Step |
Hyp |
Ref |
Expression |
1 |
|
dvnmul.s |
|
2 |
|
dvnmul.x |
|
3 |
|
dvnmul.a |
|
4 |
|
dvnmul.cc |
|
5 |
|
dvnmul.n |
|
6 |
|
dvnmulf |
|
7 |
|
dvnmul.f |
|
8 |
|
dvnmul.dvnf |
|
9 |
|
dvnmul.dvng |
|
10 |
|
dvnmul.c |
|
11 |
|
dvnmul.d |
|
12 |
|
id |
|
13 |
|
nn0uz |
|
14 |
5 13
|
eleqtrdi |
|
15 |
|
eluzfz2 |
|
16 |
14 15
|
syl |
|
17 |
|
eleq1 |
|
18 |
|
fveq2 |
|
19 |
|
oveq2 |
|
20 |
19
|
sumeq1d |
|
21 |
|
oveq1 |
|
22 |
|
fvoveq1 |
|
23 |
22
|
fveq1d |
|
24 |
23
|
oveq2d |
|
25 |
21 24
|
oveq12d |
|
26 |
25
|
sumeq2sdv |
|
27 |
20 26
|
eqtrd |
|
28 |
27
|
mpteq2dv |
|
29 |
18 28
|
eqeq12d |
|
30 |
29
|
imbi2d |
|
31 |
17 30
|
imbi12d |
|
32 |
|
fveq2 |
|
33 |
|
simpl |
|
34 |
33
|
oveq2d |
|
35 |
|
simpll |
|
36 |
35
|
oveq1d |
|
37 |
35
|
fvoveq1d |
|
38 |
37
|
fveq1d |
|
39 |
38
|
oveq2d |
|
40 |
36 39
|
oveq12d |
|
41 |
34 40
|
sumeq12rdv |
|
42 |
41
|
mpteq2dva |
|
43 |
32 42
|
eqeq12d |
|
44 |
43
|
imbi2d |
|
45 |
|
fveq2 |
|
46 |
|
simpl |
|
47 |
46
|
oveq2d |
|
48 |
|
simpll |
|
49 |
48
|
oveq1d |
|
50 |
48
|
fvoveq1d |
|
51 |
50
|
fveq1d |
|
52 |
51
|
oveq2d |
|
53 |
49 52
|
oveq12d |
|
54 |
47 53
|
sumeq12rdv |
|
55 |
54
|
mpteq2dva |
|
56 |
45 55
|
eqeq12d |
|
57 |
56
|
imbi2d |
|
58 |
|
fveq2 |
|
59 |
|
simpl |
|
60 |
59
|
oveq2d |
|
61 |
|
simpll |
|
62 |
61
|
oveq1d |
|
63 |
61
|
fvoveq1d |
|
64 |
63
|
fveq1d |
|
65 |
64
|
oveq2d |
|
66 |
62 65
|
oveq12d |
|
67 |
60 66
|
sumeq12rdv |
|
68 |
67
|
mpteq2dva |
|
69 |
58 68
|
eqeq12d |
|
70 |
69
|
imbi2d |
|
71 |
|
fveq2 |
|
72 |
|
simpl |
|
73 |
72
|
oveq2d |
|
74 |
|
simpll |
|
75 |
74
|
oveq1d |
|
76 |
74
|
fvoveq1d |
|
77 |
76
|
fveq1d |
|
78 |
77
|
oveq2d |
|
79 |
75 78
|
oveq12d |
|
80 |
73 79
|
sumeq12rdv |
|
81 |
80
|
mpteq2dva |
|
82 |
71 81
|
eqeq12d |
|
83 |
82
|
imbi2d |
|
84 |
|
recnprss |
|
85 |
1 84
|
syl |
|
86 |
3 4
|
mulcld |
|
87 |
|
restsspw |
|
88 |
87 2
|
sseldi |
|
89 |
|
elpwi |
|
90 |
88 89
|
syl |
|
91 |
|
cnex |
|
92 |
91
|
a1i |
|
93 |
86 90 92 1
|
mptelpm |
|
94 |
|
dvn0 |
|
95 |
85 93 94
|
syl2anc |
|
96 |
|
0z |
|
97 |
|
fzsn |
|
98 |
96 97
|
ax-mp |
|
99 |
98
|
sumeq1i |
|
100 |
99
|
a1i |
|
101 |
|
nfcvd |
|
102 |
|
nfv |
|
103 |
|
oveq2 |
|
104 |
|
0nn0 |
|
105 |
|
bcn0 |
|
106 |
104 105
|
ax-mp |
|
107 |
106
|
a1i |
|
108 |
103 107
|
eqtrd |
|
109 |
108
|
adantl |
|
110 |
|
fveq2 |
|
111 |
110
|
adantl |
|
112 |
|
fveq2 |
|
113 |
112
|
cbvmptv |
|
114 |
10 113
|
eqtri |
|
115 |
|
fveq2 |
|
116 |
|
eluzfz1 |
|
117 |
14 116
|
syl |
|
118 |
|
fvexd |
|
119 |
114 115 117 118
|
fvmptd3 |
|
120 |
119
|
adantr |
|
121 |
111 120
|
eqtrd |
|
122 |
3 90 92 1
|
mptelpm |
|
123 |
6 122
|
eqeltrid |
|
124 |
|
dvn0 |
|
125 |
85 123 124
|
syl2anc |
|
126 |
125
|
adantr |
|
127 |
121 126
|
eqtrd |
|
128 |
127
|
fveq1d |
|
129 |
128
|
adantlr |
|
130 |
|
simpr |
|
131 |
6
|
fvmpt2 |
|
132 |
130 3 131
|
syl2anc |
|
133 |
132
|
adantr |
|
134 |
129 133
|
eqtrd |
|
135 |
|
oveq2 |
|
136 |
|
0m0e0 |
|
137 |
136
|
a1i |
|
138 |
135 137
|
eqtrd |
|
139 |
138
|
fveq2d |
|
140 |
139
|
fveq1d |
|
141 |
140
|
adantl |
|
142 |
141
|
adantlr |
|
143 |
|
fveq2 |
