Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem64.t |
|
2 |
|
fourierdlem64.p |
|
3 |
|
fourierdlem64.m |
|
4 |
|
fourierdlem64.q |
|
5 |
|
fourierdlem64.c |
|
6 |
|
fourierdlem64.d |
|
7 |
|
fourierdlem64.cltd |
|
8 |
|
fourierdlem64.h |
|
9 |
|
fourierdlem64.n |
|
10 |
|
fourierdlem64.v |
|
11 |
|
fourierdlem64.j |
|
12 |
|
fourierdlem64.l |
|
13 |
|
fourierdlem64.i |
|
14 |
|
ssrab2 |
|
15 |
|
fzossfz |
|
16 |
|
fzssz |
|
17 |
15 16
|
sstri |
|
18 |
14 17
|
sstri |
|
19 |
18
|
a1i |
|
20 |
|
0zd |
|
21 |
3
|
nnzd |
|
22 |
3
|
nngt0d |
|
23 |
|
fzolb |
|
24 |
20 21 22 23
|
syl3anbrc |
|
25 |
|
ssrab2 |
|
26 |
25
|
a1i |
|
27 |
|
prssi |
|
28 |
5 6 27
|
syl2anc |
|
29 |
|
ssrab2 |
|
30 |
29
|
a1i |
|
31 |
5 6
|
iccssred |
|
32 |
30 31
|
sstrd |
|
33 |
28 32
|
unssd |
|
34 |
8 33
|
eqsstrid |
|
35 |
|
eqid |
|
36 |
1 2 3 4 5 6 7 35 8 9 10
|
fourierdlem54 |
|
37 |
36
|
simprd |
|
38 |
|
isof1o |
|
39 |
|
f1of |
|
40 |
37 38 39
|
3syl |
|
41 |
|
elfzofz |
|
42 |
11 41
|
syl |
|
43 |
40 42
|
ffvelrnd |
|
44 |
34 43
|
sseldd |
|
45 |
2
|
fourierdlem2 |
|
46 |
3 45
|
syl |
|
47 |
4 46
|
mpbid |
|
48 |
47
|
simpld |
|
49 |
|
elmapi |
|
50 |
48 49
|
syl |
|
51 |
3
|
nnnn0d |
|
52 |
|
nn0uz |
|
53 |
51 52
|
eleqtrdi |
|
54 |
|
eluzfz1 |
|
55 |
53 54
|
syl |
|
56 |
50 55
|
ffvelrnd |
|
57 |
44 56
|
resubcld |
|
58 |
2 3 4
|
fourierdlem11 |
|
59 |
58
|
simp2d |
|
60 |
58
|
simp1d |
|
61 |
59 60
|
resubcld |
|
62 |
1 61
|
eqeltrid |
|
63 |
58
|
simp3d |
|
64 |
60 59
|
posdifd |
|
65 |
63 64
|
mpbid |
|
66 |
65 1
|
breqtrrdi |
|
67 |
66
|
gt0ne0d |
|
68 |
57 62 67
|
redivcld |
|
69 |
|
btwnz |
|
70 |
68 69
|
syl |
|
71 |
70
|
simpld |
|
72 |
|
zre |
|
73 |
56
|
ad2antrr |
|
74 |
|
simplr |
|
75 |
62
|
ad2antrr |
|
76 |
74 75
|
remulcld |
|
77 |
73 76
|
readdcld |
|
78 |
44
|
ad2antrr |
|
79 |
|
simpr |
|
80 |
57
|
ad2antrr |
|
81 |
62 66
|
elrpd |
|
82 |
81
|
ad2antrr |
|
83 |
74 80 82
|
ltmuldivd |
|
84 |
79 83
|
mpbird |
|
85 |
56
|
adantr |
|
86 |
|
simpr |
|
87 |
62
|
adantr |
|
88 |
86 87
|
remulcld |
|
89 |
44
|
adantr |
|
90 |
85 88 89
|
ltaddsub2d |
|
91 |
90
|
adantr |
|
92 |
84 91
|
mpbird |
|
93 |
77 78 92
|
ltled |
|
94 |
93
|
ex |
|
95 |
72 94
|
sylan2 |
|
96 |
95
|
reximdva |
|
97 |
71 96
|
mpd |
|
98 |
|
rabn0 |
|
99 |
97 98
|
sylibr |
|
100 |
|
simpl |
|
101 |
26
|
sselda |
|
102 |
|
oveq1 |
|
103 |
102
|
oveq2d |
|
104 |
103
|
breq1d |
