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 |
157 158 160
|
3jca |
|
162 |
|
elfzle1 |
|
163 |
162
|
adantl |
|
164 |
160
|
zred |
|
165 |
50
|
nn0red |
|
166 |
165
|
adantr |
|
167 |
158
|
zred |
|
168 |
|
elfzle2 |
|
169 |
168
|
adantl |
|
170 |
131
|
adantr |
|
171 |
164 166 167 169 170
|
letrd |
|
172 |
161 163 171
|
jca32 |
|
173 |
|
elfz2 |
|
174 |
172 173
|
sylibr |
|
175 |
|
rspa |
|
176 |
156 174 175
|
syl2anc |
|
177 |
176
|
feq1d |
|
178 |
155 177
|
mpbird |
|
179 |
31
|
adantr |
|
180 |
|
simpl |
|
181 |
180 179 174
|
3jca |
|
182 |
34
|
3anbi2d |
|
183 |
27
|
oveq2d |
|
184 |
183
|
fveq1d |
|
185 |
184
|
feq1d |
|
186 |
182 185
|
imbi12d |
|
187 |
|
eleq1 |
|
188 |
187
|
3anbi3d |
|
189 |
|
fveq2 |
|
190 |
189
|
feq1d |
|
191 |
188 190
|
imbi12d |
|
192 |
191 6
|
chvarvv |
|
193 |
186 192
|
vtoclg |
|
194 |
179 181 193
|
sylc |
|
195 |
40
|
feqmptd |
|
196 |
195
|
eqcomd |
|
197 |
196
|
oveq2d |
|
198 |
197
|
fveq1d |
|
199 |
198
|
adantr |
|
200 |
199
|
feq1d |
|
201 |
194 200
|
mpbird |
|
202 |
|
fveq2 |
|
203 |
202
|
prodeq2ad |
|
204 |
203
|
cbvmptv |
|
205 |
204
|
oveq2i |
|
206 |
205
|
fveq1i |
|
207 |
206
|
mpteq2i |
|
208 |
|
fveq2 |
|
209 |
208
|
cbvmptv |
|
210 |
209
|
oveq2i |
|
211 |
210
|
fveq1i |
|
212 |
211
|
mpteq2i |
|
213 |
1 2 48 43 50 51 52 178 201 207 212
|
dvnmul |
|
214 |
206
|
a1i |
|
215 |
10
|
r19.21bi |
|
216 |
180 174 215
|
syl2anc |
|
217 |
214 216
|
eqtrd |
|
218 |
217
|
mpteq2dva |
|
219 |
|
mptexg |
|
220 |
2 219
|
syl |
|
221 |
220
|
adantr |
|
222 |
218 221
|
fvmpt2d |
|
223 |
222
|
adantlr |
|
224 |
223
|
fveq1d |
|
225 |
42
|
adantr |
|
226 |
154
|
an32s |
|
227 |
|
eqid |
|
228 |
227
|
fvmpt2 |
|
229 |
225 226 228
|
syl2anc |
|
230 |
224 229
|
eqtrd |
|
231 |
|
fveq2 |
|
232 |
231
|
cbvmptv |
|
233 |
232
|
a1i |
|
234 |
210 197
|
syl5eq |
|
235 |
234
|
fveq1d |
|
236 |
235
|
mpteq2dv |
|
237 |
233 236
|
eqtrd |
|
238 |
237
|
adantr |
|
239 |
|
fveq2 |
|
240 |
239
|
adantl |
|
241 |
|
0zd |
|
242 |
|
elfzel2 |
|
243 |
242 159
|
zsubcld |
|
244 |
241 242 243
|
3jca |
|
245 |
242
|
zred |
|
246 |
79
|
nn0red |
|
247 |
245 246
|
subge0d |
|
248 |
168 247
|
mpbird |
|
249 |
245 246
|
subge02d |
|
250 |
162 249
|
mpbid |
|
251 |
244 248 250
|
jca32 |
|
252 |
251
|
adantl |
|
253 |
|
elfz2 |
|
254 |
252 253
|
sylibr |
|
255 |
|
fvex |
|
256 |
255
|
a1i |
|
257 |
238 240 254 256
|
fvmptd |
|
258 |
257
|
adantlr |
|
259 |
258
|
fveq1d |
|
260 |
230 259
|
oveq12d |
|
261 |
260
|
oveq2d |
|
262 |
92
|
adantlr |
|
263 |
|
ovex |
|
264 |
|
eleq1 |
|
265 |
264
|
anbi2d |
|
266 |
239
|
feq1d |
|
267 |
265 266
|
