Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem113.f |
|
2 |
|
fourierdlem113.t |
|
3 |
|
fourierdlem113.per |
|
4 |
|
fourierdlem113.x |
|
5 |
|
fourierdlem113.l |
|
6 |
|
fourierdlem113.r |
|
7 |
|
fourierdlem113.p |
|
8 |
|
fourierdlem113.m |
|
9 |
|
fourierdlem113.q |
|
10 |
|
fourierdlem113.dvcn |
|
11 |
|
fourierdlem113.dvlb |
|
12 |
|
fourierdlem113.dvub |
|
13 |
|
fourierdlem113.a |
|
14 |
|
fourierdlem113.b |
|
15 |
|
fourierdlem113.15 |
|
16 |
|
fourierdlem113.e |
|
17 |
|
fourierdlem113.exq |
|
18 |
|
oveq1 |
|
19 |
18
|
eqeq1d |
|
20 |
|
oveq2 |
|
21 |
20
|
fveq2d |
|
22 |
|
oveq1 |
|
23 |
22
|
fveq2d |
|
24 |
23
|
oveq2d |
|
25 |
21 24
|
oveq12d |
|
26 |
19 25
|
ifbieq2d |
|
27 |
26
|
cbvmptv |
|
28 |
|
oveq2 |
|
29 |
28
|
oveq1d |
|
30 |
29
|
oveq1d |
|
31 |
|
oveq1 |
|
32 |
31
|
oveq1d |
|
33 |
32
|
fveq2d |
|
34 |
33
|
oveq1d |
|
35 |
30 34
|
ifeq12d |
|
36 |
35
|
mpteq2dv |
|
37 |
27 36
|
syl5eq |
|
38 |
37
|
cbvmptv |
|
39 |
|
oveq1 |
|
40 |
39
|
eleq1d |
|
41 |
40
|
rexbidv |
|
42 |
41
|
cbvrabv |
|
43 |
42
|
uneq2i |
|
44 |
43
|
fveq2i |
|
45 |
44
|
oveq1i |
|
46 |
|
oveq1 |
|
47 |
46
|
oveq2d |
|
48 |
47
|
eleq1d |
|
49 |
48
|
cbvrexvw |
|
50 |
49
|
a1i |
|
51 |
50
|
rabbiia |
|
52 |
51
|
uneq2i |
|
53 |
|
isoeq5 |
|
54 |
52 53
|
ax-mp |
|
55 |
54
|
a1i |
|
56 |
46
|
oveq2d |
|
57 |
56
|
eleq1d |
|
58 |
57
|
cbvrexvw |
|
59 |
58
|
a1i |
|
60 |
59
|
rabbiia |
|
61 |
60
|
uneq2i |
|
62 |
61
|
fveq2i |
|
63 |
62
|
oveq1i |
|
64 |
63
|
oveq2i |
|
65 |
|
isoeq4 |
|
66 |
64 65
|
ax-mp |
|
67 |
66
|
a1i |
|
68 |
|
isoeq1 |
|
69 |
55 67 68
|
3bitrd |
|
70 |
69
|
cbviotavw |
|
71 |
|
pire |
|
72 |
71
|
renegcli |
|
73 |
72
|
a1i |
|
74 |
71
|
a1i |
|
75 |
|
negpilt0 |
|
76 |
75
|
a1i |
|
77 |
|
pipos |
|
78 |
77
|
a1i |
|
79 |
|
picn |
|
80 |
79
|
2timesi |
|
81 |
79 79
|
subnegi |
|
82 |
80 2 81
|
3eqtr4i |
|
83 |
7
|
fourierdlem2 |
|
84 |
8 83
|
syl |
|
85 |
9 84
|
mpbid |
|
86 |
85
|
simpld |
|
87 |
|
elmapi |
|
88 |
86 87
|
syl |
|
89 |
|
fzfid |
|
90 |
|
rnffi |
|
91 |
88 89 90
|
syl2anc |
|
92 |
7 8 9
|
fourierdlem15 |
|
93 |
|
frn |
|
94 |
92 93
|
syl |
|
95 |
85
|
simprd |
|
96 |
95
|
simplrd |
|
97 |
|
ffun |
|
98 |
92 97
|
syl |
|
99 |
8
|
nnnn0d |
|
100 |
|
nn0uz |
|
101 |
99 100
|
eleqtrdi |
|
102 |
|
eluzfz2 |
|
103 |
101 102
|
syl |
|
104 |
|
fdm |
|
105 |
