392 477
|
mpd |
|
479 |
|
simpl |
|
480 |
479 31
|
syl |
|
481 |
479 136
|
syl |
|
482 |
481 478
|
sseldd |
|
483 |
479 480 482
|
3jca |
|
484 |
|
eleq1 |
|
485 |
484
|
3anbi3d |
|
486 |
|
fveq2 |
|
487 |
486
|
feq1d |
|
488 |
485 487
|
imbi12d |
|
489 |
|
simp2 |
|
490 |
|
id |
|
491 |
34
|
3anbi2d |
|
492 |
180
|
fveq1d |
|
493 |
492
|
feq1d |
|
494 |
491 493
|
imbi12d |
|
495 |
494 6
|
vtoclg |
|
496 |
489 490 495
|
sylc |
|
497 |
488 496
|
vtoclg |
|
498 |
478 483 497
|
sylc |
|
499 |
498
|
adantlr |
|
500 |
42
|
adantr |
|
501 |
499 500
|
ffvelrnd |
|
502 |
468 501
|
mulcld |
|
503 |
413 502
|
mulcld |
|
504 |
338 380 382 388 503
|
fsumf1o |
|
505 |
|
simpl |
|
506 |
367
|
adantr |
|
507 |
383 506
|
eleqtrd |
|
508 |
375
|
sseli |
|
509 |
507 508
|
syl |
|
510 |
|
elmapi |
|
511 |
509 510
|
syl |
|
512 |
|
snidg |
|
513 |
31 512
|
syl |
|
514 |
|
elun2 |
|
515 |
513 514
|
syl |
|
516 |
515
|
adantr |
|
517 |
511 516
|
ffvelrnd |
|
518 |
|
0zd |
|
519 |
128
|
adantr |
|
520 |
|
fzssz |
|
521 |
520
|
sseli |
|
522 |
521
|
adantl |
|
523 |
519 522
|
zsubcld |
|
524 |
|
elfzle2 |
|
525 |
524
|
adantl |
|
526 |
164
|
adantr |
|
527 |
522
|
zred |
|
528 |
526 527
|
subge0d |
|
529 |
525 528
|
mpbird |
|
530 |
|
elfzle1 |
|
531 |
530
|
adantl |
|
532 |
526 527
|
subge02d |
|
533 |
531 532
|
mpbid |
|
534 |
518 519 523 529 533
|
elfzd |
|
535 |
505 517 534
|
syl2anc |
|
536 |
|
bcval2 |
|
537 |
535 536
|
syl |
|
538 |
164
|
recnd |
|
539 |
538
|
adantr |
|
540 |
|
zsscn |
|
541 |
520 540
|
sstri |
|
542 |
541
|
a1i |
|
543 |
542 517
|
sseldd |
|
544 |
539 543
|
nncand |
|
545 |
544
|
fveq2d |
|
546 |
545
|
oveq1d |
|
547 |
546
|
oveq2d |
|
548 |
50
|
faccld |
|
549 |
548
|
nncnd |
|
550 |
549
|
adantr |
|
551 |
|
elfznn0 |
|
552 |
517 551
|
syl |
|
553 |
552
|
faccld |
|
554 |
553
|
nncnd |
|
555 |
|
elfznn0 |
|
556 |
535 555
|
syl |
|
557 |
556
|
faccld |
|
558 |
557
|
nncnd |
|
559 |
553
|
nnne0d |
|
560 |
557
|
nnne0d |
|
561 |
550 554 558 559 560
|
divdiv1d |
|
562 |
561
|
eqcomd |
|
563 |
537 547 562
|
3eqtrd |
|
564 |
563
|
adantlr |
|
565 |
|
fvres |
|
566 |
565
|
fveq2d |
|
567 |
566
|
prodeq2i |
|
568 |
567
|
oveq2i |
|
569 |
565
|
fveq2d |
|
570 |
569
|
fveq1d |
|
571 |
570
|
prodeq2i |
|
572 |
568 571
|
oveq12i |
|
573 |
572
|
a1i |
|
574 |
573
|
adantlr |
|
575 |
558
|
adantlr |
|
576 |
505 16
|
syl |
|
577 |
79
|
ssriv |
|
578 |
577
|
a1i |
|
579 |
511
|
adantr |
|
580 |
|
elun1 |
|
581 |
580
|
adantl |
|
582 |
579 581
|
ffvelrnd |
|
583 |
578 582
|
sseldd |
|
584 |
583
|
faccld |
|
585 |
584
|
nncnd |
|
586 |
576 585
|
fprodcl |
|
587 |
586
|
adantlr |
|
588 |
17
|
adantr |
|
589 |
505
|