|
144 |
143
|
cbvmptv |
|
145 |
11 144
|
eqtri |
|
146 |
145
|
fveq1i |
|
147 |
146
|
a1i |
|
148 |
|
eqidd |
|
149 |
|
fveq2 |
|
150 |
149
|
adantl |
|
151 |
4 90 92 1
|
mptelpm |
|
152 |
7 151
|
eqeltrid |
|
153 |
|
dvn0 |
|
154 |
85 152 153
|
syl2anc |
|
155 |
154
|
adantr |
|
156 |
150 155
|
eqtrd |
|
157 |
7
|
a1i |
|
158 |
|
mptexg |
|
159 |
88 158
|
syl |
|
160 |
157 159
|
eqeltrd |
|
161 |
148 156 117 160
|
fvmptd |
|
162 |
147 161
|
eqtrd |
|
163 |
162
|
fveq1d |
|
164 |
163
|
ad2antrr |
|
165 |
157 4
|
fvmpt2d |
|
166 |
165
|
adantr |
|
167 |
142 164 166
|
3eqtrd |
|
168 |
134 167
|
oveq12d |
|
169 |
109 168
|
oveq12d |
|
170 |
86
|
mulid2d |
|
171 |
170
|
adantr |
|
172 |
169 171
|
eqtrd |
|
173 |
|
0re |
|
174 |
173
|
a1i |
|
175 |
101 102 172 174 86
|
sumsnd |
|
176 |
100 175
|
eqtr2d |
|
177 |
176
|
mpteq2dva |
|
178 |
95 177
|
eqtrd |
|
179 |
178
|
a1i |
|
180 |
|
simp3 |
|
181 |
|
simp1 |
|
182 |
|
simp2 |
|
183 |
|
pm3.35 |
|
184 |
180 182 183
|
syl2anc |
|
185 |
85
|
adantr |
|
186 |
93
|
adantr |
|
187 |
|
elfzonn0 |
|
188 |
187
|
adantl |
|
189 |
|
dvnp1 |
|
190 |
185 186 188 189
|
syl3anc |
|
191 |
190
|
adantr |
|
192 |
|
simpr |
|
193 |
192
|
oveq2d |
|
194 |
|
eqid |
|
195 |
|
eqid |
|
196 |
1
|
adantr |
|
197 |
2
|
adantr |
|
198 |
|
fzfid |
|
199 |
187
|
adantr |
|
200 |
|
elfzelz |
|
201 |
200
|
adantl |
|
202 |
199 201
|
bccld |
|
203 |
202
|
nn0cnd |
|
204 |
203
|
adantll |
|
205 |
204
|
3adant3 |
|
206 |
|
simpll |
|
207 |
|
0zd |
|
208 |
|
elfzoel2 |
|
209 |
208
|
adantr |
|
210 |
207 209 201
|
3jca |
|
211 |
|
elfzle1 |
|
212 |
211
|
adantl |
|
213 |
201
|
zred |
|
214 |
208
|
zred |
|
215 |
214
|
adantr |
|
216 |
187
|
nn0red |
|
217 |
216
|
adantr |
|
218 |
|
elfzle2 |
|
219 |
218
|
adantl |
|
220 |
|
elfzolt2 |
|
221 |
220
|
adantr |
|
222 |
213 217 215 219 221
|
lelttrd |
|
223 |
213 215 222
|
ltled |
|
224 |
210 212 223
|
jca32 |
|
225 |
|
elfz2 |
|
226 |
224 225
|
sylibr |
|
227 |
226
|
adantll |
|
228 |
10
|
a1i |
|
229 |
|
fvexd |
|
230 |
228 229
|
fvmpt2d |
|
231 |
230
|
feq1d |
|
232 |
8 231
|
mpbird |
|
233 |
206 227 232
|
syl2anc |
|
234 |
233
|
3adant3 |
|
235 |
|
simp3 |
|
236 |
234 235
|
ffvelrnd |
|
237 |
187
|
nn0zd |
|
238 |
237
|
adantr |
|
239 |
238 201
|
zsubcld |
|
240 |
207 209 239
|
3jca |
|
241 |
|
elfzel2 |
|
242 |
241
|
zred |
|
243 |
200
|
zred |
|
244 |
242 243
|
subge0d |
|
245 |
218 244
|
mpbird |
|
246 |
245
|
adantl |
|
247 |
217 213
|
resubcld |
|
248 |
215 213
|
resubcld |
|
249 |
173
|
a1i |
|
250 |
215 249
|
jca |
|
251 |
|
resubcl |
|
252 |
250 251
|
syl |
|
253 |
217 215 213 221
|
ltsub1dd |
|
254 |
249 213 215 212
|
lesub2dd |
|
255 |
247 248 252 253 254
|
ltletrd |
|
256 |
214
|
recnd |
|
257 |
256
|
subid1d |
|
258 |
257
|
adantr |
|
259 |
255 258
|
breqtrd |
|
260 |
247 215 259
|
ltled |
|
261 |
240 246 260
|
jca32 |
|
262 |
|
elfz2 |
|
263 |
261 262
|
sylibr |
|
264 |
263
|
adantll |
|
265 |
|
ovex |
|
266 |
|
eleq1 |
|
267 |
266
|
anbi2d |
|
268 |
|
fveq2 |
|
269 |
268
|
feq1d |
|
270 |
267 269
|
imbi12d |
|
271 |
|
nfv |
|
272 |
|
eleq1 |
|
273 |
272
|
anbi2d |
|