92 104
|
syl |
|
106 |
105
|
eqcomd |
|
107 |
103 106
|
eleqtrd |
|
108 |
|
fvelrn |
|
109 |
98 107 108
|
syl2anc |
|
110 |
96 109
|
eqeltrrd |
|
111 |
|
eqid |
|
112 |
|
isoeq1 |
|
113 |
43 61 52
|
3eqtr4ri |
|
114 |
|
isoeq5 |
|
115 |
113 114
|
ax-mp |
|
116 |
112 115
|
syl6bb |
|
117 |
116
|
cbviotavw |
|
118 |
|
eqid |
|
119 |
73 74 76 78 82 91 94 110 16 4 17 111 117 118
|
fourierdlem51 |
|
120 |
|
ax-resscn |
|
121 |
120
|
a1i |
|
122 |
|
ioossre |
|
123 |
122
|
a1i |
|
124 |
1 123
|
fssresd |
|
125 |
120
|
a1i |
|
126 |
124 125
|
fssd |
|
127 |
126
|
adantr |
|
128 |
122
|
a1i |
|
129 |
1 125
|
fssd |
|
130 |
129
|
adantr |
|
131 |
|
ssid |
|
132 |
131
|
a1i |
|
133 |
|
eqid |
|
134 |
133
|
tgioo2 |
|
135 |
133 134
|
dvres |
|
136 |
121 130 132 128 135
|
syl22anc |
|
137 |
136
|
dmeqd |
|
138 |
|
ioontr |
|
139 |
138
|
reseq2i |
|
140 |
139
|
dmeqi |
|
141 |
140
|
a1i |
|
142 |
|
cncff |
|
143 |
|
fdm |
|
144 |
10 142 143
|
3syl |
|
145 |
137 141 144
|
3eqtrd |
|
146 |
|
dvcn |
|
147 |
121 127 128 145 146
|
syl31anc |
|
148 |
128 121
|
sstrd |
|
149 |
88
|
adantr |
|
150 |
|
fzofzp1 |
|
151 |
150
|
adantl |
|
152 |
149 151
|
ffvelrnd |
|
153 |
152
|
rexrd |
|
154 |
|
elfzofz |
|
155 |
154
|
adantl |
|
156 |
149 155
|
ffvelrnd |
|
157 |
85
|
simprrd |
|
158 |
157
|
r19.21bi |
|
159 |
133 153 156 158
|
lptioo1cn |
|
160 |
124
|
adantr |
|
161 |
131
|
a1i |
|
162 |
125 129 161
|
dvbss |
|
163 |
|
dvfre |
|
164 |
1 161 163
|
syl2anc |
|
165 |
|
0re |
|
166 |
72 165 71
|
lttri |
|
167 |
75 77 166
|
mp2an |
|
168 |
167
|
a1i |
|
169 |
95
|
simplld |
|
170 |
10 142
|
syl |
|
171 |
170 148 159 11 133
|
ellimciota |
|
172 |
156
|
rexrd |
|
173 |
133 172 152 158
|
lptioo2cn |
|
174 |
170 148 173 12 133
|
ellimciota |
|
175 |
129
|
adantr |
|
176 |
|
zre |
|
177 |
176
|
adantl |
|
178 |
|
2re |
|
179 |
178 71
|
remulcli |
|
180 |
179
|
a1i |
|
181 |
2 180
|
eqeltrid |
|
182 |
181
|
adantr |
|
183 |
177 182
|
remulcld |
|
184 |
175
|
adantr |
|
185 |
182
|
adantr |
|
186 |
|
simplr |
|
187 |
|
simpr |
|
188 |
3
|
ad4ant14 |
|
189 |
184 185 186 187 188
|
fperiodmul |
|
190 |
|
eqid |
|
191 |
175 183 189 190
|
fperdvper |
|
192 |
191
|
an32s |
|
193 |
192
|
simpld |
|
194 |
192
|
simprd |
|
195 |
|
fveq2 |
|
196 |
|
oveq1 |
|
197 |
196
|
fveq2d |
|
198 |
195 197
|
oveq12d |
|
199 |
198
|
cbvmptv |
