Step |
Hyp |
Ref |
Expression |
1 |
|
breprexp.n |
|
2 |
|
breprexp.s |
|
3 |
|
breprexp.z |
|
4 |
|
breprexp.h |
|
5 |
|
breprexplemc.t |
|
6 |
|
breprexplemc.s |
|
7 |
|
breprexplemc.1 |
|
8 |
|
nn0uz |
|
9 |
5 8
|
eleqtrdi |
|
10 |
|
fzosplitsn |
|
11 |
9 10
|
syl |
|
12 |
11
|
prodeq1d |
|
13 |
|
nfv |
|
14 |
|
nfcv |
|
15 |
|
fzofi |
|
16 |
15
|
a1i |
|
17 |
|
fzonel |
|
18 |
17
|
a1i |
|
19 |
|
fzfid |
|
20 |
1
|
ad2antrr |
|
21 |
2
|
ad2antrr |
|
22 |
3
|
ad2antrr |
|
23 |
4
|
adantr |
|
24 |
23
|
adantr |
|
25 |
5
|
nn0zd |
|
26 |
2
|
nn0zd |
|
27 |
5
|
nn0red |
|
28 |
|
1red |
|
29 |
27 28
|
readdcld |
|
30 |
2
|
nn0red |
|
31 |
27
|
lep1d |
|
32 |
27 29 30 31 6
|
letrd |
|
33 |
|
eluz1 |
|
34 |
33
|
biimpar |
|
35 |
25 26 32 34
|
syl12anc |
|
36 |
|
fzoss2 |
|
37 |
35 36
|
syl |
|
38 |
37
|
sselda |
|
39 |
38
|
adantr |
|
40 |
|
fz1ssnn |
|
41 |
40
|
a1i |
|
42 |
41
|
sselda |
|
43 |
20 21 22 24 39 42
|
breprexplemb |
|
44 |
|
nnssnn0 |
|
45 |
40 44
|
sstri |
|
46 |
45
|
a1i |
|
47 |
46
|
ralrimivw |
|
48 |
47
|
r19.21bi |
|
49 |
48
|
sselda |
|
50 |
22 49
|
expcld |
|
51 |
43 50
|
mulcld |
|
52 |
19 51
|
fsumcl |
|
53 |
|
simpl |
|
54 |
53
|
fveq2d |
|
55 |
54
|
fveq1d |
|
56 |
55
|
oveq1d |
|
57 |
56
|
sumeq2dv |
|
58 |
|
fzfid |
|
59 |
1
|
adantr |
|
60 |
2
|
adantr |
|
61 |
3
|
adantr |
|
62 |
4
|
adantr |
|
63 |
5
|
nn0ge0d |
|
64 |
|
zltp1le |
|
65 |
25 26 64
|
syl2anc |
|
66 |
6 65
|
mpbird |
|
67 |
|
0zd |
|
68 |
|
elfzo |
|
69 |
25 67 26 68
|
syl3anc |
|
70 |
63 66 69
|
mpbir2and |
|
71 |
70
|
adantr |
|
72 |
40
|
a1i |
|
73 |
72
|
sselda |
|
74 |
59 60 61 62 71 73
|
breprexplemb |
|
75 |
46
|
sselda |
|
76 |
61 75
|
expcld |
|
77 |
74 76
|
mulcld |
|
78 |
58 77
|
fsumcl |
|
79 |
13 14 16 5 18 52 57 78
|
fprodsplitsn |
|
80 |
7
|
oveq1d |
|
81 |
|
fzfid |
|
82 |
40
|
a1i |
|
83 |
|
fz0ssnn0 |
|
84 |
|
simpr |
|
85 |
83 84
|
sseldi |
|
86 |
85
|
nn0zd |
|
87 |
5
|
adantr |
|
88 |
58
|
adantr |
|
89 |
82 86 87 88
|
reprfi |
|
90 |
15
|
a1i |
|
91 |
1
|
adantr |
|
92 |
91
|
ad2antrr |
|
93 |
2
|
ad3antrrr |
|
94 |
3
|
ad3antrrr |
|
95 |
4
|
ad3antrrr |
|
96 |
37
|
ad2antrr |
|
97 |
96
|
sselda |
|
98 |
40
|
a1i |
|
99 |
86
|
ad2antrr |
|