274 |
|
fveq2 |
|
275 |
274
|
feq1d |
|
276 |
273 275
|
imbi12d |
|
277 |
271 276 9
|
chvarfv |
|
278 |
265 270 277
|
vtocl |
|
279 |
206 264 278
|
syl2anc |
|
280 |
|
fveq2 |
|
281 |
|
fvexd |
|
282 |
145 280 263 281
|
fvmptd3 |
|
283 |
282
|
adantll |
|
284 |
283
|
feq1d |
|
285 |
279 284
|
mpbird |
|
286 |
285
|
3adant3 |
|
287 |
286 235
|
ffvelrnd |
|
288 |
236 287
|
mulcld |
|
289 |
205 288
|
mulcld |
|
290 |
205
|
3expa |
|
291 |
238
|
peano2zd |
|
292 |
291 201
|
zsubcld |
|
293 |
207 209 292
|
3jca |
|
294 |
|
peano2re |
|
295 |
242 294
|
syl |
|
296 |
|
peano2re |
|
297 |
243 296
|
syl |
|
298 |
243
|
ltp1d |
|
299 |
|
1red |
|
300 |
243 242 299 218
|
leadd1dd |
|
301 |
243 297 295 298 300
|
ltletrd |
|
302 |
243 295 301
|
ltled |
|
303 |
302
|
adantl |
|
304 |
217 294
|
syl |
|
305 |
304 213
|
subge0d |
|
306 |
303 305
|
mpbird |
|
307 |
304 213
|
resubcld |
|
308 |
|
elfzop1le2 |
|
309 |
308
|
adantr |
|
310 |
304 215 213 309
|
lesub1dd |
|
311 |
254 258
|
breqtrd |
|
312 |
307 248 215 310 311
|
letrd |
|
313 |
293 306 312
|
jca32 |
|
314 |
|
elfz2 |
|
315 |
313 314
|
sylibr |
|
316 |
315
|
adantll |
|
317 |
|
ovex |
|
318 |
|
eleq1 |
|
319 |
318
|
anbi2d |
|
320 |
|
fveq2 |
|
321 |
320
|
feq1d |
|
322 |
319 321
|
imbi12d |
|
323 |
317 322 277
|
vtocl |
|
324 |
206 316 323
|
syl2anc |
|
325 |
145
|
a1i |
|
326 |
|
simpr |
|
327 |
326
|
fveq2d |
|
328 |
|
fvexd |
|
329 |
325 327 316 328
|
fvmptd |
|
330 |
329
|
feq1d |
|
331 |
324 330
|
mpbird |
|
332 |
331
|
ffvelrnda |
|
333 |
236
|
3expa |
|
334 |
332 333
|
mulcomd |
|
335 |
334
|
oveq2d |
|
336 |
201
|
peano2zd |
|
337 |
207 209 336
|
3jca |
|
338 |
173
|
a1i |
|
339 |
338 243 297 211 298
|
lelttrd |
|
340 |
338 297 339
|
ltled |
|
341 |
340
|
adantl |
|
342 |
213 296
|
syl |
|
343 |
300
|
adantl |
|
344 |
342 304 215 343 309
|
letrd |
|
345 |
337 341 344
|
jca32 |
|
346 |
|
elfz2 |
|
347 |
345 346
|
sylibr |
|
348 |
347
|
adantll |
|
349 |
|
ovex |
|
350 |
|
eleq1 |
|
351 |
350
|
anbi2d |
|
352 |
|
fveq2 |
|
353 |
352
|
feq1d |
|
354 |
351 353
|
imbi12d |
|
355 |
|
nfv |
|
356 |
|
nfmpt1 |
|
357 |
10 356
|
nfcxfr |
|
358 |
|
nfcv |
|
359 |
357 358
|
nffv |
|
360 |
|
nfcv |
|
361 |
|
nfcv |
|
362 |
359 360 361
|
nff |
|
363 |
355 362
|
nfim |
|
364 |
|
fveq2 |
|
365 |
364
|
feq1d |
|
366 |
273 365
|
imbi12d |
|
367 |
363 366 232
|
chvarfv |
|
368 |
349 354 367
|
vtocl |
|
369 |
206 348 368
|
syl2anc |
|
370 |
369
|
ffvelrnda |
|
371 |
287
|
3expa |
|
372 |
370 371
|
mulcld |
|
373 |
332 333
|
mulcld |
|
374 |
372 373
|
addcld |
|
375 |
335 374
|
eqeltrrd |
|
376 |
290 375
|
mulcld |
|
377 |
376
|
3impa |
|
378 |
206 1
|
syl |
|
379 |
173
|
a1i |
|
380 |
206 2
|
syl |
|
381 |
378 380 204
|
dvmptconst |
|
382 |
288
|
3expa |
|
383 |
206 227 230
|
syl2anc |
|
384 |
383
|
eqcomd |
|
385 |
233
|
feqmptd |
|
386 |
384 385
|
eqtr2d |
|
387 |
386
|
oveq2d |
|
388 |
378 84
|
syl |
|
389 |
206 123
|
syl |
|
390 |
|
elfznn0 |
|
391 |
390
|
adantl |
|
392 |
|
dvnp1 |
|
393 |
388 389 391 392
|
syl3anc |
|
394 |
393
|
eqcomd |
|
395 |
|
fveq2 |
|
396 |
|
fvexd |
|
397 |
114 395 348 396
|
