Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem89.p |
|
2 |
|
fourierdlem89.t |
|
3 |
|
fourierdlem89.m |
|
4 |
|
fourierdlem89.q |
|
5 |
|
fourierdlem89.f |
|
6 |
|
fourierdlem89.per |
|
7 |
|
fourierdlem89.fcn |
|
8 |
|
fourierdlem89.limc |
|
9 |
|
fourierdlem89.c |
|
10 |
|
fourierdlem89.d |
|
11 |
|
fourierdlem89.o |
|
12 |
|
fourierdlem89.12 |
|
13 |
|
fourierdlem89.n |
|
14 |
|
fourierdlem89.s |
|
15 |
|
fourierdlem89.e |
|
16 |
|
fourierdlem89.z |
|
17 |
|
fourierdlem89.j |
|
18 |
|
fourierdlem89.u |
|
19 |
|
fourierdlem89.20 |
|
20 |
|
fourierdlem89.21 |
|
21 |
1
|
fourierdlem2 |
|
22 |
3 21
|
syl |
|
23 |
4 22
|
mpbid |
|
24 |
23
|
simpld |
|
25 |
|
elmapi |
|
26 |
24 25
|
syl |
|
27 |
|
fzossfz |
|
28 |
1 3 4 2 15 16 19
|
fourierdlem37 |
|
29 |
28
|
simpld |
|
30 |
|
elioore |
|
31 |
10 30
|
syl |
|
32 |
|
elioo4g |
|
33 |
10 32
|
sylib |
|
34 |
33
|
simprd |
|
35 |
34
|
simpld |
|
36 |
|
oveq1 |
|
37 |
36
|
eleq1d |
|
38 |
37
|
rexbidv |
|
39 |
38
|
cbvrabv |
|
40 |
39
|
uneq2i |
|
41 |
12
|
fveq2i |
|
42 |
41
|
oveq1i |
|
43 |
13 42
|
eqtri |
|
44 |
|
isoeq5 |
|
45 |
12 44
|
ax-mp |
|
46 |
45
|
iotabii |
|
47 |
14 46
|
eqtri |
|
48 |
2 1 3 4 9 31 35 11 40 43 47
|
fourierdlem54 |
|
49 |
48
|
simpld |
|
50 |
49
|
simprd |
|
51 |
49
|
simpld |
|
52 |
11
|
fourierdlem2 |
|
53 |
51 52
|
syl |
|
54 |
50 53
|
mpbid |
|
55 |
54
|
simpld |
|
56 |
|
elmapi |
|
57 |
55 56
|
syl |
|
58 |
|
elfzofz |
|
59 |
17 58
|
syl |
|
60 |
57 59
|
ffvelrnd |
|
61 |
29 60
|
ffvelrnd |
|
62 |
27 61
|
sseldi |
|
63 |
26 62
|
ffvelrnd |
|
64 |
63
|
rexrd |
|
65 |
64
|
adantr |
|
66 |
|
fzofzp1 |
|
67 |
61 66
|
syl |
|
68 |
26 67
|
ffvelrnd |
|
69 |
68
|
rexrd |
|
70 |
69
|
adantr |
|
71 |
1 3 4
|
fourierdlem11 |
|
72 |
71
|
simp1d |
|
73 |
71
|
simp2d |
|
74 |
72 73
|
iccssred |
|
75 |
71
|
simp3d |
|
76 |
72 73 75 16
|
fourierdlem17 |
|
77 |
72 73 75 2 15
|
fourierdlem4 |
|
78 |
77 60
|
ffvelrnd |
|
79 |
76 78
|
ffvelrnd |
|
80 |
74 79
|
sseldd |
|
81 |
80
|
adantr |
|
82 |
63
|
adantr |
|
83 |
72
|
rexrd |
|
84 |
|
iocssre |
|
85 |
83 73 84
|
syl2anc |
|
86 |
|
fzofzp1 |
|
87 |
17 86
|
syl |
|
88 |
57 87
|
ffvelrnd |
|
89 |
77 88
|
ffvelrnd |
|
90 |
85 89
|
sseldd |
|
91 |
54
|
simprrd |
|
92 |
|
fveq2 |
|
93 |
|
oveq1 |
|
94 |
93
|
fveq2d |
|
95 |
92 94
|
breq12d |
|
96 |
95
|
rspccva |
|
97 |
91 17 96
|
syl2anc |
|
98 |
60 88
|
posdifd |
|
99 |
97 98
|
mpbid |
|
100 |
17
|
ancli |
|
101 |
|
eleq1 |
|
102 |
101
|
anbi2d |
|
103 |
|
oveq1 |
|
104 |
103
|
fveq2d |
|
105 |
104
|
fveq2d |
|
106 |
|
fveq2 |
|
107 |
106
|
fveq2d |
|
108 |
107
|
fveq2d |
|
109 |
105 108
|
oveq12d |
|
110 |
104 106
|
oveq12d |
|
111 |
109 110
|
eqeq12d |
|
112 |
102 111
|
imbi12d |
|
113 |
2
|
oveq2i |
|