|
105 |
104
|
elrab |
|
106 |
105
|
simprbi |
|
107 |
106
|
adantl |
|
108 |
|
zre |
|
109 |
|
simpr |
|
110 |
56
|
ad2antrr |
|
111 |
|
simpr |
|
112 |
62
|
adantr |
|
113 |
111 112
|
remulcld |
|
114 |
113
|
adantr |
|
115 |
44
|
ad2antrr |
|
116 |
110 114 115
|
leaddsub2d |
|
117 |
109 116
|
mpbid |
|
118 |
|
simplr |
|
119 |
57
|
ad2antrr |
|
120 |
81
|
ad2antrr |
|
121 |
118 119 120
|
lemuldivd |
|
122 |
117 121
|
mpbid |
|
123 |
108 122
|
sylanl2 |
|
124 |
100 101 107 123
|
syl21anc |
|
125 |
124
|
ralrimiva |
|
126 |
|
breq2 |
|
127 |
126
|
ralbidv |
|
128 |
127
|
rspcev |
|
129 |
68 125 128
|
syl2anc |
|
130 |
|
suprzcl |
|
131 |
26 99 129 130
|
syl3anc |
|
132 |
12 131
|
eqeltrid |
|
133 |
|
oveq1 |
|
134 |
133
|
oveq2d |
|
135 |
134
|
breq1d |
|
136 |
135
|
elrab |
|
137 |
132 136
|
sylib |
|
138 |
137
|
simprd |
|
139 |
|
fveq2 |
|
140 |
139
|
oveq1d |
|
141 |
140
|
breq1d |
|
142 |
141
|
elrab |
|
143 |
24 138 142
|
sylanbrc |
|
144 |
|
ne0i |
|
145 |
143 144
|
syl |
|
146 |
3
|
nnred |
|
147 |
14
|
a1i |
|
148 |
147
|
sselda |
|
149 |
|
elfzoelz |
|
150 |
149
|
zred |
|
151 |
150
|
adantl |
|
152 |
146
|
adantr |
|
153 |
|
elfzolt2 |
|
154 |
153
|
adantl |
|
155 |
151 152 154
|
ltled |
|
156 |
148 155
|
syldan |
|
157 |
156
|
ralrimiva |
|
158 |
|
breq2 |
|
159 |
158
|
ralbidv |
|
160 |
159
|
rspcev |
|
161 |
146 157 160
|
syl2anc |
|
162 |
|
suprzcl |
|
163 |
19 145 161 162
|
syl3anc |
|
164 |
14 163
|
sseldi |
|
165 |
13 164
|
eqeltrid |
|
166 |
25 131
|
sseldi |
|
167 |
12 166
|
eqeltrid |
|
168 |
15 165
|
sseldi |
|
169 |
50 168
|
ffvelrnd |
|
170 |
167
|
zred |
|
171 |
170 62
|
remulcld |
|
172 |
169 171
|
readdcld |
|
173 |
172
|
rexrd |
|
174 |
173
|
adantr |
|
175 |
|
fzofzp1 |
|
176 |
165 175
|
syl |
|
177 |
50 176
|
ffvelrnd |
|
178 |
177 171
|
readdcld |
|
179 |
178
|
rexrd |
|
180 |
179
|
adantr |
|
181 |
|
elioore |
|
182 |
181
|
adantl |
|
183 |
172
|
adantr |
|
184 |
44
|
adantr |
|
185 |
13 163
|
eqeltrid |
|
186 |
|
fveq2 |
|
187 |
186
|
oveq1d |
|
188 |
187
|
breq1d |
|
189 |
188
|
elrab |
|
190 |
185 189
|
sylib |
|
191 |
190
|
simprd |
|
192 |
191
|
adantr |
|
193 |
184
|
rexrd |
|
194 |
|
fzofzp1 |
|
195 |
11 194
|
syl |
|
196 |
40 195
|
ffvelrnd |
|
197 |
34 196
|
sseldd |
|
198 |
197
|
rexrd |
|
199 |
198
|
adantr |
|
200 |
|
simpr |
|
201 |
|
ioogtlb |
|
202 |
193 199 200 201
|
syl3anc |
|
203 |
183 184 182 192 202