fvmptd3 |
|
398 |
397
|
eqcomd |
|
399 |
369
|
feqmptd |
|
400 |
398 399
|
eqtrd |
|
401 |
387 394 400
|
3eqtrd |
|
402 |
283
|
eqcomd |
|
403 |
285
|
feqmptd |
|
404 |
402 403
|
eqtr2d |
|
405 |
404
|
oveq2d |
|
406 |
206 152
|
syl |
|
407 |
|
fznn0sub |
|
408 |
407
|
adantl |
|
409 |
|
dvnp1 |
|
410 |
388 406 408 409
|
syl3anc |
|
411 |
410
|
eqcomd |
|
412 |
217
|
recnd |
|
413 |
|
1cnd |
|
414 |
213
|
recnd |
|
415 |
412 413 414
|
addsubd |
|
416 |
415
|
eqcomd |
|
417 |
416
|
fveq2d |
|
418 |
417
|
adantll |
|
419 |
329
|
eqcomd |
|
420 |
331
|
feqmptd |
|
421 |
418 419 420
|
3eqtrd |
|
422 |
405 411 421
|
3eqtrd |
|
423 |
378 333 370 401 371 332 422
|
dvmptmul |
|
424 |
378 290 379 381 382 374 423
|
dvmptmul |
|
425 |
382
|
mul02d |
|
426 |
335
|
oveq1d |
|
427 |
375 290
|
mulcomd |
|
428 |
426 427
|
eqtrd |
|
429 |
425 428
|
oveq12d |
|
430 |
376
|
addid2d |
|
431 |
429 430
|
eqtrd |
|
432 |
431
|
mpteq2dva |
|
433 |
424 432
|
eqtrd |
|
434 |
194 195 196 197 198 289 377 433
|
dvmptfsum |
|
435 |
204
|
adantlr |
|
436 |
372
|
an32s |
|
437 |
|
anass |
|
438 |
|
ancom |
|
439 |
438
|
anbi2i |
|
440 |
|
anass |
|
441 |
440
|
bicomi |
|
442 |
439 441
|
bitri |
|
443 |
437 442
|
bitri |
|
444 |
443
|
imbi1i |
|
445 |
333 444
|
mpbi |
|
446 |
443
|
imbi1i |
|
447 |
332 446
|
mpbi |
|
448 |
445 447
|
mulcld |
|
449 |
435 436 448
|
adddid |
|
450 |
449
|
sumeq2dv |
|
451 |
198
|
adantr |
|
452 |
435 436
|
mulcld |
|
453 |
435 448
|
mulcld |
|
454 |
451 452 453
|
fsumadd |
|
455 |
|
oveq2 |
|
456 |
|
fvoveq1 |
|
457 |
456
|
fveq1d |
|
458 |
|
oveq2 |
|
459 |
458
|
fveq2d |
|
460 |
459
|
fveq1d |
|
461 |
457 460
|
oveq12d |
|
462 |
455 461
|
oveq12d |
|
463 |
|
nfcv |
|
464 |
|
nfcv |
|
465 |
|
nfcv |
|
466 |
|
nfcv |
|
467 |
|
nfcv |
|
468 |
|
nfcv |
|
469 |
357 468
|
nffv |
|
470 |
|
nfcv |
|
471 |
469 470
|
nffv |
|
472 |
|
nfmpt1 |
|
473 |
11 472
|
nfcxfr |
|
474 |
|
nfcv |
|
475 |
473 474
|
nffv |
|
476 |
475 470
|
nffv |
|
477 |
471 467 476
|
nfov |
|
478 |
466 467 477
|
nfov |
|
479 |
462 463 464 465 478
|
cbvsum |
|
480 |
479
|
a1i |
|
481 |
|
1zzd |
|
482 |
96
|
a1i |
|
483 |
237
|
ad2antlr |
|
484 |
|
nfv |
|
485 |
|
nfcv |
|
486 |
485 464
|
nfel |
|
487 |
484 486
|
nfan |
|
488 |
478 361
|
nfel |
|
489 |
487 488
|
nfim |
|
490 |
|
eleq1 |
|
491 |
490
|
anbi2d |
|
492 |
462
|
eleq1d |
|
493 |
491 492
|
imbi12d |
|
494 |
489 493 452
|
chvarfv |
|
495 |
|
oveq2 |
|
496 |
|
fvoveq1 |
|
497 |
496
|
fveq1d |
|
498 |
|
oveq2 |
|
499 |
498
|
fveq2d |
|
500 |
499
|
fveq1d |
|
501 |
497 500
|
oveq12d |
|
502 |
495 501
|
oveq12d |
|
503 |
481 482 483 494 502
|
fsumshft |
|
504 |
480 503
|
eqtrd |
|
505 |
|
0p1e1 |
|
506 |
505
|
oveq1i |
|
507 |
506
|
sumeq1i |
|
508 |
507
|
a1i |
|
509 |
|
elfzelz |
|
510 |
509
|
zcnd |
|
511 |
|
1cnd |
|
512 |
510 511
|
npcand |
|
513 |
512
|
fveq2d |
|
514 |
513
|
fveq1d |
|
515 |
514
|
adantl |
|
516 |
216
|
recnd |
|
517 |
516
|
adantr |
|
518 |
510
|
adantl |
|
519 |
511
|
adantl |
|
520 |
517 518 519
|
subsub3d |
|
521 |
520
|
fveq2d |
|
522 |
521
|
fveq1d |
|
523 |
515 522
|
oveq12d |
|
524 |
523
|
oveq2d |