100 |
87
|
ad2antrr |
|
101 |
|
simplr |
|
102 |
98 99 100 101
|
reprf |
|
103 |
|
simpr |
|
104 |
102 103
|
ffvelrnd |
|
105 |
40 104
|
sseldi |
|
106 |
92 93 94 95 97 105
|
breprexplemb |
|
107 |
90 106
|
fprodcl |
|
108 |
3
|
ad2antrr |
|
109 |
85
|
adantr |
|
110 |
108 109
|
expcld |
|
111 |
107 110
|
mulcld |
|
112 |
89 111
|
fsumcl |
|
113 |
81 58 112 77
|
fsum2mul |
|
114 |
40
|
a1i |
|
115 |
|
fzssz |
|
116 |
|
simpr |
|
117 |
115 116
|
sseldi |
|
118 |
117
|
adantr |
|
119 |
|
fzssz |
|
120 |
|
simpr |
|
121 |
119 120
|
sseldi |
|
122 |
118 121
|
zsubcld |
|
123 |
5
|
adantr |
|
124 |
123
|
adantr |
|
125 |
58
|
adantr |
|
126 |
125
|
adantr |
|
127 |
114 122 124 126
|
reprfi |
|
128 |
74
|
adantlr |
|
129 |
3
|
adantr |
|
130 |
|
fz0ssnn0 |
|
131 |
130 116
|
sseldi |
|
132 |
129 131
|
expcld |
|
133 |
132
|
adantr |
|
134 |
128 133
|
mulcld |
|
135 |
15
|
a1i |
|
136 |
1
|
adantr |
|
137 |
136
|
adantr |
|
138 |
137
|
ad2antrr |
|
139 |
2
|
ad4antr |
|
140 |
129
|
ad3antrrr |
|
141 |
4
|
ad4antr |
|
142 |
38
|
ad5ant15 |
|
143 |
40
|
a1i |
|
144 |
122
|
ad2antrr |
|
145 |
124
|
ad2antrr |
|
146 |
|
simplr |
|
147 |
143 144 145 146
|
reprf |
|
148 |
|
simpr |
|
149 |
147 148
|
ffvelrnd |
|
150 |
40 149
|
sseldi |
|
151 |
138 139 140 141 142 150
|
breprexplemb |
|
152 |
135 151
|
fprodcl |
|
153 |
127 134 152
|
fsummulc1 |
|
154 |
153
|
sumeq2dv |
|
155 |
|
elfzle2 |
|
156 |
155
|
adantl |
|
157 |
136
|
ad2antrr |
|
158 |
2
|
ad3antrrr |
|
159 |
129
|
ad2antrr |
|
160 |
4
|
ad3antrrr |
|
161 |
25
|
peano2zd |
|
162 |
|
eluz |
|
163 |
162
|
biimpar |
|
164 |
161 26 6 163
|
syl21anc |
|
165 |
|
fzoss2 |
|
166 |
164 165
|
syl |
|
167 |
166
|
ad3antrrr |
|
168 |
|
simplr |
|
169 |
167 168
|
sseldd |
|
170 |
|
simpr |
|
171 |
157 158 159 160 169 170
|
breprexplemb |
|
172 |
136 123 131 156 171
|
breprexplema |
|
173 |
172
|
oveq1d |
|
174 |
128
|
adantr |
|
175 |
152 174
|
mulcld |
|
176 |
127 175
|
fsumcl |
|
177 |
125 132 176
|
fsummulc1 |
|
178 |
127 133 175
|
fsummulc1 |
|
179 |
133
|
adantr |
|
180 |
152 174 179
|
mulassd |
|
181 |
180
|
sumeq2dv |
|
182 |
178 181
|
eqtrd |
|
183 |
182
|
sumeq2dv |
|
184 |
173 177 183
|
3eqtrd |
|
185 |
40
|
a1i |