imbi12d |
|
268 |
|
eleq1 |
|
269 |
268
|
anbi2d |
|
270 |
|
fveq2 |
|
271 |
270
|
feq1d |
|
272 |
269 271
|
imbi12d |
|
273 |
272 194
|
chvarvv |
|
274 |
263 267 273
|
vtocl |
|
275 |
180 254 274
|
syl2anc |
|
276 |
275
|
adantlr |
|
277 |
276 225
|
ffvelrnd |
|
278 |
|
anass |
|
279 |
|
ancom |
|
280 |
279
|
anbi2i |
|
281 |
|
anass |
|
282 |
281
|
bicomi |
|
283 |
280 282
|
bitri |
|
284 |
278 283
|
bitri |
|
285 |
284
|
anbi1i |
|
286 |
285
|
imbi1i |
|
287 |
153 286
|
mpbi |
|
288 |
262 277 287
|
fsummulc1 |
|
289 |
288
|
oveq2d |
|
290 |
180 50
|
syl |
|
291 |
290 160
|
bccld |
|
292 |
291
|
nn0cnd |
|
293 |
292
|
adantlr |
|
294 |
277
|
adantr |
|
295 |
287 294
|
mulcld |
|
296 |
262 293 295
|
fsummulc2 |
|
297 |
261 289 296
|
3eqtrd |
|
298 |
297
|
sumeq2dv |
|
299 |
|
vex |
|
300 |
|
vex |
|
301 |
299 300
|
op1std |
|
302 |
301
|
oveq2d |
|
303 |
301
|
fveq2d |
|
304 |
299 300
|
op2ndd |
|
305 |
304
|
fveq1d |
|
306 |
305
|
fveq2d |
|
307 |
306
|
prodeq2ad |
|
308 |
303 307
|
oveq12d |
|
309 |
305
|
fveq2d |
|
310 |
309
|
fveq1d |
|
311 |
310
|
prodeq2ad |
|
312 |
308 311
|
oveq12d |
|
313 |
301
|
oveq2d |
|
314 |
313
|
fveq2d |
|
315 |
314
|
fveq1d |
|
316 |
312 315
|
oveq12d |
|
317 |
302 316
|
oveq12d |
|
318 |
|
fzfid |
|
319 |
293
|
adantrr |
|
320 |
295
|
anasss |
|
321 |
319 320
|
mulcld |
|
322 |
317 318 262 321
|
fsum2d |
|
323 |
|
ovex |
|
324 |
300
|
resex |
|
325 |
323 324
|
op1std |
|
326 |
325
|
oveq2d |
|
327 |
325
|
fveq2d |
|
328 |
323 324
|
op2ndd |
|
329 |
328
|
fveq1d |
|
330 |
329
|
fveq2d |
|
331 |
330
|
prodeq2ad |
|
332 |
327 331
|
oveq12d |
|
333 |
329
|
fveq2d |
|
334 |
333
|
fveq1d |
|
335 |
334
|
prodeq2ad |
|
336 |
332 335
|
oveq12d |
|
337 |
325
|
oveq2d |
|
338 |
337
|
fveq2d |
|
339 |
338
|
fveq1d |
|
340 |
336 339
|
oveq12d |
|
341 |
326 340
|
oveq12d |
|
342 |
|
oveq2 |
|
343 |
|
rabeq |
|
344 |
342 343
|
syl |
|
345 |
|
sumeq1 |
|
346 |
345
|
eqeq1d |
|
347 |
346
|
rabbidv |
|
348 |
344 347
|
eqtrd |
|
349 |
348
|
mpteq2dv |
|
350 |
31
|
snssd |
|
351 |
8 350
|
unssd |
|
352 |
3 351
|
ssexd |
|
353 |
|
elpwg |
|
354 |
352 353
|
syl |
|
355 |
351 354
|
mpbird |
|
356 |
67
|
mptex |
|
357 |
356
|
a1i |
|
358 |
7 349 355 357
|
fvmptd3 |
|
359 |
|
oveq2 |
|
360 |
359
|
oveq1d |
|
361 |
|
rabeq |
|
362 |
360 361
|
syl |
|
363 |
|
eqeq2 |
|
364 |
363
|
rabbidv |
|
365 |
362 364
|
eqtrd |
|
366 |
365
|
adantl |
|
367 |
|
ovex |
|
368 |
367
|
rabex |
|
369 |
368
|
a1i |
|
370 |
358 366 50 369
|
fvmptd |
|
371 |
|
fzfid |
|
372 |
|
snfi |
|
373 |
372
|
a1i |
|
374 |
|
unfi |
|
375 |
16 373 374
|
syl2anc |
|
376 |
|
mapfi |
