Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem97.f |
|
2 |
|
fourierdlem97.g |
|
3 |
|
fourierdlem97.p |
|
4 |
|
fourierdlem97.a |
|
5 |
|
fourierdlem97.b |
|
6 |
|
fourierdlem97.t |
|
7 |
|
fourierdlem97.m |
|
8 |
|
fourierdlem97.q |
|
9 |
|
fourierdlem97.fper |
|
10 |
|
fourierdlem97.qcn |
|
11 |
|
fourierdlem97.c |
|
12 |
|
fourierdlem97.d |
|
13 |
|
fourierdlem97.j |
|
14 |
|
fourierdlem97.v |
|
15 |
|
fourierdlem97.h |
|
16 |
|
ioossre |
|
17 |
16
|
a1i |
|
18 |
17
|
sselda |
|
19 |
|
iftrue |
|
20 |
19
|
adantl |
|
21 |
|
ssid |
|
22 |
|
dvfre |
|
23 |
1 21 22
|
sylancl |
|
24 |
2
|
feq1i |
|
25 |
23 24
|
sylibr |
|
26 |
25
|
adantr |
|
27 |
|
id |
|
28 |
2
|
dmeqi |
|
29 |
27 28
|
eleqtrdi |
|
30 |
29
|
adantl |
|
31 |
26 30
|
ffvelrnd |
|
32 |
20 31
|
eqeltrd |
|
33 |
32
|
adantlr |
|
34 |
|
iffalse |
|
35 |
|
0red |
|
36 |
34 35
|
eqeltrd |
|
37 |
36
|
adantl |
|
38 |
33 37
|
pm2.61dan |
|
39 |
18 38
|
syldan |
|
40 |
15
|
fvmpt2 |
|
41 |
18 39 40
|
syl2anc |
|
42 |
|
elioore |
|
43 |
12 42
|
syl |
|
44 |
11
|
rexrd |
|
45 |
|
pnfxr |
|
46 |
45
|
a1i |
|
47 |
|
ioogtlb |
|
48 |
44 46 12 47
|
syl3anc |
|
49 |
|
oveq1 |
|
50 |
49
|
eleq1d |
|
51 |
50
|
rexbidv |
|
52 |
51
|
cbvrabv |
|
53 |
52
|
uneq2i |
|
54 |
|
oveq1 |
|
55 |
54
|
oveq2d |
|
56 |
55
|
eleq1d |
|
57 |
56
|
cbvrexvw |
|
58 |
57
|
a1i |
|
59 |
58
|
rabbiia |
|
60 |
59
|
uneq2i |
|
61 |
|
oveq1 |
|
62 |
61
|
oveq2d |
|
63 |
62
|
eleq1d |
|
64 |
63
|
cbvrexvw |
|
65 |
64
|
a1i |
|
66 |
65
|
rabbiia |
|
67 |
66
|
uneq2i |
|
68 |
60 67
|
eqtri |
|
69 |
68
|
fveq2i |
|
70 |
69
|
oveq1i |
|
71 |
|
oveq1 |
|
72 |
71
|
oveq2d |
|
73 |
72
|
breq1d |
|
74 |
73
|
cbvrabv |
|
75 |
74
|
supeq1i |
|
76 |
|
fveq2 |
|
77 |
76
|
oveq1d |
|
78 |
77
|
breq1d |
|
79 |
78
|
cbvrabv |
|
80 |
79
|
supeq1i |
|
81 |
6 3 7 8 11 43 48 53 70 14 13 75 80
|
fourierdlem64 |
|
82 |
81
|
simprd |
|
83 |
|
simpl1 |
|
84 |
|
simpl2l |
|
85 |
|
cncff |
|
86 |
10 85
|
syl |
|
87 |
|
ffun |
|
88 |
25 87
|
syl |
|
89 |
88
|
adantr |
|
90 |
|
ffvresb |
|
91 |
89 90
|
syl |
|
92 |
86 91
|
mpbid |
|
93 |
92
|
r19.21bi |
|
94 |
93
|
simpld |
|
95 |
94
|
ralrimiva |
|
96 |
|
dfss3 |
|
97 |
