Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem65.p |
|
2 |
|
fourierdlem65.t |
|
3 |
|
fourierdlem65.m |
|
4 |
|
fourierdlem65.q |
|
5 |
|
fourierdlem65.c |
|
6 |
|
fourierdlem65.d |
|
7 |
|
fourierdlem65.o |
|
8 |
|
fourierdlem65.n |
|
9 |
|
fourierdlem65.s |
|
10 |
|
fourierdlem65.e |
|
11 |
|
fourierdlem65.l |
|
12 |
|
fourierdlem65.z |
|
13 |
11
|
a1i |
|
14 |
|
simpr |
|
15 |
|
simpl |
|
16 |
14 15
|
eqtrd |
|
17 |
16
|
iftrued |
|
18 |
17
|
adantll |
|
19 |
1 3 4
|
fourierdlem11 |
|
20 |
19
|
simp1d |
|
21 |
19
|
simp2d |
|
22 |
19
|
simp3d |
|
23 |
20 21 22 2 10
|
fourierdlem4 |
|
24 |
23
|
adantr |
|
25 |
|
ioossre |
|
26 |
25 6
|
sseldi |
|
27 |
5
|
rexrd |
|
28 |
|
pnfxr |
|
29 |
28
|
a1i |
|
30 |
|
ioogtlb |
|
31 |
27 29 6 30
|
syl3anc |
|
32 |
|
id |
|
33 |
2
|
eqcomi |
|
34 |
33
|
oveq2i |
|
35 |
34
|
a1i |
|
36 |
32 35
|
oveq12d |
|
37 |
36
|
eleq1d |
|
38 |
37
|
rexbidv |
|
39 |
38
|
cbvrabv |
|
40 |
39
|
uneq2i |
|
41 |
2 1 3 4 5 26 31 7 40 8 9
|
fourierdlem54 |
|
42 |
41
|
simpld |
|
43 |
42
|
simprd |
|
44 |
42
|
simpld |
|
45 |
7
|
fourierdlem2 |
|
46 |
44 45
|
syl |
|
47 |
43 46
|
mpbid |
|
48 |
47
|
simpld |
|
49 |
|
elmapi |
|
50 |
48 49
|
syl |
|
51 |
50
|
adantr |
|
52 |
|
elfzofz |
|
53 |
52
|
adantl |
|
54 |
51 53
|
ffvelrnd |
|
55 |
24 54
|
ffvelrnd |
|
56 |
55
|
adantr |
|
57 |
20
|
ad2antrr |
|
58 |
13 18 56 57
|
fvmptd |
|
59 |
58
|
oveq2d |
|
60 |
21
|
ad2antrr |
|
61 |
22
|
ad2antrr |
|
62 |
54
|
adantr |
|
63 |
|
simpr |
|
64 |
|
fzofzp1 |
|
65 |
64
|
adantl |
|
66 |
51 65
|
ffvelrnd |
|
67 |
66
|
adantr |
|
68 |
|
elfzoelz |
|
69 |
68
|
zred |
|
70 |
69
|
adantl |
|
71 |
70
|
ltp1d |
|
72 |
41
|
simprd |
|
73 |
72
|
adantr |
|
74 |
|
isorel |
|
75 |
73 53 65 74
|
syl12anc |
|
76 |
71 75
|
mpbid |
|
77 |
76
|
adantr |
|
78 |
|
isof1o |
|
79 |
|
f1ofo |
|
80 |
72 78 79
|
3syl |
|
81 |
80
|
ad3antrrr |
|
82 |
5
|
ad2antrr |
|
83 |
26
|
ad2antrr |
|
84 |
21 20
|
resubcld |
|
85 |
2 84
|
eqeltrid |
|
86 |
85
|
adantr |
|
87 |
54 86
|
readdcld |
|
88 |
87
|
adantr |
|
89 |
5
|
adantr |
|
90 |
7 44 43
|
fourierdlem15 |
|
91 |
90
|
adantr |
|
92 |
91 53
|
ffvelrnd |
|
93 |
26
|
adantr |
|
94 |
|
elicc2 |
|
95 |
89 93 94
|
syl2anc |
|
96 |
92 95
|
mpbid |
|
97 |
96
|
simp2d |
|
98 |
20 21
|
posdifd |
|
99 |
22 98
|
mpbid |
|
100 |
99 2
|
breqtrrdi |
|
101 |