|
lelttrd |
|
204 |
|
zssre |
|
205 |
25 204
|
sstri |
|
206 |
205
|
a1i |
|
207 |
99
|
ad2antrr |
|
208 |
129
|
ad2antrr |
|
209 |
167
|
peano2zd |
|
210 |
209
|
ad2antrr |
|
211 |
|
oveq1 |
|
212 |
146
|
recnd |
|
213 |
|
1cnd |
|
214 |
212 213
|
npcand |
|
215 |
211 214
|
sylan9eqr |
|
216 |
215
|
fveq2d |
|
217 |
47
|
simprd |
|
218 |
217
|
simpld |
|
219 |
218
|
simprd |
|
220 |
219
|
adantr |
|
221 |
59
|
recnd |
|
222 |
60
|
recnd |
|
223 |
221 222
|
npcand |
|
224 |
223
|
eqcomd |
|
225 |
1
|
eqcomi |
|
226 |
225
|
a1i |
|
227 |
226
|
oveq1d |
|
228 |
218
|
simpld |
|
229 |
228
|
eqcomd |
|
230 |
229
|
oveq2d |
|
231 |
224 227 230
|
3eqtrd |
|
232 |
231
|
adantr |
|
233 |
216 220 232
|
3eqtrd |
|
234 |
62
|
recnd |
|
235 |
228 222
|
eqeltrd |
|
236 |
234 235
|
addcomd |
|
237 |
236
|
adantr |
|
238 |
233 237
|
eqtrd |
|
239 |
238
|
oveq1d |
|
240 |
171
|
recnd |
|
241 |
235 234 240
|
addassd |
|
242 |
234
|
mulid2d |
|
243 |
242 234
|
eqeltrd |
|
244 |
243 240
|
addcomd |
|
245 |
242
|
eqcomd |
|
246 |
245
|
oveq1d |
|
247 |
170
|
recnd |
|
248 |
247 213 234
|
adddird |
|
249 |
244 246 248
|
3eqtr4d |
|
250 |
249
|
oveq2d |
|
251 |
241 250
|
eqtrd |
|
252 |
251
|
adantr |
|
253 |
239 252
|
eqtr2d |
|
254 |
253
|
adantr |
|
255 |
|
simpr |
|
256 |
254 255
|
eqbrtrd |
|
257 |
|
oveq1 |
|
258 |
257
|
oveq2d |
|
259 |
258
|
breq1d |
|
260 |
259
|
elrab |
|
261 |
210 256 260
|
sylanbrc |
|
262 |
|
suprub |
|
263 |
206 207 208 261 262
|
syl31anc |
|
264 |
263 12
|
breqtrrdi |
|
265 |
170
|
ltp1d |
|
266 |
|
peano2re |
|
267 |
170 266
|
syl |
|
268 |
170 267
|
ltnled |
|
269 |
265 268
|
mpbid |
|
270 |
269
|
ad2antrr |
|
271 |
264 270
|
pm2.65da |
|
272 |
17 165
|
sseldi |
|
273 |
272
|
zred |
|
274 |
273
|
adantr |
|
275 |
|
peano2rem |
|
276 |
146 275
|
syl |
|
277 |
276
|
adantr |
|
278 |
|
elfzolt2 |
|
279 |
|
elfzoelz |
|
280 |
|
elfzoel2 |
|
281 |
|
zltlem1 |
|
282 |
279 280 281
|
syl2anc |
|
283 |
278 282
|
mpbid |
|
284 |
165 283
|
syl |
|
285 |
284
|
adantr |
|
286 |
|
neqne |
|
287 |
286
|
necomd |
|
288 |
287
|
adantl |
|
289 |
274 277 285 288
|
leneltd |
|
290 |
18 204
|
sstri |
|
291 |
290
|
a1i |
|
292 |
145
|
ad2antrr |
|
293 |
161
|
ad2antrr |
|
294 |
176
|
adantr |
|
295 |
273
|
adantr |
|
296 |
276
|
adantr |
|
297 |
|
1red |
|
298 |
|
simpr |
|
299 |
295 296 297 298
|
ltadd1dd |
|
300 |
214
|
adantr |
|
301 |
299 300