95 96
|
sylibr |
|
98 |
83 84 97
|
syl2anc |
|
99 |
|
simpl2 |
|
100 |
83 99
|
jca |
|
101 |
|
simpl3 |
|
102 |
|
simpr |
|
103 |
101 102
|
sseldd |
|
104 |
3
|
fourierdlem2 |
|
105 |
7 104
|
syl |
|
106 |
8 105
|
mpbid |
|
107 |
106
|
simpld |
|
108 |
|
elmapi |
|
109 |
107 108
|
syl |
|
110 |
109
|
adantr |
|
111 |
|
elfzofz |
|
112 |
111
|
adantl |
|
113 |
110 112
|
ffvelrnd |
|
114 |
113
|
rexrd |
|
115 |
114
|
adantrr |
|
116 |
115
|
adantr |
|
117 |
|
fzofzp1 |
|
118 |
117
|
adantl |
|
119 |
110 118
|
ffvelrnd |
|
120 |
119
|
adantrr |
|
121 |
120
|
adantr |
|
122 |
121
|
rexrd |
|
123 |
|
elioore |
|
124 |
123
|
adantl |
|
125 |
|
zre |
|
126 |
125
|
adantl |
|
127 |
126
|
ad2antlr |
|
128 |
4 5
|
resubcld |
|
129 |
6 128
|
eqeltrid |
|
130 |
129
|
ad2antrr |
|
131 |
127 130
|
remulcld |
|
132 |
124 131
|
resubcld |
|
133 |
113
|
adantrr |
|
134 |
125
|
ad2antll |
|
135 |
129
|
adantr |
|
136 |
134 135
|
remulcld |
|
137 |
133 136
|
readdcld |
|
138 |
137
|
rexrd |
|
139 |
138
|
adantr |
|
140 |
120 136
|
readdcld |
|
141 |
140
|
rexrd |
|
142 |
141
|
adantr |
|
143 |
|
simpr |
|
144 |
|
ioogtlb |
|
145 |
139 142 143 144
|
syl3anc |
|
146 |
133
|
adantr |
|
147 |
146 131 124
|
ltaddsubd |
|
148 |
145 147
|
mpbid |
|
149 |
|
iooltub |
|
150 |
139 142 143 149
|
syl3anc |
|
151 |
124 131 121
|
ltsubaddd |
|
152 |
150 151
|
mpbird |
|
153 |
116 122 132 148 152
|
eliood |
|
154 |
100 103 153
|
syl2anc |
|
155 |
98 154
|
sseldd |
|
156 |
|
elioore |
|
157 |
|
recn |
|
158 |
157
|
adantl |
|
159 |
|
zcn |
|
160 |
159
|
ad2antlr |
|
161 |
129
|
recnd |
|
162 |
161
|
ad2antrr |
|
163 |
160 162
|
mulcld |
|
164 |
158 163
|
npcand |
|
165 |
164
|
eqcomd |
|
166 |
165
|
adantr |
|
167 |
|
ovex |
|
168 |
|
eleq1 |
|
169 |
168
|
anbi2d |
|
170 |
|
oveq1 |
|
171 |
170
|
eleq1d |
|
172 |
170
|
fveq2d |
|
173 |
|
fveq2 |
|
174 |
172 173
|
eqeq12d |
|
175 |
171 174
|
anbi12d |
|
176 |
169 175
|
imbi12d |
|
177 |
|
ax-resscn |
|
178 |
177
|
a1i |
|
179 |
1 178
|
fssd |
|
180 |
179
|
adantr |
|
181 |
125
|
adantl |
|
182 |
129
|
adantr |
|
183 |
181 182
|
remulcld |
|
184 |
179
|
ad2antrr |
|
185 |
129
|
ad2antrr |
|
186 |
|
simplr |
|
187 |
