Step |
Hyp |
Ref |
Expression |
1 |
|
lgseisen.1 |
|
2 |
|
lgseisen.2 |
|
3 |
|
lgseisen.3 |
|
4 |
|
lgsquad.4 |
|
5 |
|
lgsquad.5 |
|
6 |
|
lgsquad.6 |
|
7 |
1 2 3
|
lgseisen |
|
8 |
4
|
oveq2i |
|
9 |
8
|
sumeq1i |
|
10 |
1 4
|
gausslemma2dlem0b |
|
11 |
10
|
nnred |
|
12 |
11
|
rehalfcld |
|
13 |
12
|
flcld |
|
14 |
13
|
zred |
|
15 |
14
|
ltp1d |
|
16 |
|
fzdisj |
|
17 |
15 16
|
syl |
|
18 |
10
|
nnrpd |
|
19 |
18
|
rphalfcld |
|
20 |
19
|
rpge0d |
|
21 |
|
flge0nn0 |
|
22 |
12 20 21
|
syl2anc |
|
23 |
10
|
nnnn0d |
|
24 |
|
rphalflt |
|
25 |
18 24
|
syl |
|
26 |
10
|
nnzd |
|
27 |
|
fllt |
|
28 |
12 26 27
|
syl2anc |
|
29 |
25 28
|
mpbid |
|
30 |
14 11 29
|
ltled |
|
31 |
|
elfz2nn0 |
|
32 |
22 23 30 31
|
syl3anbrc |
|
33 |
|
nn0uz |
|
34 |
23 33
|
eleqtrdi |
|
35 |
|
elfzp12 |
|
36 |
34 35
|
syl |
|
37 |
32 36
|
mpbid |
|
38 |
|
un0 |
|
39 |
|
uncom |
|
40 |
38 39
|
eqtr3i |
|
41 |
|
oveq2 |
|
42 |
|
fz10 |
|
43 |
41 42
|
eqtrdi |
|
44 |
|
oveq1 |
|
45 |
|
0p1e1 |
|
46 |
44 45
|
eqtrdi |
|
47 |
46
|
oveq1d |
|
48 |
43 47
|
uneq12d |
|
49 |
40 48
|
eqtr4id |
|
50 |
|
fzsplit |
|
51 |
45
|
oveq1i |
|
52 |
50 51
|
eleq2s |
|
53 |
49 52
|
jaoi |
|
54 |
37 53
|
syl |
|
55 |
|
fzfid |
|
56 |
2
|
gausslemma2dlem0a |
|
57 |
56
|
nnred |
|
58 |
1
|
gausslemma2dlem0a |
|
59 |
57 58
|
nndivred |
|
60 |
59
|
adantr |
|
61 |
|
2nn |
|
62 |
|
elfznn |
|
63 |
62
|
adantl |
|
64 |
|
nnmulcl |
|
65 |
61 63 64
|
sylancr |
|
66 |
65
|
nnred |
|
67 |
60 66
|
remulcld |
|
68 |
56
|
nnrpd |
|
69 |
58
|
nnrpd |
|
70 |
68 69
|
rpdivcld |
|
71 |
70
|
adantr |
|
72 |
65
|
nnrpd |
|
73 |
71 72
|
rpmulcld |
|
74 |
73
|
rpge0d |
|
75 |
|
flge0nn0 |
|
76 |
67 74 75
|
syl2anc |
|
77 |
76
|
nn0cnd |
|
78 |
17 54 55 77
|
fsumsplit |
|
79 |
9 78
|
syl5eqr |
|
80 |
79
|
oveq2d |
|
81 |
|
neg1cn |
|
82 |
81
|
a1i |
|
83 |
|
fzfid |
|
84 |
|
ssun2 |
|
85 |
84 54
|
sseqtrrid |
|
86 |
85
|
sselda |
|
87 |
86 76
|
syldan |
|
88 |
83 87
|
fsumnn0cl |
|
89 |
|
fzfid |
|
90 |
|
ssun1 |
|
91 |
90 54
|
sseqtrrid |
|
92 |
91
|
sselda |
|
93 |
92 76
|
syldan |
|
94 |
89 93
|
fsumnn0cl |
|
95 |
82 88 94
|
expaddd |
|
96 |
|
fzfid |
|
97 |
|
xpfi |
|
98 |
55 96 97
|
syl2anc |
|
99 |
|
opabssxp |
|
100 |
6 99
|
eqsstri |
|
101 |
|
ssfi |
|
102 |
98 100 101
|
sylancl |
|
103 |
|
ssrab2 |
|
104 |
|
ssfi |
|
105 |
102 103 104
|
sylancl |
|
106 |
|
hashcl |
|
107 |
105 106
|
syl |
|
108 |
|
ssrab2 |
|
109 |
|
ssfi |
|
110 |
102 108 109
|
sylancl |
|
111 |
|
hashcl |
|
112 |
110 111
|
syl |
|
113 |
82 107 112
|
expaddd |
|
114 |
92 65
|
syldan |
|
115 |
|
fzfid |
|
116 |