85 100
|
elrpd |
|
102 |
101
|
adantr |
|
103 |
54 102
|
ltaddrpd |
|
104 |
89 54 87 97 103
|
lelttrd |
|
105 |
89 87 104
|
ltled |
|
106 |
105
|
adantr |
|
107 |
66
|
adantr |
|
108 |
|
simpr |
|
109 |
88 107
|
ltnled |
|
110 |
108 109
|
mpbird |
|
111 |
91 65
|
ffvelrnd |
|
112 |
|
elicc2 |
|
113 |
89 93 112
|
syl2anc |
|
114 |
111 113
|
mpbid |
|
115 |
114
|
simp3d |
|
116 |
115
|
adantr |
|
117 |
88 107 83 110 116
|
ltletrd |
|
118 |
88 83 117
|
ltled |
|
119 |
82 83 88 106 118
|
eliccd |
|
120 |
119
|
adantlr |
|
121 |
10
|
a1i |
|
122 |
|
id |
|
123 |
|
oveq2 |
|
124 |
123
|
oveq1d |
|
125 |
124
|
fveq2d |
|
126 |
125
|
oveq1d |
|
127 |
122 126
|
oveq12d |
|
128 |
127
|
adantl |
|
129 |
21
|
adantr |
|
130 |
129 54
|
resubcld |
|
131 |
130 102
|
rerpdivcld |
|
132 |
131
|
flcld |
|
133 |
132
|
zred |
|
134 |
133 86
|
remulcld |
|
135 |
54 134
|
readdcld |
|
136 |
121 128 54 135
|
fvmptd |
|
137 |
136
|
oveq1d |
|
138 |
137
|
oveq1d |
|
139 |
54
|
recnd |
|
140 |
134
|
recnd |
|
141 |
139 140
|
pncan2d |
|
142 |
141
|
oveq1d |
|
143 |
133
|
recnd |
|
144 |
86
|
recnd |
|
145 |
102
|
rpne0d |
|
146 |
143 144 145
|
divcan4d |
|
147 |
138 142 146
|
3eqtrd |
|
148 |
147 132
|
eqeltrd |
|
149 |
|
peano2zm |
|
150 |
148 149
|
syl |
|
151 |
150
|
ad2antrr |
|
152 |
33
|
oveq2i |
|
153 |
152
|
oveq2i |
|
154 |
153
|
a1i |
|
155 |
136
|
adantr |
|
156 |
|
oveq1 |
|
157 |
156
|
eqcomd |
|
158 |
157
|
oveq1d |
|
159 |
158
|
fveq2d |
|
160 |
159
|
oveq1d |
|
161 |
160
|
oveq2d |
|
162 |
161
|
adantl |
|
163 |
147 143
|
eqeltrd |
|
164 |
|
1cnd |
|
165 |
163 164 144
|
subdird |
|
166 |
85
|
recnd |
|
167 |
166
|
mulid2d |
|
168 |
167
|
oveq2d |
|
169 |
168
|
adantr |
|
170 |
165 169
|
eqtrd |
|
171 |
170
|
oveq2d |
|
172 |
163 144
|
mulcld |
|
173 |
139 144 172
|
ppncand |
|
174 |
|
flid |
|
175 |
148 174
|
syl |
|
176 |
175
|
eqcomd |
|
177 |
176
|
oveq1d |
|
178 |
177
|
oveq2d |
|
179 |
171 173 178
|
3eqtrrd |
|
180 |
179
|
adantr |
|
181 |
155 162 180
|
3eqtrrd |
|
182 |
154 181 63
|
3eqtrd |
|
183 |
1
|
fourierdlem2 |
|
184 |
3 183
|
syl |
|
185 |
4 184
|
mpbid |
|
186 |
185
|
simprd |
|
187 |
186
|
simpld |
|
188 |
187
|
simprd |
|
189 |
188
|
eqcomd |
|
190 |
1 3 4
|
fourierdlem15 |
|
191 |
|
ffn |
|
192 |
190 191
|
syl |
|
193 |
3
|
nnnn0d |
|
194 |
|
nn0uz |
|
195 |
193 194
|
eleqtrdi |
|
196 |