|
525 |
524
|
sumeq2dv |
|
526 |
525
|
ad2antlr |
|
527 |
|
nfv |
|
528 |
|
nfcv |
|
529 |
|
fzfid |
|
530 |
187
|
adantr |
|
531 |
509
|
adantl |
|
532 |
|
1zzd |
|
533 |
531 532
|
zsubcld |
|
534 |
530 533
|
bccld |
|
535 |
534
|
nn0cnd |
|
536 |
535
|
adantll |
|
537 |
536
|
adantlr |
|
538 |
12
|
ad2antrr |
|
539 |
|
0zd |
|
540 |
208
|
adantr |
|
541 |
539 540 531
|
3jca |
|
542 |
173
|
a1i |
|
543 |
509
|
zred |
|
544 |
|
1red |
|
545 |
|
0lt1 |
|
546 |
545
|
a1i |
|
547 |
|
elfzle1 |
|
548 |
542 544 543 546 547
|
ltletrd |
|
549 |
542 543 548
|
ltled |
|
550 |
549
|
adantl |
|
551 |
543
|
adantl |
|
552 |
216
|
adantr |
|
553 |
|
1red |
|
554 |
552 553
|
readdcld |
|
555 |
214
|
adantr |
|
556 |
|
elfzle2 |
|
557 |
556
|
adantl |
|
558 |
308
|
adantr |
|
559 |
551 554 555 557 558
|
letrd |
|
560 |
541 550 559
|
jca32 |
|
561 |
|
elfz2 |
|
562 |
560 561
|
sylibr |
|
563 |
562
|
adantll |
|
564 |
538 563 367
|
syl2anc |
|
565 |
564
|
adantlr |
|
566 |
|
simplr |
|
567 |
565 566
|
ffvelrnd |
|
568 |
237
|
adantr |
|
569 |
568
|
peano2zd |
|
570 |
569 531
|
zsubcld |
|
571 |
539 540 570
|
3jca |
|
572 |
554 551
|
subge0d |
|
573 |
557 572
|
mpbird |
|
574 |
554 551
|
resubcld |
|
575 |
574
|
leidd |
|
576 |
543 548
|
elrpd |
|
577 |
576
|
adantl |
|
578 |
554 577
|
ltsubrpd |
|
579 |
574 554 555 578 558
|
ltletrd |
|
580 |
574 574 555 575 579
|
lelttrd |
|
581 |
574 555 580
|
ltled |
|
582 |
571 573 581
|
jca32 |
|
583 |
|
elfz2 |
|
584 |
582 583
|
sylibr |
|
585 |
584
|
adantll |
|
586 |
|
nfv |
|
587 |
|
nfcv |
|
588 |
473 587
|
nffv |
|
589 |
588 360 361
|
nff |
|
590 |
586 589
|
nfim |
|
591 |
|
ovex |
|
592 |
|
eleq1 |
|
593 |
592
|
anbi2d |
|
594 |
|
fveq2 |
|
595 |
594
|
feq1d |
|
596 |
593 595
|
imbi12d |
|
597 |
11
|
a1i |
|
598 |
|
fvexd |
|
599 |
597 598
|
fvmpt2d |
|
600 |
599
|
feq1d |
|
601 |
9 600
|
mpbird |
|
602 |
590 591 596 601
|
vtoclf |
|
603 |
538 585 602
|
syl2anc |
|
604 |
603
|
adantlr |
|
605 |
604 566
|
ffvelrnd |
|
606 |
567 605
|
mulcld |
|
607 |
537 606
|
mulcld |
|
608 |
|
1zzd |
|
609 |
237
|
peano2zd |
|
610 |
505
|
eqcomi |
|
611 |
610
|
a1i |
|
612 |
173
|
a1i |
|
613 |
|
1red |
|
614 |
187
|
nn0ge0d |
|
615 |
612 216 613 614
|
leadd1dd |
|
616 |
611 615
|
eqbrtrd |
|
617 |
608 609 616
|
3jca |
|
618 |
|
eluz2 |
|
619 |
617 618
|
sylibr |
|
620 |
|
eluzfz2 |
|
621 |
619 620
|
syl |
|
622 |
621
|
ad2antlr |
|
623 |
|
oveq1 |
|
624 |
623
|
oveq2d |
|
625 |
|
fveq2 |
|
626 |
625
|
fveq1d |
|
627 |
|
oveq2 |
|
628 |
627
|
fveq2d |
|
629 |
628
|
fveq1d |
|
630 |
626 629
|
oveq12d |
|
631 |
624 630
|
oveq12d |
|
632 |
527 528 529 607 622 631
|
fsumsplit1 |
|
633 |
|
1cnd |
|
634 |
516 633
|
pncand |
|
635 |
634
|
oveq2d |
|
636 |
|
bcnn |
|
637 |
187 636
|
syl |
|
638 |
635 637
|
eqtrd |
|
639 |
516 633
|
addcld |
|
640 |
639
|
subidd |
|
641 |
640
|
fveq2d |
|
642 |
641
|
fveq1d |
|
643 |
642
|
oveq2d |
|
644 |
638 643
|
oveq12d |
|
645 |
644
|
ad2antlr |
|
646 |
|
simpl |
|
647 |
|
fzofzp1 |
|
648 |
647
|
adantl |
|
649 |
|
nfv |
|
650 |
|
nfcv |
|
651 |
357 650
|
nffv |
|
652 |
651 360 361
|
nff |
|
653 |