|
xpsnen2g |
|
117 |
114 115 116
|
syl2anc |
|
118 |
|
hasheni |
|
119 |
117 118
|
syl |
|
120 |
|
ssrab2 |
|
121 |
6
|
relopabi |
|
122 |
|
relss |
|
123 |
120 121 122
|
mp2 |
|
124 |
|
relxp |
|
125 |
6
|
eleq2i |
|
126 |
|
opabidw |
|
127 |
125 126
|
bitri |
|
128 |
|
anass |
|
129 |
114
|
adantr |
|
130 |
129
|
nnred |
|
131 |
58
|
ad2antrr |
|
132 |
131
|
nnred |
|
133 |
132
|
rehalfcld |
|
134 |
11
|
adantr |
|
135 |
134
|
adantr |
|
136 |
|
elfzle2 |
|
137 |
136
|
adantl |
|
138 |
134
|
rehalfcld |
|
139 |
|
elfzelz |
|
140 |
139
|
adantl |
|
141 |
|
flge |
|
142 |
138 140 141
|
syl2anc |
|
143 |
137 142
|
mpbird |
|
144 |
|
elfznn |
|
145 |
144
|
adantl |
|
146 |
145
|
nnred |
|
147 |
|
2re |
|
148 |
147
|
a1i |
|
149 |
|
2pos |
|
150 |
149
|
a1i |
|
151 |
|
lemuldiv2 |
|
152 |
146 134 148 150 151
|
syl112anc |
|
153 |
143 152
|
mpbird |
|
154 |
153
|
adantr |
|
155 |
132
|
ltm1d |
|
156 |
|
peano2rem |
|
157 |
132 156
|
syl |
|
158 |
147
|
a1i |
|
159 |
149
|
a1i |
|
160 |
|
ltdiv1 |
|
161 |
157 132 158 159 160
|
syl112anc |
|
162 |
155 161
|
mpbid |
|
163 |
4 162
|
eqbrtrid |
|
164 |
130 135 133 154 163
|
lelttrd |
|
165 |
131
|
nnrpd |
|
166 |
|
rphalflt |
|
167 |
165 166
|
syl |
|
168 |
130 133 132 164 167
|
lttrd |
|
169 |
130 132
|
ltnled |
|
170 |
168 169
|
mpbid |
|
171 |
1
|
eldifad |
|
172 |
171
|
ad2antrr |
|
173 |
|
prmz |
|
174 |
172 173
|
syl |
|
175 |
|
dvdsle |
|
176 |
174 129 175
|
syl2anc |
|
177 |
170 176
|
mtod |
|
178 |
2
|
eldifad |
|
179 |
|
prmrp |
|
180 |
171 178 179
|
syl2anc |
|
181 |
3 180
|
mpbird |
|
182 |
181
|
ad2antrr |
|
183 |
178
|
ad2antrr |
|
184 |
|
prmz |
|
185 |
183 184
|
syl |
|
186 |
129
|
nnzd |
|
187 |
|
coprmdvds |
|
188 |
174 185 186 187
|
syl3anc |
|
189 |
182 188
|
mpan2d |
|
190 |
177 189
|
mtod |
|
191 |
|
nnz |
|
192 |
191
|
adantl |
|
193 |
|
dvdsmul2 |
|
194 |
192 174 193
|
syl2anc |
|
195 |
|
breq2 |
|
196 |
194 195
|
syl5ibrcom |
|
197 |
196
|
necon3bd |
|
198 |
190 197
|
mpd |
|
199 |
|
simpr |
|
200 |
199 131
|
nnmulcld |
|
201 |
200
|
nnred |
|
202 |
56
|
adantr |
|
203 |
202 114
|
nnmulcld |
|
204 |
203
|
adantr |
|
205 |
204
|
nnred |
|
206 |
201 205
|
ltlend |
|
207 |
198 206
|
mpbiran2d |
|
208 |
|
nnre |
|
209 |
208
|
adantl |
|
210 |
131
|
nngt0d |
|
211 |
|
lemuldiv |
|
212 |
209 205 132 210 211
|
syl112anc |
|
213 |
202
|
adantr |
|
214 |
213
|
nncnd |
|
215 |
129
|
nncnd |
|
216 |
131
|
nncnd |
|
217 |
131
|
nnne0d |
|
218 |
214 215 216 217
|
div23d |
|
219 |
218
|
breq2d |
|
220 |
207 212 219
|
3bitrd |
|
221 |
213
|
nnred |
|
222 |
213
|
nngt0d |
|