|
200 |
|
eqid |
|
201 |
162 164 73 74 168 82 8 88 169 96 10 171 174 193 194 199 200
|
fourierdlem71 |
|
202 |
201
|
adantr |
|
203 |
|
nfv |
|
204 |
|
nfra1 |
|
205 |
203 204
|
nfan |
|
206 |
136 139
|
eqtrdi |
|
207 |
206
|
fveq1d |
|
208 |
|
fvres |
|
209 |
207 208
|
sylan9eq |
|
210 |
209
|
fveq2d |
|
211 |
210
|
adantlr |
|
212 |
|
simplr |
|
213 |
|
ssdmres |
|
214 |
144 213
|
sylibr |
|
215 |
214
|
ad2antrr |
|
216 |
|
simpr |
|
217 |
215 216
|
sseldd |
|
218 |
|
rspa |
|
219 |
212 217 218
|
syl2anc |
|
220 |
211 219
|
eqbrtrd |
|
221 |
220
|
ex |
|
222 |
205 221
|
ralrimi |
|
223 |
222
|
ex |
|
224 |
223
|
reximdv |
|
225 |
202 224
|
mpd |
|
226 |
156 152 160 145 225
|
ioodvbdlimc1 |
|
227 |
127 148 159 226 133
|
ellimciota |
|
228 |
156 152 160 145 225
|
ioodvbdlimc2 |
|
229 |
127 148 173 228 133
|
ellimciota |
|
230 |
|
frel |
|
231 |
164 230
|
syl |
|
232 |
|
resindm |
|
233 |
231 232
|
syl |
|
234 |
|
inss2 |
|
235 |
234
|
a1i |
|
236 |
164 235
|
fssresd |
|
237 |
233 236
|
feq1dd |
|
238 |
237 125
|
fssd |
|
239 |
|
ioosscn |
|
240 |
|
ssinss1 |
|
241 |
239 240
|
ax-mp |
|
242 |
241
|
a1i |
|
243 |
|
3simpb |
|
244 |
|
simp2 |
|
245 |
175
|
adantr |
|
246 |
182
|
adantr |
|
247 |
|
simplr |
|
248 |
|
simpr |
|
249 |
|
eleq1w |
|
250 |
249
|
anbi2d |
|
251 |
|
oveq1 |
|
252 |
251
|
fveq2d |
|
253 |
|
fveq2 |
|
254 |
252 253
|
eqeq12d |
|
255 |
250 254
|
imbi12d |
|
256 |
255 3
|
chvarvv |
|
257 |
256
|
ad4ant14 |
|
258 |
245 246 247 248 257
|
fperiodmul |
|
259 |
175 183 258 190
|
fperdvper |
|
260 |
243 244 259
|
syl2anc |
|
261 |
260
|
simpld |
|
262 |
|
oveq2 |
|
263 |
262
|
oveq1d |
|
264 |
263
|
fveq2d |
|
265 |
264
|
oveq1d |
|
266 |
265
|
cbvmptv |
|
267 |
|
eqid |
|
268 |
73 74 168 82 261 4 266 267 7 8 9 214
|
fourierdlem41 |
|
269 |
268
|
simpld |
|
270 |
133
|
cnfldtop |
|
271 |
270
|
a1i |
|
272 |
241
|
a1i |
|
273 |
|
mnfxr |
|
274 |
273
|
a1i |
|
275 |
|
rexr |
|
276 |
|
mnflt |
|
277 |
274 275 276
|
xrltled |
|
278 |
|
iooss1 |
|
279 |
274 277 278
|
syl2anc |
|
280 |
279
|
3ad2ant2 |
|
281 |
|
simp3 |
|
282 |
280 281
|
ssind |
|
283 |
|
unicntop |
|
284 |
283
|
lpss3 |
|
285 |
271 272 282 284
|
syl3anc |
|
286 |
285
|
3adant3l |
|
287 |
275
|
3ad2ant2 |
|
288 |
4
|
3ad2ant1 |
|
289 |
|
simp3l |
|
290 |
133 287 288 289
|
lptioo2cn |
|
291 |
286 290
|
sseldd |
|
292 |