649 652
|
nfim |
|
654 |
|
ovex |
|
655 |
|
eleq1 |
|
656 |
655
|
anbi2d |
|
657 |
|
fveq2 |
|
658 |
657
|
feq1d |
|
659 |
656 658
|
imbi12d |
|
660 |
653 654 659 232
|
vtoclf |
|
661 |
646 648 660
|
syl2anc |
|
662 |
661
|
ffvelrnda |
|
663 |
|
nfv |
|
664 |
|
nfcv |
|
665 |
473 664
|
nffv |
|
666 |
665 360 361
|
nff |
|
667 |
663 666
|
nfim |
|
668 |
|
c0ex |
|
669 |
|
eleq1 |
|
670 |
669
|
anbi2d |
|
671 |
|
fveq2 |
|
672 |
671
|
feq1d |
|
673 |
670 672
|
imbi12d |
|
674 |
667 668 673 601
|
vtoclf |
|
675 |
12 117 674
|
syl2anc |
|
676 |
675
|
adantr |
|
677 |
676
|
ffvelrnda |
|
678 |
662 677
|
mulcld |
|
679 |
678
|
mulid2d |
|
680 |
645 679
|
eqtrd |
|
681 |
|
1m1e0 |
|
682 |
681
|
fveq2i |
|
683 |
13
|
eqcomi |
|
684 |
682 683
|
eqtr2i |
|
685 |
684
|
a1i |
|
686 |
187 685
|
eleqtrd |
|
687 |
|
fzdifsuc2 |
|
688 |
686 687
|
syl |
|
689 |
688
|
eqcomd |
|
690 |
689
|
sumeq1d |
|
691 |
690
|
ad2antlr |
|
692 |
680 691
|
oveq12d |
|
693 |
526 632 692
|
3eqtrd |
|
694 |
504 508 693
|
3eqtrd |
|
695 |
|
nfcv |
|
696 |
357 664
|
nffv |
|
697 |
696 470
|
nffv |
|
698 |
|
nfcv |
|
699 |
473 698
|
nffv |
|
700 |
699 470
|
nffv |
|
701 |
697 467 700
|
nfov |
|
702 |
695 467 701
|
nfov |
|
703 |
683
|
a1i |
|
704 |
187 703
|
eleqtrrd |
|
705 |
|
eluzfz1 |
|
706 |
704 705
|
syl |
|
707 |
706
|
ad2antlr |
|
708 |
|
oveq2 |
|
709 |
110
|
fveq1d |
|
710 |
|
oveq2 |
|
711 |
710
|
fveq2d |
|
712 |
711
|
fveq1d |
|
713 |
709 712
|
oveq12d |
|
714 |
708 713
|
oveq12d |
|
715 |
484 702 451 453 707 714
|
fsumsplit1 |
|
716 |
639
|
subid1d |
|
717 |
716
|
fveq2d |
|
718 |
717
|
fveq1d |
|
719 |
718
|
oveq2d |
|
720 |
719
|
oveq2d |
|
721 |
720
|
oveq1d |
|
722 |
721
|
ad2antlr |
|
723 |
|
bcn0 |
|
724 |
187 723
|
syl |
|
725 |
724
|
oveq1d |
|
726 |
725
|
ad2antlr |
|
727 |
696 360 361
|
nff |
|
728 |
663 727
|
nfim |
|
729 |
110
|
feq1d |
|
730 |
670 729
|
imbi12d |
|
731 |
728 668 730 232
|
vtoclf |
|
732 |
12 117 731
|
syl2anc |
|
733 |
732
|
adantr |
|
734 |
733
|
ffvelrnda |
|
735 |
473 650
|
nffv |
|
736 |
735 360 361
|
nff |
|
737 |
649 736
|
nfim |
|
738 |
|
fveq2 |
|
739 |
738
|
feq1d |
|
740 |
656 739
|
imbi12d |
|
741 |
737 654 740 601
|
vtoclf |
|
742 |
646 648 741
|
syl2anc |
|
743 |
742
|
ffvelrnda |
|
744 |
734 743
|
mulcld |
|
745 |
744
|
mulid2d |
|
746 |
726 745
|
eqtrd |
|
747 |
|
nfv |
|
748 |
|
1zzd |
|
749 |
237
|
adantr |
|
750 |
|
eldifi |
|
751 |
|
elfzelz |
|
752 |
750 751
|
syl |
|
753 |
752
|
adantl |
|
754 |
748 749 753
|
3jca |
|
755 |
|
elfznn0 |
|
756 |
750 755
|
syl |
|
757 |
|
eldifsni |
|
758 |
756 757
|
jca |
|
759 |
|
elnnne0 |
|
760 |
758 759
|
sylibr |
|
761 |
|
nnge1 |
|
762 |
760 761
|
syl |
|
763 |
762
|
adantl |
|
764 |
|
elfzle2 |
|
765 |
750 764
|
syl |
|
766 |
765
|
adantl |
|
767 |
754 763 766
|
jca32 |
|
768 |
|
elfz2 |
|
769 |
767 768
|
sylibr |
|
770 |
769
|
ex |
|
771 |
|
0zd |
|
772 |
|
elfzel2 |
|
773 |
|
elfzelz |
|
774 |
771 772 773
|
3jca |
|
775 |
173
|
a1i |
|
776 |
773
|
zred |
|
777 |
|
1red |
|
778 |
545
|
a1i |
|
779 |
|
elfzle1 |
|
780 |
775 777 776 778 779
|
ltletrd |
|
781 |
775 776 780
|