|
breqtrd |
|
302 |
|
elfzfzo |
|
303 |
294 301 302
|
sylanbrc |
|
304 |
303
|
anim1i |
|
305 |
|
fveq2 |
|
306 |
305
|
oveq1d |
|
307 |
306
|
breq1d |
|
308 |
307
|
elrab |
|
309 |
304 308
|
sylibr |
|
310 |
|
suprub |
|
311 |
291 292 293 309 310
|
syl31anc |
|
312 |
311 13
|
breqtrrdi |
|
313 |
273
|
ltp1d |
|
314 |
|
peano2re |
|
315 |
273 314
|
syl |
|
316 |
273 315
|
ltnled |
|
317 |
313 316
|
mpbid |
|
318 |
317
|
ad2antrr |
|
319 |
312 318
|
pm2.65da |
|
320 |
289 319
|
syldan |
|
321 |
271 320
|
pm2.61dan |
|
322 |
44 178
|
ltnled |
|
323 |
321 322
|
mpbird |
|
324 |
197
|
adantr |
|
325 |
6
|
adantr |
|
326 |
178
|
adantr |
|
327 |
5
|
rexrd |
|
328 |
6
|
rexrd |
|
329 |
5 6 7
|
ltled |
|
330 |
|
lbicc2 |
|
331 |
327 328 329 330
|
syl3anc |
|
332 |
|
ubicc2 |
|
333 |
327 328 329 332
|
syl3anc |
|
334 |
331 333
|
jca |
|
335 |
|
prssg |
|
336 |
5 6 335
|
syl2anc |
|
337 |
334 336
|
mpbid |
|
338 |
337 30
|
unssd |
|
339 |
8 338
|
eqsstrid |
|
340 |
339 196
|
sseldd |
|
341 |
|
iccleub |
|
342 |
327 328 340 341
|
syl3anc |
|
343 |
342
|
adantr |
|
344 |
|
simpr |
|
345 |
324 325 326 343 344
|
letrd |
|
346 |
345
|
adantlr |
|
347 |
|
simpr |
|
348 |
178
|
adantr |
|
349 |
6
|
adantr |
|
350 |
348 349
|
ltnled |
|
351 |
347 350
|
mpbird |
|
352 |
351
|
adantlr |
|
353 |
|
simpll |
|
354 |
|
simpr |
|
355 |
178
|
adantr |
|
356 |
197
|
adantr |
|
357 |
355 356
|
ltnled |
|
358 |
354 357
|
mpbird |
|
359 |
358
|
ad4ant14 |
|
360 |
5
|
ad2antrr |
|
361 |
6
|
ad2antrr |
|
362 |
178
|
ad2antrr |
|
363 |
5
|
adantr |
|
364 |
178
|
adantr |
|
365 |
44
|
adantr |
|
366 |
339 43
|
sseldd |
|
367 |
|
iccgelb |
|
368 |
327 328 366 367
|
syl3anc |
|
369 |
368
|
adantr |
|
370 |
|
simpr |
|
371 |
363 365 364 369 370
|
lelttrd |
|
372 |
363 364 371
|
ltled |
|
373 |
372
|
adantr |
|
374 |
178
|
adantr |
|
375 |
6
|
adantr |
|
376 |
|
simpr |
|
377 |
374 375 376
|
ltled |
|
378 |
377
|
adantlr |
|
379 |
360 361 362 373 378
|
eliccd |
|
380 |
167
|
znegcld |
|
381 |
247 234
|
mulneg1d |
|
382 |
381
|
oveq2d |
|
383 |
178
|
recnd |
|
384 |
383 240
|
negsubd |
|
385 |
177
|
recnd |
|
386 |
385 240
|
pncand |
|
387 |
382 384 386
|
3eqtrd |
|
388 |
|
ffn |
|
389 |
50 388
|
syl |
|
390 |
|
fnfvelrn |
|
391 |
389 176 390
|
syl2anc |
|
392 |
387 391
|
eqeltrd |
|
393 |
|
oveq1 |
|
394 |
393
|
oveq2d |
|
395 |
394
|
eleq1d |
|
396 |
395
|
rspcev |
|
397 |
380 392 396