223 |
|
ltmul2 |
|
224 |
130 133 221 222 223
|
syl112anc |
|
225 |
164 224
|
mpbid |
|
226 |
|
2cnd |
|
227 |
|
2ne0 |
|
228 |
227
|
a1i |
|
229 |
|
divass |
|
230 |
|
div23 |
|
231 |
229 230
|
eqtr3d |
|
232 |
214 216 226 228 231
|
syl112anc |
|
233 |
225 232
|
breqtrd |
|
234 |
221
|
rehalfcld |
|
235 |
234 132
|
remulcld |
|
236 |
|
lttr |
|
237 |
201 205 235 236
|
syl3anc |
|
238 |
233 237
|
mpan2d |
|
239 |
|
ltmul1 |
|
240 |
209 234 132 210 239
|
syl112anc |
|
241 |
238 240
|
sylibrd |
|
242 |
|
peano2rem |
|
243 |
221 242
|
syl |
|
244 |
243
|
recnd |
|
245 |
214 244 226 228
|
divsubdird |
|
246 |
5
|
oveq2i |
|
247 |
245 246
|
eqtr4di |
|
248 |
|
ax-1cn |
|
249 |
|
nncan |
|
250 |
214 248 249
|
sylancl |
|
251 |
250
|
oveq1d |
|
252 |
|
halflt1 |
|
253 |
251 252
|
eqbrtrdi |
|
254 |
247 253
|
eqbrtrrd |
|
255 |
2 5
|
gausslemma2dlem0b |
|
256 |
255
|
ad2antrr |
|
257 |
256
|
nnred |
|
258 |
|
1red |
|
259 |
234 257 258
|
ltsubadd2d |
|
260 |
254 259
|
mpbid |
|
261 |
|
peano2re |
|
262 |
257 261
|
syl |
|
263 |
|
lttr |
|
264 |
209 234 262 263
|
syl3anc |
|
265 |
260 264
|
mpan2d |
|
266 |
241 265
|
syld |
|
267 |
|
nnleltp1 |
|
268 |
199 256 267
|
syl2anc |
|
269 |
266 268
|
sylibrd |
|
270 |
269
|
pm4.71rd |
|
271 |
92 67
|
syldan |
|
272 |
|
flge |
|
273 |
271 191 272
|
syl2an |
|
274 |
220 270 273
|
3bitr3d |
|
275 |
274
|
pm5.32da |
|
276 |
128 275
|
syl5bb |
|
277 |
276
|
adantr |
|
278 |
|
simpr |
|
279 |
|
nnuz |
|
280 |
114 279
|
eleqtrdi |
|
281 |
26
|
adantr |
|
282 |
|
elfz5 |
|
283 |
280 281 282
|
syl2anc |
|
284 |
153 283
|
mpbird |
|
285 |
284
|
adantr |
|
286 |
278 285
|
eqeltrd |
|
287 |
286
|
biantrurd |
|
288 |
255
|
nnzd |
|
289 |
288
|
ad2antrr |
|
290 |
|
fznn |
|
291 |
289 290
|
syl |
|
292 |
287 291
|
bitr3d |
|
293 |
|
oveq1 |
|
294 |
114
|
nncnd |
|
295 |
202
|
nncnd |
|
296 |
294 295
|
mulcomd |
|
297 |
293 296
|
sylan9eqr |
|
298 |
297
|
breq2d |
|
299 |
292 298
|
anbi12d |
|
300 |
271
|
flcld |
|
301 |
|
fznn |
|
302 |
300 301
|
syl |
|
303 |
302
|
adantr |
|
304 |
277 299 303
|
3bitr4d |
|
305 |
127 304
|
syl5bb |
|
306 |
305
|
pm5.32da |
|
307 |
|
vex |
|
308 |
|
vex |
|
309 |
307 308
|
op1std |
|
310 |
309
|
eqeq2d |
|
311 |
|
eqcom |
|
312 |
310 311
|
bitrdi |
|
313 |
312
|
elrab |
|
314 |
313
|
biancomi |
|
315 |
|
opelxp |
|
316 |
|
velsn |
|
317 |
316
|
anbi1i |
|
318 |
315 317
|
bitri |
|
319 |
306 314 318
|
3bitr4g |
|
320 |
123 124 319
|
eqrelrdv |
|
321 |
320
|
eqcomd |
|
322 |
321
|
fveq2d |
|
323 |
|
hashfz1 |
|
324 |
93 323
|
syl |
|
325 |
119 322 324
|
3eqtr3rd |
|
326 |