|
377 |
371 375 376
|
syl2anc |
|
378 |
|
ssrab2 |
|
379 |
378
|
a1i |
|
380 |
|
ssfi |
|
381 |
377 379 380
|
syl2anc |
|
382 |
370 381
|
eqeltrd |
|
383 |
382
|
adantr |
|
384 |
7 50 12 3 31 19 351
|
dvnprodlem1 |
|
385 |
384
|
adantr |
|
386 |
|
simpr |
|
387 |
|
opex |
|
388 |
387
|
a1i |
|
389 |
12
|
fvmpt2 |
|
390 |
386 388 389
|
syl2anc |
|
391 |
390
|
adantlr |
|
392 |
50
|
adantr |
|
393 |
|
eliun |
|
394 |
393
|
biimpi |
|
395 |
394
|
adantl |
|
396 |
|
nfv |
|
397 |
|
nfcv |
|
398 |
|
nfiu1 |
|
399 |
397 398
|
nfel |
|
400 |
396 399
|
nfan |
|
401 |
|
nfv |
|
402 |
|
xp1st |
|
403 |
|
elsni |
|
404 |
402 403
|
syl |
|
405 |
404
|
adantl |
|
406 |
|
simpl |
|
407 |
405 406
|
eqeltrd |
|
408 |
407
|
ex |
|
409 |
408
|
a1i |
|
410 |
400 401 409
|
rexlimd |
|
411 |
395 410
|
mpd |
|
412 |
|
elfzelz |
|
413 |
411 412
|
syl |
|
414 |
392 413
|
bccld |
|
415 |
414
|
nn0cnd |
|
416 |
415
|
adantlr |
|
417 |
|
elfznn0 |
|
418 |
411 417
|
syl |
|
419 |
418
|
faccld |
|
420 |
419
|
nncnd |
|
421 |
420
|
adantlr |
|
422 |
16
|
adantr |
|
423 |
|
nfv |
|
424 |
88 86
|
eqsstrd |
|
425 |
|
ovex |
|
426 |
425
|
a1i |
|
427 |
|
mapss |
|
428 |
426 126 427
|
syl2anc |
|
429 |
428
|
adantl |
|
430 |
424 429
|
sstrd |
|
431 |
430
|
3adant3 |
|
432 |
|
xp2nd |
|
433 |
432
|
3ad2ant3 |
|
434 |
431 433
|
sseldd |
|
435 |
|
elmapi |
|
436 |
434 435
|
syl |
|
437 |
436
|
3exp |
|
438 |
437
|
adantr |
|
439 |
400 423 438
|
rexlimd |
|
440 |
395 439
|
mpd |
|
441 |
440
|
ffvelrnda |
|
442 |
|
elfznn0 |
|
443 |
442
|
faccld |
|
444 |
443
|
nncnd |
|
445 |
441 444
|
syl |
|
446 |
422 445
|
fprodcl |
|
447 |
446
|
adantlr |
|
448 |
441 443
|
syl |
|
449 |
|
nnne0 |
|
450 |
448 449
|
syl |
|
451 |
422 445 450
|
fprodn0 |
|
452 |
451
|
adantlr |
|
453 |
421 447 452
|
divcld |
|
454 |
17
|
adantr |
|
455 |
|
simpll |
|
456 |
455 22
|
sylancom |
|
457 |
455 136
|
syl |
|
458 |
457 441
|
sseldd |
|
459 |
455 456 458
|
3jca |
|
460 |
|
eleq1 |
|
461 |
460
|
3anbi3d |
|
462 |
|
fveq2 |
|
463 |
462
|
feq1d |
|
464 |
461 463
|
imbi12d |
|
465 |
464 6
|
vtoclg |
|
466 |
441 459 465
|
sylc |
|
467 |
466
|
adantllr |
|
468 |
25
|
adantlr |
|
469 |
467 468
|
ffvelrnd |
|
470 |
454 469
|
fprodcl |
|
471 |
453 470
|
mulcld |
|
472 |
|
nfv |
|
473 |
|
simp1 |
|
474 |
407
|
3adant1 |
|
475 |
|
fznn0sub2 |
|
476 |
475
|
adantl |
|
477 |
473 474 476
|
syl2anc |
|
478 |
477
|
3exp |
|
479 |
478
|
adantr |
|
480 |
400 472 479
|
rexlimd |
|
481 |
395 480
|
mpd |
|
482 |
|
simpl |
|
483 |
482 31
|
syl |
|
484 |
482 136
|
syl |
|
485 |
484 481
|
sseldd |
|
486 |
482 483 485
|
3jca |
|
487 |
|
eleq1 |