|
eluzfz2 |
|
197 |
195 196
|
syl |
|
198 |
|
fnfvelrn |
|
199 |
192 197 198
|
syl2anc |
|
200 |
189 199
|
eqeltrd |
|
201 |
200
|
ad2antrr |
|
202 |
182 201
|
eqeltrd |
|
203 |
202
|
adantr |
|
204 |
|
oveq1 |
|
205 |
204
|
oveq2d |
|
206 |
205
|
eleq1d |
|
207 |
206
|
rspcev |
|
208 |
151 203 207
|
syl2anc |
|
209 |
|
oveq1 |
|
210 |
209
|
eleq1d |
|
211 |
210
|
rexbidv |
|
212 |
211
|
elrab |
|
213 |
120 208 212
|
sylanbrc |
|
214 |
|
elun2 |
|
215 |
213 214
|
syl |
|
216 |
|
foelrn |
|
217 |
81 215 216
|
syl2anc |
|
218 |
|
eqcom |
|
219 |
218
|
rexbii |
|
220 |
217 219
|
sylib |
|
221 |
103
|
ad2antrr |
|
222 |
218
|
biimpri |
|
223 |
222
|
adantl |
|
224 |
221 223
|
breqtrd |
|
225 |
110
|
adantr |
|
226 |
223 225
|
eqbrtrrd |
|
227 |
224 226
|
jca |
|
228 |
227
|
adantlr |
|
229 |
|
simplll |
|
230 |
|
simplr |
|
231 |
|
elfzelz |
|
232 |
231
|
ad2antlr |
|
233 |
68
|
ad3antlr |
|
234 |
|
simpr |
|
235 |
73
|
ad2antrr |
|
236 |
53
|
ad2antrr |
|
237 |
|
simplr |
|
238 |
|
isorel |
|
239 |
235 236 237 238
|
syl12anc |
|
240 |
234 239
|
mpbird |
|
241 |
240
|
adantrr |
|
242 |
|
simpr |
|
243 |
73
|
ad2antrr |
|
244 |
|
simplr |
|
245 |
65
|
ad2antrr |
|
246 |
|
isorel |
|
247 |
243 244 245 246
|
syl12anc |
|
248 |
242 247
|
mpbird |
|
249 |
248
|
adantrl |
|
250 |
|
btwnnz |
|
251 |
233 241 249 250
|
syl3anc |
|
252 |
232 251
|
pm2.65da |
|
253 |
229 230 252
|
syl2anc |
|
254 |
228 253
|
pm2.65da |
|
255 |
254
|
nrexdv |
|
256 |
255
|
adantlr |
|
257 |
220 256
|
condan |
|
258 |
62
|
rexrd |
|
259 |
85
|
ad2antrr |
|
260 |
62 259
|
readdcld |
|
261 |
|
elioc2 |
|
262 |
258 260 261
|
syl2anc |
|
263 |
67 77 257 262
|
mpbir3and |
|
264 |
57 60 61 2 10 62 63 263
|
fourierdlem26 |
|
265 |
264
|
oveq1d |
|
266 |
57
|
recnd |
|
267 |
66
|
recnd |
|
268 |
267 139
|
subcld |
|
269 |
268
|
adantr |
|
270 |
266 269
|
pncan2d |
|
271 |
59 265 270
|
3eqtrd |
|
272 |
11
|
a1i |
|
273 |
|
eqcom |
|
274 |
273
|
biimpi |
|
275 |
274
|
adantl |
|
276 |
|
neqne |
|
277 |
276
|
adantr |
|
278 |
275 277
|
eqnetrrd |
|
279 |
278
|
neneqd |
|
280 |
279
|
iffalsed |
|
281 |
|
simpr |
|
282 |
280 281
|
eqtrd |
|
283 |
282
|
adantll |
|
284 |
55
|
adantr |
|
285 |
272 283 284 284
|
fvmptd |
|
286 |
285
|
oveq2d |
|
287 |
|
id |
|
288 |
|
oveq2 |
|
289 |
288
|
oveq1d |
|
290 |
289
|
fveq2d |
|
291 |
290
|
oveq1d |
