Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem107.a |
|
2 |
|
fourierdlem107.b |
|
3 |
|
fourierdlem107.t |
|
4 |
|
fourierdlem107.x |
|
5 |
|
fourierdlem107.p |
|
6 |
|
fourierdlem107.m |
|
7 |
|
fourierdlem107.q |
|
8 |
|
fourierdlem107.f |
|
9 |
|
fourierdlem107.fper |
|
10 |
|
fourierdlem107.fcn |
|
11 |
|
fourierdlem107.r |
|
12 |
|
fourierdlem107.l |
|
13 |
|
fourierdlem107.o |
|
14 |
|
fourierdlem107.h |
|
15 |
|
fourierdlem107.n |
|
16 |
|
fourierdlem107.s |
|
17 |
|
fourierdlem107.e |
|
18 |
|
fourierdlem107.z |
|
19 |
|
fourierdlem107.i |
|
20 |
3
|
oveq2i |
|
21 |
1
|
recnd |
|
22 |
4
|
rpred |
|
23 |
22
|
recnd |
|
24 |
2
|
recnd |
|
25 |
21 23 24 21
|
subadd4b |
|
26 |
20 25
|
syl5eq |
|
27 |
21
|
subidd |
|
28 |
27
|
oveq1d |
|
29 |
2 22
|
resubcld |
|
30 |
29
|
recnd |
|
31 |
30
|
addid2d |
|
32 |
26 28 31
|
3eqtrd |
|
33 |
3
|
oveq2i |
|
34 |
21 24
|
pncan3d |
|
35 |
33 34
|
syl5eq |
|
36 |
32 35
|
oveq12d |
|
37 |
36
|
eqcomd |
|
38 |
37
|
itgeq1d |
|
39 |
1 22
|
resubcld |
|
40 |
|
fveq2 |
|
41 |
|
oveq1 |
|
42 |
41
|
fveq2d |
|
43 |
40 42
|
breq12d |
|
44 |
43
|
cbvralvw |
|
45 |
44
|
a1i |
|
46 |
45
|
anbi2d |
|
47 |
46
|
rabbidv |
|
48 |
47
|
mpteq2ia |
|
49 |
13 48
|
eqtri |
|
50 |
1 4
|
ltsubrpd |
|
51 |
3 5 6 7 39 1 50 13 14 15 16
|
fourierdlem54 |
|
52 |
51
|
simpld |
|
53 |
52
|
simpld |
|
54 |
2 1
|
resubcld |
|
55 |
3 54
|
eqeltrid |
|
56 |
52
|
simprd |
|
57 |
39
|
adantr |
|
58 |
1
|
adantr |
|
59 |
|
simpr |
|
60 |
|
eliccre |
|
61 |
57 58 59 60
|
syl3anc |
|
62 |
61 9
|
syldan |
|
63 |
|
fveq2 |
|
64 |
63
|
oveq1d |
|
65 |
64
|
cbvmptv |
|
66 |
|
eqid |
|
67 |
6
|
adantr |
|
68 |
7
|
adantr |
|
69 |
8
|
adantr |
|
70 |
9
|
adantlr |
|
71 |
10
|
adantlr |
|
72 |
39
|
adantr |
|
73 |
72
|
rexrd |
|
74 |
|
pnfxr |
|
75 |
74
|
a1i |
|
76 |
1
|
adantr |
|
77 |
50
|
adantr |
|
78 |
1
|
ltpnfd |
|
79 |
78
|
adantr |
|
80 |
73 75 76 77 79
|
eliood |
|
81 |
|
simpr |
|
82 |
|
eqid |
|
83 |
|
eqid |
|
84 |
|
eqid |
|
85 |
5 3 67 68 69 70 71 72 80 13 14 15 16 17 18 81 82 83 84 19
|
fourierdlem90 |
|
86 |
11
|
adantlr |
|
87 |
|
eqid |
|
88 |
5 3 67 68 69 70 71 86 72 80 13 14 15 16 17 18 81 82 19 87
|
fourierdlem89 |
|
89 |
12
|
adantlr |
|
90 |
|
eqid |
|
91 |
5 3 67 68 69 70 71 89 72 80 13 14 15 16 17 18 81 82 19 90
|
fourierdlem91 |
|
92 |
39 1 49 53 55 56 62 65 66 8 85 88 91
|
fourierdlem92 |
|
93 |
38 92
|
eqtrd |
|
94 |
8
|
adantr |
|
95 |
29
|
adantr |
|
96 |
2
|
adantr |
|
97 |
|
simpr |
|
98 |
|
eliccre |
|
99 |
95 96 97 98
|
syl3anc |
|
100 |
94 99
|
ffvelrnd |
|
101 |
29
|
rexrd |
|
102 |
74
|
a1i |
|
103 |
2 4
|
ltsubrpd |
|
104 |
2
|
ltpnfd |
|
105 |
101 102 2 103 104
|
eliood |
|
106 |
5 3 6 7 8 9 10 11 12 29 105
|
fourierdlem105 |
|
107 |
100 106
|
itgcl |
|
108 |
93 107
|
eqeltrrd |
|
109 |
108
|
subidd |
|
110 |
109