|
488 |
487
|
3anbi3d |
|
489 |
|
fveq2 |
|
490 |
489
|
feq1d |
|
491 |
488 490
|
imbi12d |
|
492 |
|
simp2 |
|
493 |
|
id |
|
494 |
34
|
3anbi2d |
|
495 |
183
|
fveq1d |
|
496 |
495
|
feq1d |
|
497 |
494 496
|
imbi12d |
|
498 |
497 6
|
vtoclg |
|
499 |
492 493 498
|
sylc |
|
500 |
491 499
|
vtoclg |
|
501 |
481 486 500
|
sylc |
|
502 |
501
|
adantlr |
|
503 |
42
|
adantr |
|
504 |
502 503
|
ffvelrnd |
|
505 |
471 504
|
mulcld |
|
506 |
416 505
|
mulcld |
|
507 |
341 383 385 391 506
|
fsumf1o |
|
508 |
|
simpl |
|
509 |
370
|
adantr |
|
510 |
386 509
|
eleqtrd |
|
511 |
378
|
sseli |
|
512 |
510 511
|
syl |
|
513 |
|
elmapi |
|
514 |
512 513
|
syl |
|
515 |
|
snidg |
|
516 |
31 515
|
syl |
|
517 |
|
elun2 |
|
518 |
516 517
|
syl |
|
519 |
518
|
adantr |
|
520 |
514 519
|
ffvelrnd |
|
521 |
|
0zd |
|
522 |
128
|
adantr |
|
523 |
|
fzssz |
|
524 |
523
|
sseli |
|
525 |
524
|
adantl |
|
526 |
522 525
|
zsubcld |
|
527 |
521 522 526
|
3jca |
|
528 |
|
elfzle2 |
|
529 |
528
|
adantl |
|
530 |
165
|
adantr |
|
531 |
525
|
zred |
|
532 |
530 531
|
subge0d |
|
533 |
529 532
|
mpbird |
|
534 |
|
elfzle1 |
|
535 |
534
|
adantl |
|
536 |
530 531
|
subge02d |
|
537 |
535 536
|
mpbid |
|
538 |
527 533 537
|
jca32 |
|
539 |
|
elfz2 |
|
540 |
538 539
|
sylibr |
|
541 |
508 520 540
|
syl2anc |
|
542 |
|
bcval2 |
|
543 |
541 542
|
syl |
|
544 |
165
|
recnd |
|
545 |
544
|
adantr |
|
546 |
|
zsscn |
|
547 |
523 546
|
sstri |
|
548 |
547
|
a1i |
|
549 |
548 520
|
sseldd |
|
550 |
545 549
|
nncand |
|
551 |
550
|
fveq2d |
|
552 |
551
|
oveq1d |
|
553 |
552
|
oveq2d |
|
554 |
50
|
faccld |
|
555 |
554
|
nncnd |
|
556 |
555
|
adantr |
|
557 |
|
elfznn0 |
|
558 |
520 557
|
syl |
|
559 |
558
|
faccld |
|
560 |
559
|
nncnd |
|
561 |
|
elfznn0 |
|
562 |
541 561
|
syl |
|
563 |
562
|
faccld |
|
564 |
563
|
nncnd |
|
565 |
559
|
nnne0d |
|
566 |
563
|
nnne0d |
|
567 |
556 560 564 565 566
|
divdiv1d |
|
568 |
567
|
eqcomd |
|
569 |
543 553 568
|
3eqtrd |
|
570 |
569
|
adantlr |
|
571 |
|
fvres |
|
572 |
571
|
fveq2d |
|
573 |
572
|
prodeq2i |
|
574 |
573
|
oveq2i |
|
575 |
571
|
fveq2d |
|
576 |
575
|
fveq1d |
|
577 |
576
|
prodeq2i |
|
578 |
574 577
|
oveq12i |
|
579 |
578
|
a1i |
|
580 |
579
|
adantlr |
|
581 |
564
|
adantlr |
|
582 |
508 16
|
syl |
|
583 |
79
|
ssriv |
|
584 |
583
|
a1i |
|
585 |
514
|
adantr |
|
586 |
|
elun1 |
|
587 |
586
|
adantl |
|
588 |
585 587
|
ffvelrnd |
|
589 |
584 588
|
sseldd |
|
590 |
589
|
faccld |
|
591 |
590
|
nncnd |
|
592 |
582 591
|
fprodcl |
|
593 |
592
|
adantlr |
|
594 |
17
|
adantr |
|
595 |
508
|
adantr |
|
596 |
508 22
|
sylan |
|
597 |
595 136