adantr |
|
590 |
505 22
|
sylan |
|
591 |
589 136
|
syl |
|
592 |
591 582
|
sseldd |
|
593 |
589 590 592 148
|
syl3anc |
|
594 |
593
|
adantllr |
|
595 |
25
|
adantlr |
|
596 |
594 595
|
ffvelrnd |
|
597 |
588 596
|
fprodcl |
|
598 |
576 584
|
fprodnncl |
|
599 |
|
nnne0 |
|
600 |
598 599
|
syl |
|
601 |
600
|
adantlr |
|
602 |
575 587 597 601
|
div32d |
|
603 |
574 602
|
eqtrd |
|
604 |
544
|
fveq2d |
|
605 |
604
|
fveq1d |
|
606 |
605
|
adantlr |
|
607 |
603 606
|
oveq12d |
|
608 |
597 587 601
|
divcld |
|
609 |
505 31
|
syl |
|
610 |
505 136
|
syl |
|
611 |
610 517
|
sseldd |
|
612 |
505 609 611
|
3jca |
|
613 |
|
eleq1 |
|
614 |
613
|
3anbi3d |
|
615 |
|
fveq2 |
|
616 |
615
|
feq1d |
|
617 |
614 616
|
imbi12d |
|
618 |
617 496
|
vtoclg |
|
619 |
517 612 618
|
sylc |
|
620 |
619
|
adantlr |
|
621 |
42
|
adantr |
|
622 |
620 621
|
ffvelrnd |
|
623 |
575 608 622
|
mulassd |
|
624 |
607 623
|
eqtrd |
|
625 |
564 624
|
oveq12d |
|
626 |
549
|
ad2antrr |
|
627 |
554
|
adantlr |
|
628 |
559
|
adantlr |
|
629 |
626 627 628
|
divcld |
|
630 |
608 622
|
mulcld |
|
631 |
560
|
adantlr |
|
632 |
629 575 630 631
|
dmmcand |
|
633 |
597 622 587 601
|
div23d |
|
634 |
633
|
eqcomd |
|
635 |
|
nfv |
|
636 |
|
nfcv |
|
637 |
609
|
adantlr |
|
638 |
20
|
adantr |
|
639 |
|
fveq2 |
|
640 |
180 639
|
fveq12d |
|
641 |
640
|
fveq1d |
|
642 |
635 636 588 637 638 596 641 622
|
fprodsplitsn |
|
643 |
642
|
eqcomd |
|
644 |
643
|
oveq1d |
|
645 |
634 644
|
eqtrd |
|
646 |
645
|
oveq2d |
|
647 |
588 369 371
|
sylancl |
|
648 |
505
|
adantr |
|
649 |
348
|
sselda |
|
650 |
649
|
adantlr |
|
651 |
511 610
|
fssd |
|
652 |
651
|
ffvelrnda |
|
653 |
648 650 652 148
|
syl3anc |
|
654 |
653
|
adantllr |
|
655 |
621
|
adantr |
|
656 |
654 655
|
ffvelrnd |
|
657 |
647 656
|
fprodcl |
|
658 |
626 627 657 587 628 601
|
divmuldivd |
|
659 |
554 586
|
mulcomd |
|
660 |
|
nfv |
|
661 |
|
nfcv |
|
662 |
505 19
|
syl |
|
663 |
639
|
fveq2d |
|
664 |
660 661 576 609 662 585 663 554
|
fprodsplitsn |
|
665 |
664
|
eqcomd |
|
666 |
659 665
|
eqtrd |
|
667 |
666
|
oveq2d |
|
668 |
667
|
adantlr |
|
669 |
505 372
|
syl |
|
670 |
577
|
a1i |
|
671 |
511
|
ffvelrnda |
|
672 |
670 671
|
sseldd |
|
673 |
672
|
faccld |
|
674 |
673
|
nncnd |
|
675 |
669 674
|
fprodcl |
|
676 |
675
|
adantlr |
|
677 |
673
|
nnne0d |
|
678 |
669 674 677
|
fprodn0 |
|
679 |
678
|
adantlr |
|
680 |
626 657 676 679
|
div23d |
|
681 |
|
eqidd |
|
682 |
668 680 681
|
3eqtrd |
|
683 |
646 658 682
|
3eqtrd |
|
684 |
625 632 683
|
3eqtrd |
|
685 |
684
|
sumeq2dv |
|
686 |
504 685
|
eqtrd |
|
687 |
295 319 686
|
3eqtrd |
|
688 |
687
|
mpteq2dva |
|
689 |
47 210 688
|
3eqtrd |
|