ltled |
|
782 |
|
elfzle2 |
|
783 |
774 781 782
|
jca32 |
|
784 |
|
elfz2 |
|
785 |
783 784
|
sylibr |
|
786 |
775 780
|
gtned |
|
787 |
|
nelsn |
|
788 |
786 787
|
syl |
|
789 |
785 788
|
eldifd |
|
790 |
789
|
adantl |
|
791 |
790
|
ex |
|
792 |
770 791
|
impbid |
|
793 |
747 792
|
alrimi |
|
794 |
|
dfcleq |
|
795 |
793 794
|
sylibr |
|
796 |
795
|
sumeq1d |
|
797 |
796
|
ad2antlr |
|
798 |
746 797
|
oveq12d |
|
799 |
715 722 798
|
3eqtrd |
|
800 |
694 799
|
oveq12d |
|
801 |
|
fzfid |
|
802 |
187
|
adantr |
|
803 |
790 752
|
syl |
|
804 |
|
1zzd |
|
805 |
803 804
|
zsubcld |
|
806 |
802 805
|
bccld |
|
807 |
806
|
nn0cnd |
|
808 |
807
|
adantll |
|
809 |
808
|
adantlr |
|
810 |
|
simpl |
|
811 |
|
fzelp1 |
|
812 |
811
|
adantl |
|
813 |
810 812 567
|
syl2anc |
|
814 |
812 605
|
syldan |
|
815 |
813 814
|
mulcld |
|
816 |
809 815
|
mulcld |
|
817 |
801 816
|
fsumcl |
|
818 |
187
|
adantr |
|
819 |
|
elfzelz |
|
820 |
819
|
adantl |
|
821 |
818 820
|
bccld |
|
822 |
821
|
nn0cnd |
|
823 |
822
|
adantll |
|
824 |
823
|
adantlr |
|
825 |
|
simpll |
|
826 |
|
simplr |
|
827 |
785
|
ssriv |
|
828 |
|
id |
|
829 |
827 828
|
sseldi |
|
830 |
829
|
adantl |
|
831 |
825 826 830 445
|
syl21anc |
|
832 |
830 447
|
syldan |
|
833 |
831 832
|
mulcld |
|
834 |
824 833
|
mulcld |
|
835 |
801 834
|
fsumcl |
|
836 |
678 817 744 835
|
add4d |
|
837 |
|
oveq1 |
|
838 |
837
|
oveq2d |
|
839 |
|
fveq2 |
|
840 |
839
|
fveq1d |
|
841 |
|
oveq2 |
|
842 |
841
|
fveq2d |
|
843 |
842
|
fveq1d |
|
844 |
840 843
|
oveq12d |
|
845 |
838 844
|
oveq12d |
|
846 |
|
nfcv |
|
847 |
|
nfcv |
|
848 |
|
nfcv |
|
849 |
359 470
|
nffv |
|
850 |
588 470
|
nffv |
|
851 |
849 467 850
|
nfov |
|
852 |
848 467 851
|
nfov |
|
853 |
|
nfcv |
|
854 |
845 846 847 852 853
|
cbvsum |
|
855 |
854
|
a1i |
|
856 |
855
|
oveq1d |
|
857 |
|
peano2zm |
|
858 |
820 857
|
syl |
|
859 |
818 858
|
bccld |
|
860 |
859
|
nn0cnd |
|
861 |
860
|
adantll |
|
862 |
861
|
adantlr |
|
863 |
862 833
|
mulcld |
|
864 |
801 863 834
|
fsumadd |
|
865 |
864
|
eqcomd |
|
866 |
860 822
|
addcomd |
|
867 |
|
bcpasc |
|
868 |
818 820 867
|
syl2anc |
|
869 |
866 868
|
eqtr2d |
|
870 |
869
|
oveq1d |
|
871 |
870
|
adantll |
|
872 |
871
|
adantlr |
|
873 |
862 824 833
|
adddird |
|
874 |
872 873
|
eqtr2d |
|
875 |
874
|
sumeq2dv |
|
876 |
856 865 875
|
3eqtrd |
|
877 |
876
|
oveq2d |
|
878 |
|
peano2nn0 |
|
879 |
818 878
|
syl |
|
880 |
879 820
|
bccld |
|
881 |
880
|
nn0cnd |
|
882 |
881
|
adantll |
|
883 |
882
|
adantlr |
|
884 |
883 833
|
mulcld |
|
885 |
801 884
|
fsumcl |
|
886 |
678 744 885
|
addassd |
|
887 |
187 878
|
syl |
|
888 |
|
bcn0 |
|
889 |
887 888
|
syl |
|
890 |
889 719
|
oveq12d |
|
891 |
890
|
ad2antlr |
|
892 |
891 745
|
eqtr2d |
|
893 |
795
|
ad2antlr |
|
894 |
893
|
eqcomd |
|
895 |
894
|
sumeq1d |
|
896 |
892 895
|
oveq12d |
|
897 |
|
nfcv |
|
898 |
897 467 701
|
nfov |
|
899 |
199 878
|
syl |
|
900 |
899 201
|
bccld |
|
901 |
900
|
nn0cnd |
|
902 |
901
|
adantll |
|
903 |
902
|
adantlr |
|
904 |
903 448
|
mulcld |
|
905 |
|
oveq2 |
|
906 |
905 713
|
oveq12d |
|
907 |
484 898 451 904 707 906
|