|
eqcomd |
|
111 |
110
|
adantr |
|
112 |
39
|
adantr |
|
113 |
1
|
adantr |
|
114 |
29
|
adantr |
|
115 |
5 6 7
|
fourierdlem11 |
|
116 |
115
|
simp3d |
|
117 |
1 2 116
|
ltled |
|
118 |
117
|
adantr |
|
119 |
1 2 22
|
lesub1d |
|
120 |
119
|
adantr |
|
121 |
118 120
|
mpbid |
|
122 |
2
|
adantr |
|
123 |
22
|
adantr |
|
124 |
|
simpr |
|
125 |
3 124
|
eqbrtrrid |
|
126 |
122 113 123 125
|
ltsub23d |
|
127 |
114 113 126
|
ltled |
|
128 |
112 113 114 121 127
|
eliccd |
|
129 |
8
|
adantr |
|
130 |
129 61
|
ffvelrnd |
|
131 |
130
|
adantlr |
|
132 |
39
|
rexrd |
|
133 |
1 2 22 116
|
ltsub1dd |
|
134 |
29
|
ltpnfd |
|
135 |
132 102 29 133 134
|
eliood |
|
136 |
5 3 6 7 8 9 10 11 12 39 135
|
fourierdlem105 |
|
137 |
136
|
adantr |
|
138 |
6
|
adantr |
|
139 |
7
|
adantr |
|
140 |
8
|
adantr |
|
141 |
9
|
adantlr |
|
142 |
10
|
adantlr |
|
143 |
11
|
adantlr |
|
144 |
12
|
adantlr |
|
145 |
101
|
adantr |
|
146 |
74
|
a1i |
|
147 |
113
|
ltpnfd |
|
148 |
145 146 113 126 147
|
eliood |
|
149 |
5 3 138 139 140 141 142 143 144 114 148
|
fourierdlem105 |
|
150 |
112 113 128 131 137 149
|
itgspliticc |
|
151 |
150
|
oveq1d |
|
152 |
8
|
adantr |
|
153 |
39
|
adantr |
|
154 |
29
|
adantr |
|
155 |
|
simpr |
|
156 |
|
eliccre |
|
157 |
153 154 155 156
|
syl3anc |
|
158 |
152 157
|
ffvelrnd |
|
159 |
158 136
|
itgcl |
|
160 |
159
|
adantr |
|
161 |
8
|
adantr |
|
162 |
29
|
adantr |
|
163 |
1
|
adantr |
|
164 |
|
simpr |
|
165 |
|
eliccre |
|
166 |
162 163 164 165
|
syl3anc |
|
167 |
161 166
|
ffvelrnd |
|
168 |
167
|
adantlr |
|
169 |
168 149
|
itgcl |
|
170 |
108
|
adantr |
|
171 |
160 169 170
|
addsubassd |
|
172 |
111 151 171
|
3eqtrd |
|
173 |
172
|
oveq2d |
|
174 |
160
|
subid1d |
|
175 |
159
|
subidd |
|
176 |
175
|
oveq1d |
|
177 |
176
|
adantr |
|
178 |
169 170
|
subcld |
|
179 |
160 160 178
|
subsub4d |
|
180 |
|
df-neg |
|
181 |
169 170
|
negsubdi2d |
|
182 |
180 181
|
eqtr3id |
|
183 |
177 179 182
|
3eqtr3d |
|
184 |
173 174 183
|
3eqtr3d |
|
185 |
107
|
subidd |
|
186 |
185
|
eqcomd |
|
187 |
186
|
oveq2d |
|
188 |
187
|
adantr |
|
189 |
169
|
addid1d |
|
190 |
114 122 113 127 118
|
eliccd |
|
191 |
100
|
adantlr |
|
192 |
1 2
|
iccssred |
|
193 |
8 192
|
feqresmpt |
|
194 |
8 192
|
fssresd |
|
195 |
|
ioossicc |
|
196 |
1
|
rexrd |
|
197 |
196
|
adantr |
|
198 |
2
|
rexrd |
|
199 |
198
|
adantr |
|
200 |
5 6 7
|
fourierdlem15 |
|
201 |
200
|
adantr |
|
202 |
|
simpr |
|
203 |
197 199 201 202
|
fourierdlem8 |
|
204 |
195 203
|
sstrid |
|
205 |
204
|
resabs1d |
|
206 |
205 10
|
eqeltrd |
|
207 |
205
|
eqcomd |
|
208 |
207
|
oveq1d |
|
209 |
11 208
|
eleqtrd |
|
210 |
207
|
oveq1d |
|
211 |
12 210
|
eleqtrd |
|
212 |
5 6 7 194 206 209 211
|
fourierdlem69 |
|
213 |
193 212
|
eqeltrrd |
|
214 |
213
|
adantr |
|
215 |
114 122 190 191 149 214
|
itgspliticc |
|
216 |