114 |
113
|
oveq2i |
|
115 |
114
|
eleq1i |
|
116 |
115
|
rexbii |
|
117 |
116
|
rgenw |
|
118 |
|
rabbi |
|
119 |
117 118
|
mpbi |
|
120 |
119
|
uneq2i |
|
121 |
120
|
fveq2i |
|
122 |
121
|
oveq1i |
|
123 |
43 122
|
eqtri |
|
124 |
|
isoeq5 |
|
125 |
120 124
|
ax-mp |
|
126 |
125
|
iotabii |
|
127 |
47 126
|
eqtri |
|
128 |
|
eqid |
|
129 |
1 2 3 4 9 10 11 123 127 15 16 128
|
fourierdlem65 |
|
130 |
112 129
|
vtoclg |
|
131 |
17 100 130
|
sylc |
|
132 |
99 131
|
breqtrrd |
|
133 |
80 90
|
posdifd |
|
134 |
132 133
|
mpbird |
|
135 |
|
id |
|
136 |
108 105
|
oveq12d |
|
137 |
106
|
fveq2d |
|
138 |
137
|
fveq2d |
|
139 |
137
|
oveq1d |
|
140 |
139
|
fveq2d |
|
141 |
138 140
|
oveq12d |
|
142 |
136 141
|
sseq12d |
|
143 |
102 142
|
imbi12d |
|
144 |
|
eqid |
|
145 |
2 1 3 4 9 31 35 11 40 43 47 15 16 144 19
|
fourierdlem79 |
|
146 |
143 145
|
vtoclg |
|
147 |
146
|
anabsi7 |
|
148 |
135 17 147
|
syl2anc |
|
149 |
63 68 80 90 134 148
|
fourierdlem10 |
|
150 |
149
|
simpld |
|
151 |
150
|
adantr |
|
152 |
|
neqne |
|
153 |
152
|
adantl |
|
154 |
82 81 151 153
|
leneltd |
|
155 |
149
|
simprd |
|
156 |
80 90 68 134 155
|
ltletrd |
|
157 |
156
|
adantr |
|
158 |
65 70 81 154 157
|
eliood |
|
159 |
|
fvres |
|
160 |
158 159
|
syl |
|
161 |
160
|
eqcomd |
|
162 |
161
|
ifeq2da |
|
163 |
|
fdm |
|
164 |
5 163
|
syl |
|
165 |
164
|
feq2d |
|
166 |
5 165
|
mpbird |
|
167 |
|
ioosscn |
|
168 |
167
|
a1i |
|
169 |
|
ioossre |
|
170 |
169 164
|
sseqtrrid |
|
171 |
88 90
|
resubcld |
|
172 |
18 171
|
eqeltrid |
|
173 |
172
|
recnd |
|
174 |
|
eqid |
|
175 |
80 90 172
|
iooshift |
|
176 |
|
ioossre |
|
177 |
176 164
|
sseqtrrid |
|
178 |
175 177
|
eqsstrrd |
|
179 |
|
elioore |
|
180 |
73 72
|
resubcld |
|
181 |
2 180
|
eqeltrid |
|
182 |
181
|
recnd |
|
183 |
72 73
|
posdifd |
|
184 |
75 183
|
mpbid |
|
185 |
184 2
|
breqtrrdi |
|
186 |
185
|
gt0ne0d |
|
187 |
173 182 186
|
divcan1d |
|
188 |
187
|
eqcomd |
|
189 |
188
|
oveq2d |
|
190 |
189
|
adantr |
|
191 |
190
|
fveq2d |
|
192 |
5
|
adantr |
|
193 |
181
|
adantr |
|
194 |
90
|
recnd |
|
195 |
88
|
recnd |
|
196 |
194 195
|
negsubdi2d |
|
197 |
196
|
eqcomd |
|
198 |
197
|
oveq1d |
|
199 |
18
|
oveq1i |
|
200 |
199
|
a1i |
|
201 |
15
|
a1i |
|
202 |
|
id |
|
203 |
|
oveq2 |
|
204 |
203
|
oveq1d |
|
205 |
204
|
fveq2d |
|
206 |
205
|
oveq1d |
|
207 |
202 206
|
oveq12d |
|
208 |
207
|
adantl |
|
209 |
73 88
|
resubcld |
|
210 |
209 181 186
|
redivcld |
|
211 |
210
|
flcld |
|
212 |
211
|
zred |
|
213 |
212 181
|
remulcld |
|
214 |
88 213
|
readdcld |
|
215 |
201 208 88 214
|
fvmptd |
|
216 |
215
|
oveq1d |
|
217 |
212
|
recnd |
|
218 |
217 182
|
mulcld |
|
219 |
195 218
|
pncan2d |
|
220 |
216 219
|
eqtrd |
|
221 |
220 218
|
eqeltrd |
|