|
simpr |
|
188 |
9
|
ad4ant14 |
|
189 |
184 185 186 187 188
|
fperiodmul |
|
190 |
180 183 189 2
|
fperdvper |
|
191 |
167 176 190
|
vtocl |
|
192 |
191
|
simpld |
|
193 |
192
|
adantlr |
|
194 |
166 193
|
eqeltrd |
|
195 |
194
|
ex |
|
196 |
156 195
|
sylan2 |
|
197 |
196
|
adantlrl |
|
198 |
197
|
3adantl3 |
|
199 |
155 198
|
mpd |
|
200 |
199
|
ralrimiva |
|
201 |
|
dfss3 |
|
202 |
200 201
|
sylibr |
|
203 |
202
|
3exp |
|
204 |
203
|
rexlimdvv |
|
205 |
82 204
|
mpd |
|
206 |
205
|
sselda |
|
207 |
206
|
iftrued |
|
208 |
41 207
|
eqtr2d |
|
209 |
208
|
mpteq2dva |
|
210 |
28
|
a1i |
|
211 |
210
|
feq2d |
|
212 |
25 211
|
mpbird |
|
213 |
212 205
|
feqresmpt |
|
214 |
38 15
|
fmptd |
|
215 |
214 17
|
feqresmpt |
|
216 |
209 213 215
|
3eqtr4d |
|
217 |
214 178
|
fssd |
|
218 |
15
|
a1i |
|
219 |
|
eleq1 |
|
220 |
|
fveq2 |
|
221 |
219 220
|
ifbieq1d |
|
222 |
179 129 9 2
|
fperdvper |
|
223 |
222
|
simpld |
|
224 |
223
|
iftrued |
|
225 |
221 224
|
sylan9eqr |
|
226 |
225
|
adantllr |
|
227 |
|
simpr |
|
228 |
129
|
adantr |
|
229 |
227 228
|
readdcld |
|
230 |
229
|
adantr |
|
231 |
212
|
ad2antrr |
|
232 |
223
|
adantlr |
|
233 |
231 232
|
ffvelrnd |
|
234 |
218 226 230 233
|
fvmptd |
|
235 |
222
|
simprd |
|
236 |
235
|
adantlr |
|
237 |
|
eleq1 |
|
238 |
|
fveq2 |
|
239 |
237 238
|
ifbieq1d |
|
240 |
239
|
adantl |
|
241 |
|
simplr |
|
242 |
|
simpr |
|
243 |
242
|
iftrued |
|
244 |
212
|
ffvelrnda |
|
245 |
243 244
|
eqeltrd |
|
246 |
245
|
adantlr |
|
247 |
218 240 241 246
|
fvmptd |
|
248 |
|
simpr |
|
249 |
248
|
iftrued |
|
250 |
247 249
|
eqtr2d |
|
251 |
234 236 250
|
3eqtrd |
|
252 |
229
|
recnd |
|
253 |
228
|
recnd |
|
254 |
252 253
|
negsubd |
|
255 |
227
|
recnd |
|
256 |
255 253
|
pncand |
|
257 |
254 256
|
eqtr2d |
|
258 |
257
|
adantr |
|
259 |
|
simpr |
|
260 |
|
simpll |
|
261 |
260 259
|
jca |
|
262 |
|
eleq1 |
|
263 |
262
|
anbi2d |
|
264 |
|
oveq1 |
|
265 |
264
|
eleq1d |
|
266 |
264
|
fveq2d |
|
267 |
|
fveq2 |
|
268 |
266 267
|
eqeq12d |
|
269 |
265 268
|
anbi12d |
|
270 |
263 269
|
imbi12d |
|
271 |
129
|
renegcld |
|
272 |
161
|
mulm1d |
|
273 |
272
|
eqcomd |
|
274 |
273
|
adantr |
|
275 |
274
|