fsumsplit1 |
|
908 |
907
|
eqcomd |
|
909 |
896 908
|
eqtrd |
|
910 |
909
|
oveq2d |
|
911 |
|
bcnn |
|
912 |
887 911
|
syl |
|
913 |
912
|
ad2antlr |
|
914 |
913
|
oveq1d |
|
915 |
641
|
adantl |
|
916 |
915
|
feq1d |
|
917 |
676 916
|
mpbird |
|
918 |
917
|
adantr |
|
919 |
|
simpr |
|
920 |
918 919
|
ffvelrnd |
|
921 |
662 920
|
mulcld |
|
922 |
921
|
mulid2d |
|
923 |
643
|
ad2antlr |
|
924 |
914 922 923
|
3eqtrrd |
|
925 |
|
fzdifsuc |
|
926 |
704 925
|
syl |
|
927 |
926
|
sumeq1d |
|
928 |
927
|
ad2antlr |
|
929 |
924 928
|
oveq12d |
|
930 |
|
nfcv |
|
931 |
651 470
|
nffv |
|
932 |
|
nfcv |
|
933 |
473 932
|
nffv |
|
934 |
933 470
|
nffv |
|
935 |
931 467 934
|
nfov |
|
936 |
930 467 935
|
nfov |
|
937 |
|
fzfid |
|
938 |
887
|
adantr |
|
939 |
|
elfzelz |
|
940 |
939
|
adantl |
|
941 |
938 940
|
bccld |
|
942 |
941
|
nn0cnd |
|
943 |
942
|
adantll |
|
944 |
943
|
adantlr |
|
945 |
646
|
adantr |
|
946 |
96
|
a1i |
|
947 |
208
|
adantr |
|
948 |
946 947 940
|
3jca |
|
949 |
|
elfzle1 |
|
950 |
949
|
adantl |
|
951 |
940
|
zred |
|
952 |
938
|
nn0red |
|
953 |
214
|
adantr |
|
954 |
|
elfzle2 |
|
955 |
954
|
adantl |
|
956 |
308
|
adantr |
|
957 |
951 952 953 955 956
|
letrd |
|
958 |
948 950 957
|
jca32 |
|
959 |
958 225
|
sylibr |
|
960 |
959
|
adantll |
|
961 |
945 960 232
|
syl2anc |
|
962 |
961
|
adantlr |
|
963 |
|
simplr |
|
964 |
962 963
|
ffvelrnd |
|
965 |
945
|
adantlr |
|
966 |
609
|
adantr |
|
967 |
966 940
|
zsubcld |
|
968 |
946 947 967
|
3jca |
|
969 |
952 951
|
subge0d |
|
970 |
955 969
|
mpbird |
|
971 |
952 951
|
resubcld |
|
972 |
953 951
|
resubcld |
|
973 |
953 173 251
|
sylancl |
|
974 |
952 953 951 956
|
lesub1dd |
|
975 |
173
|
a1i |
|
976 |
975 951 953 950
|
lesub2dd |
|
977 |
971 972 973 974 976
|
letrd |
|
978 |
257
|
adantr |
|
979 |
977 978
|
breqtrd |
|
980 |
968 970 979
|
jca32 |
|
981 |
980 314
|
sylibr |
|
982 |
981
|
adantll |
|
983 |
982
|
adantlr |
|
984 |
|
fveq2 |
|
985 |
984
|
feq1d |
|
986 |
319 985
|
imbi12d |
|
987 |
473 358
|
nffv |
|
988 |
987 360 361
|
nff |
|
989 |
355 988
|
nfim |
|
990 |
|
fveq2 |
|
991 |
990
|
feq1d |
|
992 |
273 991
|
imbi12d |
|
993 |
989 992 601
|
chvarfv |
|
994 |
317 986 993
|
vtocl |
|
995 |
965 983 994
|
syl2anc |
|
996 |
995 963
|
ffvelrnd |
|
997 |
964 996
|
mulcld |
|
998 |
944 997
|
mulcld |
|
999 |
887 703
|
eleqtrrd |
|
1000 |
|
eluzfz2 |
|
1001 |
999 1000
|
syl |
|
1002 |
1001
|
ad2antlr |
|
1003 |
|
oveq2 |
|
1004 |
657
|
fveq1d |
|
1005 |
|
oveq2 |
|
1006 |
1005
|
fveq2d |
|
1007 |
1006
|
fveq1d |
|
1008 |
1004 1007
|
oveq12d |
|
1009 |
1003 1008
|
oveq12d |
|
1010 |
484 936 937 998 1002 1009
|
fsumsplit1 |
|
1011 |
1010
|
eqcomd |
|
1012 |
910 929 1011
|
3eqtrd |
|
1013 |
877 886 1012
|
3eqtrd |
|
1014 |
800 836 1013
|
3eqtrd |
|
1015 |
450 454 1014
|
3eqtrd |
|
1016 |
1015
|
mpteq2dva |
|
1017 |
434 1016
|
eqtrd |
|
1018 |
1017
|
adantr |
|
1019 |
191 193 1018
|
3eqtrd |
|
1020 |
180 181 184 1019
|
syl21anc |
|
1021 |
1020
|
3exp |
|
1022 |
44 57 70 83 179 1021
|
fzind2 |
|
1023 |
31 1022
|
vtoclg |
|
1024 |
5 16 1023
|
sylc |
|
1025 |
12 1024
|
mpd |
|