325
|
sumeq2dv |
|
327 |
102
|
adantr |
|
328 |
|
ssfi |
|
329 |
327 120 328
|
sylancl |
|
330 |
|
fveq2 |
|
331 |
330
|
eqeq2d |
|
332 |
331
|
elrab |
|
333 |
332
|
simprbi |
|
334 |
333
|
ad2antll |
|
335 |
334
|
oveq1d |
|
336 |
145
|
nncnd |
|
337 |
336
|
adantrr |
|
338 |
|
2cnd |
|
339 |
227
|
a1i |
|
340 |
337 338 339
|
divcan3d |
|
341 |
335 340
|
eqtr3d |
|
342 |
341
|
ralrimivva |
|
343 |
|
invdisj |
|
344 |
342 343
|
syl |
|
345 |
89 329 344
|
hashiun |
|
346 |
|
iunrab |
|
347 |
|
2cn |
|
348 |
|
zcn |
|
349 |
348
|
adantl |
|
350 |
|
mulcom |
|
351 |
347 349 350
|
sylancr |
|
352 |
351
|
eqeq1d |
|
353 |
352
|
rexbidva |
|
354 |
139
|
anim1i |
|
355 |
354
|
reximi2 |
|
356 |
|
simprr |
|
357 |
|
simpr |
|
358 |
100 357
|
sseldi |
|
359 |
|
xp1st |
|
360 |
358 359
|
syl |
|
361 |
360
|
adantr |
|
362 |
|
elfzle2 |
|
363 |
361 362
|
syl |
|
364 |
356 363
|
eqbrtrd |
|
365 |
|
zre |
|
366 |
365
|
ad2antrl |
|
367 |
11
|
ad2antrr |
|
368 |
147
|
a1i |
|
369 |
149
|
a1i |
|
370 |
366 367 368 369 151
|
syl112anc |
|
371 |
364 370
|
mpbid |
|
372 |
12
|
ad2antrr |
|
373 |
|
simprl |
|
374 |
372 373 141
|
syl2anc |
|
375 |
371 374
|
mpbid |
|
376 |
|
2t0e0 |
|
377 |
|
elfznn |
|
378 |
361 377
|
syl |
|
379 |
356 378
|
eqeltrd |
|
380 |
379
|
nngt0d |
|
381 |
376 380
|
eqbrtrid |
|
382 |
|
0red |
|
383 |
|
ltmul2 |
|
384 |
382 366 368 369 383
|
syl112anc |
|
385 |
381 384
|
mpbird |
|
386 |
|
elnnz |
|
387 |
373 385 386
|
sylanbrc |
|
388 |
387 279
|
eleqtrdi |
|
389 |
13
|
ad2antrr |
|
390 |
|
elfz5 |
|
391 |
388 389 390
|
syl2anc |
|
392 |
375 391
|
mpbird |
|
393 |
392 356
|
jca |
|
394 |
393
|
ex |
|
395 |
394
|
reximdv2 |
|
396 |
355 395
|
impbid2 |
|
397 |
|
2z |
|
398 |
|
elfzelz |
|
399 |
360 398
|
syl |
|
400 |
|
divides |
|
401 |
397 399 400
|
sylancr |
|
402 |
353 396 401
|
3bitr4d |
|
403 |
402
|
rabbidva |
|
404 |
346 403
|
syl5eq |
|
405 |
404
|
fveq2d |
|
406 |
326 345 405
|
3eqtr2d |
|
407 |
406
|
oveq2d |
|
408 |
1 2 3 4 5 6
|
lgsquadlem1 |
|
409 |
407 408
|
oveq12d |
|
410 |
113 409
|
eqtr4d |
|
411 |
|
unrab |
|
412 |
|
exmid |
|
413 |
412
|
rgenw |
|
414 |
|
rabid2 |
|
415 |
413 414
|
mpbir |
|
416 |
411 415
|
eqtr4i |
|
417 |
416
|
fveq2i |
|
418 |
|
inrab |
|
419 |
|
pm3.24 |
|
420 |
419
|
a1i |
|
421 |
420
|
ralrimivw |
|
422 |
|
rabeq0 |
|
423 |
421 422
|
sylibr |
|
424 |
418 423
|
syl5eq |
|
425 |
|
hashun |
|
426 |
110 105 424 425
|
syl3anc |
|
427 |
417 426
|
syl5reqr |
|
428 |
427
|
oveq2d |
|
429 |
95 410 428
|
3eqtr2d |
|
430 |
7 80 429
|
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|