222 |
221 182 186
|
divnegd |
|
223 |
198 200 222
|
3eqtr4d |
|
224 |
220
|
oveq1d |
|
225 |
217 182 186
|
divcan4d |
|
226 |
224 225
|
eqtrd |
|
227 |
226 211
|
eqeltrd |
|
228 |
227
|
znegcld |
|
229 |
223 228
|
eqeltrd |
|
230 |
229
|
adantr |
|
231 |
|
simpr |
|
232 |
6
|
adantlr |
|
233 |
192 193 230 231 232
|
fperiodmul |
|
234 |
191 233
|
eqtrd |
|
235 |
179 234
|
sylan2 |
|
236 |
23
|
simprrd |
|
237 |
|
fveq2 |
|
238 |
|
oveq1 |
|
239 |
238
|
fveq2d |
|
240 |
237 239
|
breq12d |
|
241 |
240
|
rspccva |
|
242 |
236 61 241
|
syl2anc |
|
243 |
61
|
ancli |
|
244 |
|
eleq1 |
|
245 |
244
|
anbi2d |
|
246 |
237 239
|
oveq12d |
|
247 |
246
|
reseq2d |
|
248 |
246
|
oveq1d |
|
249 |
247 248
|
eleq12d |
|
250 |
245 249
|
imbi12d |
|
251 |
250 7
|
vtoclg |
|
252 |
61 243 251
|
sylc |
|
253 |
|
nfv |
|
254 |
|
nfmpt1 |
|
255 |
20 254
|
nfcxfr |
|
256 |
|
nfcv |
|
257 |
255 256
|
nffv |
|
258 |
257
|
nfel1 |
|
259 |
253 258
|
nfim |
|
260 |
245
|
biimpar |
|
261 |
260
|
3adant2 |
|
262 |
261 8
|
syl |
|
263 |
|
fveq2 |
|
264 |
263
|
eqcomd |
|
265 |
264
|
adantr |
|
266 |
260
|
simprd |
|
267 |
|
elex |
|
268 |
260 8 267
|
3syl |
|
269 |
20
|
fvmpt2 |
|
270 |
266 268 269
|
syl2anc |
|
271 |
265 270
|
eqtrd |
|
272 |
271
|
3adant2 |
|
273 |
247 237
|
oveq12d |
|
274 |
273
|
eqcomd |
|
275 |
274
|
3ad2ant1 |
|
276 |
262 272 275
|
3eltr4d |
|
277 |
276
|
3exp |
|
278 |
8
|
2a1i |
|
279 |
277 278
|
impbid |
|
280 |
259 279 8
|
vtoclg1f |
|
281 |
61 243 280
|
sylc |
|
282 |
|
eqid |
|
283 |
|
eqid |
|
284 |
63 68 242 252 281 80 90 134 148 282 283
|
fourierdlem32 |
|
285 |
148
|
resabs1d |
|
286 |
285
|
oveq1d |
|
287 |
284 286
|
eleqtrd |
|
288 |
166 168 170 173 174 178 235 287
|
limcperiod |
|
289 |
18
|
oveq2i |
|
290 |
289
|
a1i |
|
291 |
9 31
|
iccssred |
|
292 |
|
ax-resscn |
|
293 |
291 292
|
sstrdi |
|
294 |
11 51 50
|
fourierdlem15 |
|
295 |
294 59
|
ffvelrnd |
|
296 |
293 295
|
sseldd |
|
297 |
195 296
|
subcld |
|
298 |
80
|
recnd |
|
299 |
194 297 298
|
subsub23d |
|
300 |
131 299
|
mpbird |
|
301 |
300
|
eqcomd |
|
302 |
301
|
oveq1d |
|
303 |
194 297
|
subcld |
|
304 |
303 195 194
|
addsub12d |
|
305 |
194 297 194
|
sub32d |
|
306 |
194
|
subidd |
|
307 |
306
|
oveq1d |
|
308 |
|
df-neg |
|
309 |
195 296
|
negsubdi2d |
|
310 |
308 309
|
syl5eqr |
|
311 |
305 307 310
|
3eqtrd |
|
312 |
311
|
oveq2d |
|
313 |
195 296
|
pncan3d |
|
314 |
304 312 313
|
3eqtrd |
|
315 |
290 302 314
|
3eqtrd |
|
316 |
315
|
oveq2d |
|
317 |
288 316
|
eleqtrd |
|
318 |
18
|
oveq2i |
|
319 |
194 195
|
pncan3d |
|
320 |
318 319
|
syl5eq |
|
321 |
315 320
|
oveq12d |
|
322 |
175 321
|
eqtr3d |
|
323 |
322
|
reseq2d |
|
324 |
323
|
oveq1d |
|
325 |
317 324
|
eleqtrd |
|
326 |
162 325
|
eqeltrd |
|