215
|
oveq2d |
|
217 |
216
|
oveq2d |
|
218 |
107
|
adantr |
|
219 |
215 218
|
eqeltrrd |
|
220 |
169 218 219
|
addsub12d |
|
221 |
8
|
adantr |
|
222 |
1
|
adantr |
|
223 |
2
|
adantr |
|
224 |
|
simpr |
|
225 |
|
eliccre |
|
226 |
222 223 224 225
|
syl3anc |
|
227 |
221 226
|
ffvelrnd |
|
228 |
227 213
|
itgcl |
|
229 |
228
|
adantr |
|
230 |
169 169 229
|
subsub4d |
|
231 |
230
|
eqcomd |
|
232 |
231
|
oveq2d |
|
233 |
169
|
subidd |
|
234 |
233
|
oveq1d |
|
235 |
|
df-neg |
|
236 |
234 235
|
eqtr4di |
|
237 |
236
|
oveq2d |
|
238 |
218 229
|
negsubd |
|
239 |
232 237 238
|
3eqtrd |
|
240 |
217 220 239
|
3eqtrd |
|
241 |
188 189 240
|
3eqtr3d |
|
242 |
241
|
oveq2d |
|
243 |
108 107 228
|
subsubd |
|
244 |
93
|
oveq2d |
|
245 |
244 109
|
eqtrd |
|
246 |
245
|
oveq1d |
|
247 |
228
|
addid2d |
|
248 |
243 246 247
|
3eqtrd |
|
249 |
248
|
adantr |
|
250 |
184 242 249
|
3eqtrd |
|
251 |
39
|
adantr |
|
252 |
29
|
adantr |
|
253 |
1
|
adantr |
|
254 |
39 1 50
|
ltled |
|
255 |
254
|
adantr |
|
256 |
22
|
adantr |
|
257 |
2
|
adantr |
|
258 |
|
id |
|
259 |
258 3
|
breqtrdi |
|
260 |
259
|
adantl |
|
261 |
256 257 253 260
|
lesubd |
|
262 |
251 252 253 255 261
|
eliccd |
|
263 |
158
|
adantlr |
|
264 |
132 102 1 50 78
|
eliood |
|
265 |
5 3 6 7 8 9 10 11 12 39 264
|
fourierdlem105 |
|
266 |
265
|
adantr |
|
267 |
1
|
leidd |
|
268 |
4
|
rpge0d |
|
269 |
2 22
|
subge02d |
|
270 |
268 269
|
mpbid |
|
271 |
|
iccss |
|
272 |
1 2 267 270 271
|
syl22anc |
|
273 |
|
iccmbl |
|
274 |
1 29 273
|
syl2anc |
|
275 |
272 274 227 213
|
iblss |
|
276 |
275
|
adantr |
|
277 |
251 252 262 263 266 276
|
itgspliticc |
|
278 |
268
|
adantr |
|
279 |
269
|
adantr |
|
280 |
278 279
|
mpbid |
|
281 |
253 257 252 261 280
|
eliccd |
|
282 |
227
|
adantlr |
|
283 |
2
|
leidd |
|
284 |
283
|
adantr |
|
285 |
|
iccss |
|
286 |
253 257 261 284 285
|
syl22anc |
|
287 |
|
iccmbl |
|
288 |
29 2 287
|
syl2anc |
|
289 |
288
|
adantr |
|
290 |
213
|
adantr |
|
291 |
286 289 282 290
|
iblss |
|
292 |
253 257 281 282 276 291
|
itgspliticc |
|
293 |
292
|
oveq1d |
|
294 |
8
|
adantr |
|
295 |
1
|
adantr |
|
296 |
29
|
adantr |
|
297 |
|
simpr |
|
298 |
|
eliccre |
|
299 |
295 296 297 298
|
syl3anc |
|
300 |
294 299
|
ffvelrnd |
|
301 |
300 275
|
itgcl |
|
302 |
301 107 107
|
addsubassd |
|
303 |
302
|
adantr |
|
304 |
185
|
oveq2d |
|
305 |
301
|
addid1d |
|
306 |
304 305
|
eqtrd |
|
307 |
306
|
adantr |
|
308 |
293 303 307
|
3eqtrrd |
|
309 |
308
|
oveq2d |
|
310 |
93
|
adantr |
|
311 |
107
|
adantr |
|
312 |
310 311
|
eqeltrrd |
|
313 |
282 290
|
itgcl |
|
314 |
312 313 311
|
addsub12d |
|
315 |
313 312 311
|
addsubassd |
|
316 |
314 315
|
eqtr4d |
|
317 |
277 309 316
|
3eqtrd |
|
318 |
310
|
oveq2d |
|
319 |
313 312
|
pncand |
|
320 |
317 318 319
|
3eqtrd |
|
321 |
250 320 55 22
|
ltlecasei |
|