|
292 |
287 291
|
oveq12d |
|
293 |
292
|
adantl |
|
294 |
129 66
|
resubcld |
|
295 |
294 102
|
rerpdivcld |
|
296 |
295
|
flcld |
|
297 |
296
|
zred |
|
298 |
297 86
|
remulcld |
|
299 |
66 298
|
readdcld |
|
300 |
121 293 66 299
|
fvmptd |
|
301 |
300 136
|
oveq12d |
|
302 |
301
|
adantr |
|
303 |
|
flle |
|
304 |
295 303
|
syl |
|
305 |
54 66 76
|
ltled |
|
306 |
54 66 129 305
|
lesub2dd |
|
307 |
294 130 102 306
|
lediv1dd |
|
308 |
297 295 131 304 307
|
letrd |
|
309 |
308
|
adantr |
|
310 |
297
|
adantr |
|
311 |
|
1red |
|
312 |
310 311
|
readdcld |
|
313 |
131
|
adantr |
|
314 |
|
simpr |
|
315 |
312 313 314
|
nltled |
|
316 |
315
|
adantlr |
|
317 |
80
|
ad3antrrr |
|
318 |
89
|
ad2antrr |
|
319 |
93
|
ad2antrr |
|
320 |
136 135
|
eqeltrd |
|
321 |
129 320
|
resubcld |
|
322 |
54 321
|
readdcld |
|
323 |
12 322
|
eqeltrid |
|
324 |
323
|
ad2antrr |
|
325 |
20
|
rexrd |
|
326 |
325
|
adantr |
|
327 |
|
elioc2 |
|
328 |
326 129 327
|
syl2anc |
|
329 |
55 328
|
mpbid |
|
330 |
329
|
simp3d |
|
331 |
129 320
|
subge0d |
|
332 |
330 331
|
mpbird |
|
333 |
54 321
|
addge01d |
|
334 |
332 333
|
mpbid |
|
335 |
89 54 322 97 334
|
letrd |
|
336 |
335 12
|
breqtrrdi |
|
337 |
336
|
ad2antrr |
|
338 |
66
|
ad2antrr |
|
339 |
295
|
ad2antrr |
|
340 |
|
reflcl |
|
341 |
|
peano2re |
|
342 |
339 340 341
|
3syl |
|
343 |
129
|
ad2antrr |
|
344 |
343 324
|
resubcld |
|
345 |
102
|
ad2antrr |
|
346 |
344 345
|
rerpdivcld |
|
347 |
|
flltp1 |
|
348 |
295 347
|
syl |
|
349 |
348
|
ad2antrr |
|
350 |
296
|
peano2zd |
|
351 |
350
|
ad2antrr |
|
352 |
131
|
ad2antrr |
|
353 |
|
simpr |
|
354 |
321 102
|
rerpdivcld |
|
355 |
354
|
ad2antrr |
|
356 |
20
|
adantr |
|
357 |
329
|
simp2d |
|
358 |
356 320 129 357
|
ltsub2dd |
|
359 |
358 2
|
breqtrrdi |
|
360 |
321 86 102 359
|
ltdiv1dd |
|
361 |
144 145
|
dividd |
|
362 |
360 361
|
breqtrd |
|
363 |
362
|
ad2antrr |
|
364 |
130
|
recnd |
|
365 |
321
|
recnd |
|
366 |
364 365 144 145
|
divsubdird |
|
367 |
366
|
eqcomd |
|
368 |
129
|
recnd |
|
369 |
320
|
recnd |
|
370 |
368 139 369
|
nnncan1d |
|
371 |
370
|
oveq1d |
|
372 |
367 371
|
eqtrd |
|
373 |
372 148
|
eqeltrd |
|
374 |
373
|
ad2antrr |
|
375 |
351 352 353 355 363 374
|
zltlesub |
|
376 |
12
|
a1i |
|
377 |
376
|
oveq2d |
|
378 |
139 368 369
|
addsub12d |
|
379 |
368 369 139
|
subsub2d |
|
380 |