|
syl |
|
598 |
597 588
|
sseldd |
|
599 |
595 596 598 148
|
syl3anc |
|
600 |
599
|
adantllr |
|
601 |
25
|
adantlr |
|
602 |
600 601
|
ffvelrnd |
|
603 |
594 602
|
fprodcl |
|
604 |
582 590
|
fprodnncl |
|
605 |
|
nnne0 |
|
606 |
604 605
|
syl |
|
607 |
606
|
adantlr |
|
608 |
581 593 603 607
|
div32d |
|
609 |
580 608
|
eqtrd |
|
610 |
550
|
fveq2d |
|
611 |
610
|
fveq1d |
|
612 |
611
|
adantlr |
|
613 |
609 612
|
oveq12d |
|
614 |
603 593 607
|
divcld |
|
615 |
508 31
|
syl |
|
616 |
508 136
|
syl |
|
617 |
616 520
|
sseldd |
|
618 |
508 615 617
|
3jca |
|
619 |
|
eleq1 |
|
620 |
619
|
3anbi3d |
|
621 |
|
fveq2 |
|
622 |
621
|
feq1d |
|
623 |
620 622
|
imbi12d |
|
624 |
623 499
|
vtoclg |
|
625 |
520 618 624
|
sylc |
|
626 |
625
|
adantlr |
|
627 |
42
|
adantr |
|
628 |
626 627
|
ffvelrnd |
|
629 |
581 614 628
|
mulassd |
|
630 |
613 629
|
eqtrd |
|
631 |
570 630
|
oveq12d |
|
632 |
555
|
ad2antrr |
|
633 |
560
|
adantlr |
|
634 |
565
|
adantlr |
|
635 |
632 633 634
|
divcld |
|
636 |
614 628
|
mulcld |
|
637 |
566
|
adantlr |
|
638 |
635 581 636 637
|
dmmcand |
|
639 |
603 628 593 607
|
div23d |
|
640 |
639
|
eqcomd |
|
641 |
|
nfv |
|
642 |
|
nfcv |
|
643 |
615
|
adantlr |
|
644 |
20
|
adantr |
|
645 |
|
fveq2 |
|
646 |
183 645
|
fveq12d |
|
647 |
646
|
fveq1d |
|
648 |
641 642 594 643 644 602 647 628
|
fprodsplitsn |
|
649 |
648
|
eqcomd |
|
650 |
649
|
oveq1d |
|
651 |
640 650
|
eqtrd |
|
652 |
651
|
oveq2d |
|
653 |
594 372 374
|
sylancl |
|
654 |
508
|
adantr |
|
655 |
351
|
sselda |
|
656 |
655
|
adantlr |
|
657 |
514 616
|
fssd |
|
658 |
657
|
ffvelrnda |
|
659 |
654 656 658 148
|
syl3anc |
|
660 |
659
|
adantllr |
|
661 |
627
|
adantr |
|
662 |
660 661
|
ffvelrnd |
|
663 |
653 662
|
fprodcl |
|
664 |
632 633 663 593 634 607
|
divmuldivd |
|
665 |
560 592
|
mulcomd |
|
666 |
|
nfv |
|
667 |
|
nfcv |
|
668 |
508 19
|
syl |
|
669 |
645
|
fveq2d |
|
670 |
666 667 582 615 668 591 669 560
|
fprodsplitsn |
|
671 |
670
|
eqcomd |
|
672 |
665 671
|
eqtrd |
|
673 |
672
|
oveq2d |
|
674 |
673
|
adantlr |
|
675 |
508 375
|
syl |
|
676 |
583
|
a1i |
|
677 |
514
|
ffvelrnda |
|
678 |
676 677
|
sseldd |
|
679 |
678
|
faccld |
|
680 |
679
|
nncnd |
|
681 |
675 680
|
fprodcl |
|
682 |
681
|
adantlr |
|
683 |
679
|
nnne0d |
|
684 |
675 680 683
|
fprodn0 |
|
685 |
684
|
adantlr |
|
686 |
632 663 682 685
|
div23d |
|
687 |
|
eqidd |
|
688 |
674 686 687
|
3eqtrd |
|
689 |
652 664 688
|
3eqtrd |
|
690 |
631 638 689
|
3eqtrd |
|
691 |
690
|
sumeq2dv |
|
692 |
507 691
|
eqtrd |
|
693 |
298 322 692
|
3eqtrd |
|
694 |
693
|
mpteq2dva |
|
695 |
47 213 694
|
3eqtrd |
|