oveq2d |
|
276 |
275
|
fveq2d |
|
277 |
179
|
adantr |
|
278 |
129
|
adantr |
|
279 |
|
1zzd |
|
280 |
279
|
znegcld |
|
281 |
|
simpr |
|
282 |
9
|
adantlr |
|
283 |
277 278 280 281 282
|
fperiodmul |
|
284 |
276 283
|
eqtrd |
|
285 |
179 271 284 2
|
fperdvper |
|
286 |
270 285
|
vtoclg |
|
287 |
259 261 286
|
sylc |
|
288 |
287
|
simpld |
|
289 |
258 288
|
eqeltrd |
|
290 |
289
|
stoic1a |
|
291 |
290
|
iffalsed |
|
292 |
15
|
a1i |
|
293 |
221
|
adantl |
|
294 |
229
|
adantr |
|
295 |
|
0red |
|
296 |
291 295
|
eqeltrd |
|
297 |
292 293 294 296
|
fvmptd |
|
298 |
|
simpr |
|
299 |
298
|
iffalsed |
|
300 |
239 299
|
sylan9eqr |
|
301 |
|
simplr |
|
302 |
292 300 301 295
|
fvmptd |
|
303 |
291 297 302
|
3eqtr4d |
|
304 |
251 303
|
pm2.61dan |
|
305 |
|
elioore |
|
306 |
305
|
adantl |
|
307 |
305 38
|
sylan2 |
|
308 |
306 307 40
|
syl2anc |
|
309 |
308
|
adantlr |
|
310 |
94
|
iftrued |
|
311 |
309 310
|
eqtrd |
|
312 |
311
|
mpteq2dva |
|
313 |
214
|
adantr |
|
314 |
|
ioossre |
|
315 |
314
|
a1i |
|
316 |
313 315
|
feqresmpt |
|
317 |
212
|
adantr |
|
318 |
317 97
|
feqresmpt |
|
319 |
312 316 318
|
3eqtr4d |
|
320 |
319 10
|
eqeltrd |
|
321 |
|
eqid |
|
322 |
|
oveq1 |
|
323 |
322
|
eleq1d |
|
324 |
323
|
rexbidv |
|
325 |
324
|
cbvrabv |
|
326 |
325
|
uneq2i |
|
327 |
326
|
eqcomi |
|
328 |
60
|
fveq2i |
|
329 |
328
|
oveq1i |
|
330 |
|
isoeq5 |
|
331 |
67 330
|
ax-mp |
|
332 |
331
|
iotabii |
|
333 |
|
isoeq1 |
|
334 |
333
|
cbviotavw |
|
335 |
332 334 14
|
3eqtr4ri |
|
336 |
|
id |
|
337 |
|
oveq2 |
|
338 |
337
|
oveq1d |
|
339 |
338
|
fveq2d |
|
340 |
339
|
oveq1d |
|
341 |
336 340
|
oveq12d |
|
342 |
341
|
cbvmptv |
|
343 |
|
eqeq1 |
|
344 |
|
id |
|
345 |
343 344
|
ifbieq2d |
|
346 |
345
|
cbvmptv |
|
347 |
|
eqid |
|
348 |
|
eqid |
|
349 |
|
eqid |
|
350 |
|
fveq2 |
|
351 |
350
|
breq1d |
|
352 |
351
|
cbvrabv |
|
353 |
|
fveq2 |
|
354 |
353
|
fveq2d |
|
355 |
354
|
eqcomd |
|
356 |
355
|
breq2d |
|
357 |
356
|
rabbidv |
|
358 |
352 357
|
syl5req |
|
359 |
358
|
supeq1d |
|
360 |
359
|
cbvmptv |
|
361 |
3 6 7 8 217 304 320 11 12 321 327 329 335 342 346 13 347 348 349 360
|
fourierdlem90 |
|
362 |
216 361
|
eqeltrd |
|