291
|
rexlimdv3a |
|
293 |
269 292
|
mpd |
|
294 |
260
|
simprd |
|
295 |
|
oveq2 |
|
296 |
295
|
oveq1d |
|
297 |
296
|
fveq2d |
|
298 |
297
|
oveq1d |
|
299 |
298
|
cbvmptv |
|
300 |
|
id |
|
301 |
|
fveq2 |
|
302 |
300 301
|
oveq12d |
|
303 |
302
|
cbvmptv |
|
304 |
73 74 168 7 82 8 9 162 164 261 294 10 174 4 299 303
|
fourierdlem49 |
|
305 |
238 242 293 304 133
|
ellimciota |
|
306 |
|
resindm |
|
307 |
231 306
|
syl |
|
308 |
|
inss2 |
|
309 |
308
|
a1i |
|
310 |
164 309
|
fssresd |
|
311 |
307 310
|
feq1dd |
|
312 |
311 125
|
fssd |
|
313 |
|
ioosscn |
|
314 |
|
ssinss1 |
|
315 |
313 314
|
ax-mp |
|
316 |
315
|
a1i |
|
317 |
268
|
simprd |
|
318 |
270
|
a1i |
|
319 |
315
|
a1i |
|
320 |
|
pnfxr |
|
321 |
320
|
a1i |
|
322 |
|
ltpnf |
|
323 |
275 321 322
|
xrltled |
|
324 |
|
iooss2 |
|
325 |
321 323 324
|
syl2anc |
|
326 |
325
|
3ad2ant2 |
|
327 |
|
simp3 |
|
328 |
326 327
|
ssind |
|
329 |
283
|
lpss3 |
|
330 |
318 319 328 329
|
syl3anc |
|
331 |
330
|
3adant3l |
|
332 |
275
|
3ad2ant2 |
|
333 |
4
|
3ad2ant1 |
|
334 |
|
simp3l |
|
335 |
133 332 333 334
|
lptioo1cn |
|
336 |
331 335
|
sseldd |
|
337 |
336
|
rexlimdv3a |
|
338 |
317 337
|
mpd |
|
339 |
|
biid |
|
340 |
73 74 168 7 82 8 9 164 261 294 10 171 4 299 303 339
|
fourierdlem48 |
|
341 |
312 316 338 340 133
|
ellimciota |
|
342 |
|
fveq2 |
|
343 |
|
oveq1 |
|
344 |
343
|
fveq2d |
|
345 |
342 344
|
oveq12d |
|
346 |
|
fveq2 |
|
347 |
343
|
fveq2d |
|
348 |
346 347
|
oveq12d |
|
349 |
345 348
|
oveq12d |
|
350 |
349
|
cbvsumv |
|
351 |
|
oveq2 |
|
352 |
351
|
eqcomd |
|
353 |
352
|
sumeq1d |
|
354 |
350 353
|
syl5req |
|
355 |
354
|
oveq2d |
|
356 |
355
|
cbvmptv |
|
357 |
|
fdm |
|
358 |
1 357
|
syl |
|
359 |
358 161
|
eqsstrd |
|
360 |
358
|
feq2d |
|
361 |
1 360
|
mpbird |
|
362 |
359
|
sselda |
|
363 |
362
|
adantr |
|
364 |
176
|
adantl |
|
365 |
182
|
adantlr |
|
366 |
364 365
|
remulcld |
|
367 |
363 366
|
readdcld |
|
368 |
358
|
eqcomd |
|
369 |
368
|
ad2antrr |
|
370 |
367 369
|
eleqtrd |
|
371 |
|
id |
|
372 |
371
|
adantlr |
|
373 |
372 363 189
|
syl2anc |
|
374 |
359 361 73 74 168 82 8 88 169 96 147 227 229 370 373 199 200
|
fourierdlem71 |
|
375 |
358
|
raleqdv |
|
376 |
375
|
rexbidv |
|
377 |
374 376
|
mpbid |
|
378 |
1 38 7 8 9 45 70 4 119 2 3 147 227 229 10 305 341 5 6 13 14 356 15 377 201 4
|
fourierdlem112 |
|