378 379
|
eqtr4d |
|
381 |
380
|
oveq2d |
|
382 |
369 139
|
subcld |
|
383 |
368 382
|
nncand |
|
384 |
377 381 383
|
3eqtrd |
|
385 |
384
|
oveq1d |
|
386 |
371 367 385
|
3eqtr4d |
|
387 |
386
|
ad2antrr |
|
388 |
375 387
|
breqtrd |
|
389 |
339 342 346 349 388
|
ltletrd |
|
390 |
294
|
ad2antrr |
|
391 |
390 344 345
|
ltdiv1d |
|
392 |
389 391
|
mpbird |
|
393 |
324 338 343
|
ltsub2d |
|
394 |
392 393
|
mpbird |
|
395 |
115
|
ad2antrr |
|
396 |
324 338 319 394 395
|
ltletrd |
|
397 |
324 319 396
|
ltled |
|
398 |
318 319 324 337 397
|
eliccd |
|
399 |
33
|
a1i |
|
400 |
399
|
oveq2d |
|
401 |
382 144 145
|
divcan1d |
|
402 |
400 401
|
eqtrd |
|
403 |
376 402
|
oveq12d |
|
404 |
139 365
|
addcomd |
|
405 |
404
|
oveq1d |
|
406 |
365 139 369
|
ppncand |
|
407 |
368 369
|
npcand |
|
408 |
406 407
|
eqtrd |
|
409 |
403 405 408
|
3eqtrd |
|
410 |
200
|
adantr |
|
411 |
409 410
|
eqeltrd |
|
412 |
|
oveq1 |
|
413 |
412
|
oveq2d |
|
414 |
413
|
eleq1d |
|
415 |
414
|
rspcev |
|
416 |
148 411 415
|
syl2anc |
|
417 |
416
|
ad2antrr |
|
418 |
|
oveq1 |
|
419 |
418
|
eleq1d |
|
420 |
419
|
rexbidv |
|
421 |
420
|
elrab |
|
422 |
398 417 421
|
sylanbrc |
|
423 |
|
elun2 |
|
424 |
422 423
|
syl |
|
425 |
|
foelrn |
|
426 |
317 424 425
|
syl2anc |
|
427 |
54
|
adantr |
|
428 |
321
|
adantr |
|
429 |
320
|
adantr |
|
430 |
21
|
ad2antrr |
|
431 |
330
|
adantr |
|
432 |
276
|
necomd |
|
433 |
432
|
adantl |
|
434 |
429 430 431 433
|
leneltd |
|
435 |
429 430
|
posdifd |
|
436 |
434 435
|
mpbid |
|
437 |
428 436
|
elrpd |
|
438 |
427 437
|
ltaddrpd |
|
439 |
438 12
|
breqtrrdi |
|
440 |
439
|
ad2antrr |
|
441 |
|
simpr |
|
442 |
440 441
|
breqtrd |
|
443 |
394
|
adantr |
|
444 |
441 443
|
eqbrtrrd |
|
445 |
442 444
|
jca |
|
446 |
445
|
ex |
|
447 |
446
|
reximdv |
|
448 |
426 447
|
mpd |
|
449 |
316 448
|
syldan |
|
450 |
252
|
nrexdv |
|
451 |
450
|
ad2antrr |
|
452 |
449 451
|
condan |
|
453 |
309 452
|
jca |
|
454 |
131
|
adantr |
|
455 |
296
|
adantr |
|
456 |
|
flbi |
|
457 |
454 455 456
|
syl2anc |
|
458 |
453 457
|
mpbird |
|
459 |
458
|
eqcomd |
|
460 |
459
|
oveq1d |
|
461 |
460
|
oveq2d |
|
462 |
461
|
oveq1d |
|
463 |
267
|
adantr |
|
464 |
139
|
adantr |
|
465 |
140
|
adantr |
|
466 |
463 464 465
|
pnpcan2d |
|
467 |
462 466
|
eqtrd |
|
468 |
286 302 467
|
3eqtrd |
|
469 |
271 468
|
pm2.61dan |
|