|
syl2anc |
|
398 |
397
|
ad2antrr |
|
399 |
|
oveq1 |
|
400 |
399
|
eleq1d |
|
401 |
400
|
rexbidv |
|
402 |
401
|
elrab |
|
403 |
379 398 402
|
sylanbrc |
|
404 |
|
elun2 |
|
405 |
403 404
|
syl |
|
406 |
8
|
eqcomi |
|
407 |
405 406
|
eleqtrdi |
|
408 |
407
|
adantr |
|
409 |
|
f1ofo |
|
410 |
37 38 409
|
3syl |
|
411 |
|
foelrn |
|
412 |
410 411
|
sylan |
|
413 |
|
id |
|
414 |
413
|
eqcomd |
|
415 |
414
|
a1i |
|
416 |
415
|
reximdv |
|
417 |
412 416
|
mpd |
|
418 |
417
|
ad4ant14 |
|
419 |
|
simpl |
|
420 |
413
|
eqcoms |
|
421 |
420
|
adantl |
|
422 |
419 421
|
breqtrd |
|
423 |
422
|
adantll |
|
424 |
423
|
adantlr |
|
425 |
37
|
ad3antrrr |
|
426 |
42
|
ad3antrrr |
|
427 |
|
simplr |
|
428 |
|
isorel |
|
429 |
425 426 427 428
|
syl12anc |
|
430 |
424 429
|
mpbird |
|
431 |
430
|
adantllr |
|
432 |
|
simpr |
|
433 |
|
simpl |
|
434 |
432 433
|
eqbrtrd |
|
435 |
434
|
adantll |
|
436 |
435
|
adantlr |
|
437 |
37
|
ad3antrrr |
|
438 |
|
simplr |
|
439 |
195
|
ad3antrrr |
|
440 |
|
isorel |
|
441 |
437 438 439 440
|
syl12anc |
|
442 |
436 441
|
mpbird |
|
443 |
442
|
adantl3r |
|
444 |
431 443
|
jca |
|
445 |
444
|
ex |
|
446 |
445
|
adantlr |
|
447 |
446
|
reximdva |
|
448 |
418 447
|
mpd |
|
449 |
353 359 408 448
|
syl21anc |
|
450 |
|
elfzelz |
|
451 |
450
|
ad2antlr |
|
452 |
|
elfzelz |
|
453 |
42 452
|
syl |
|
454 |
453
|
ad2antrr |
|
455 |
|
simprl |
|
456 |
|
simprr |
|
457 |
|
btwnnz |
|
458 |
454 455 456 457
|
syl3anc |
|
459 |
451 458
|
pm2.65da |
|
460 |
459
|
nrexdv |
|
461 |
460
|
ad3antrrr |
|
462 |
449 461
|
condan |
|
463 |
352 462
|
syldan |
|
464 |
346 463
|
pm2.61dan |
|
465 |
323 464
|
mpdan |
|
466 |
465
|
adantr |
|
467 |
182
|
adantr |
|
468 |
197
|
ad2antrr |
|
469 |
178
|
ad2antrr |
|
470 |
|
iooltub |
|
471 |
193 199 200 470
|
syl3anc |
|
472 |
471
|
adantr |
|
473 |
|
simpr |
|
474 |
467 468 469 472 473
|
ltletrd |
|
475 |
466 474
|
mpdan |
|
476 |
174 180 182 203 475
|
eliood |
|
477 |
476
|
ralrimiva |
|
478 |
|
dfss3 |
|
479 |
477 478
|
sylibr |
|
480 |
|
fveq2 |
|
481 |
480
|
oveq1d |
|
482 |
|
oveq1 |
|
483 |
482
|
fveq2d |
|
484 |
483
|
oveq1d |
|
485 |
481 484
|
oveq12d |
|
486 |
485
|
sseq2d |
|
487 |
|
oveq1 |
|
488 |
487
|
oveq2d |
|
489 |
487
|
oveq2d |
|
490 |
488 489
|
oveq12d |
|
491 |
490
|
sseq2d |
|
492 |
486 491
|
rspc2ev |
|
493 |
165 167 479 492
|
syl3anc |
|
494 |
165 167 493
|
jca31 |
|