|
186 |
|
1nn0 |
|
187 |
186
|
a1i |
|
188 |
123 187
|
nn0addcld |
|
189 |
185 117 188 125
|
reprfi |
|
190 |
|
fzofi |
|
191 |
190
|
a1i |
|
192 |
136
|
ad2antrr |
|
193 |
2
|
ad3antrrr |
|
194 |
129
|
ad2antrr |
|
195 |
4
|
ad3antrrr |
|
196 |
166
|
ad2antrr |
|
197 |
196
|
sselda |
|
198 |
40
|
a1i |
|
199 |
117
|
ad2antrr |
|
200 |
188
|
ad2antrr |
|
201 |
|
simplr |
|
202 |
198 199 200 201
|
reprf |
|
203 |
|
simpr |
|
204 |
202 203
|
ffvelrnd |
|
205 |
40 204
|
sseldi |
|
206 |
192 193 194 195 197 205
|
breprexplemb |
|
207 |
191 206
|
fprodcl |
|
208 |
189 132 207
|
fsummulc1 |
|
209 |
154 184 208
|
3eqtr2rd |
|
210 |
209
|
sumeq2dv |
|
211 |
|
oveq1 |
|
212 |
211
|
oveq2d |
|
213 |
212
|
sumeq1d |
|
214 |
|
oveq2 |
|
215 |
214
|
oveq2d |
|
216 |
213 215
|
oveq12d |
|
217 |
216
|
adantr |
|
218 |
217
|
sumeq2dv |
|
219 |
218
|
cbvsumv |
|
220 |
210 219
|
eqtr4di |
|
221 |
5 1
|
nn0mulcld |
|
222 |
|
oveq2 |
|
223 |
222
|
sumeq1d |
|
224 |
|
oveq1 |
|
225 |
224
|
oveq2d |
|
226 |
225
|
oveq2d |
|
227 |
223 226
|
oveq12d |
|
228 |
40
|
a1i |
|
229 |
|
uzssz |
|
230 |
|
simp2 |
|
231 |
229 230
|
sseldi |
|
232 |
5
|
3ad2ant1 |
|
233 |
58
|
3ad2ant1 |
|
234 |
228 231 232 233
|
reprfi |
|
235 |
15
|
a1i |
|
236 |
59
|
3adant2 |
|
237 |
236
|
ad2antrr |
|
238 |
60
|
3adant2 |
|
239 |
238
|
ad2antrr |
|
240 |
61
|
3adant2 |
|
241 |
240
|
ad2antrr |
|
242 |
62
|
3adant2 |
|
243 |
242
|
ad2antrr |
|
244 |
37
|
3ad2ant1 |
|
245 |
244
|
adantr |
|
246 |
245
|
sselda |
|
247 |
40
|
a1i |
|
248 |
231
|
adantr |
|
249 |
232
|
adantr |
|
250 |
|
simpr |
|
251 |
247 248 249 250
|
reprf |
|
252 |
251
|
adantr |
|
253 |
|
simpr |
|
254 |
252 253
|
ffvelrnd |
|
255 |
40 254
|
sseldi |
|
256 |
237 239 241 243 246 255
|
breprexplemb |
|
257 |
235 256
|
fprodcl |
|
258 |
234 257
|
fsumcl |
|
259 |
71
|
3adant2 |
|
260 |
73
|
3adant2 |
|
261 |
236 238 240 242 259 260
|
breprexplemb |
|
262 |
231
|
zcnd |
|
263 |
|
simp3 |
|
264 |
119 263
|
sseldi |
|
265 |
264
|
zcnd |
|
266 |
262 265
|
subnegd |
|
267 |
264
|
znegcld |
|
268 |
|
eluzle |
|
269 |
230 268
|
syl |
|
270 |
|
znn0sub |
|
271 |
270
|
biimpa |
|
272 |
267 231 269 271
|
syl21anc |
|
273 |
266 272
|
eqeltrrd |
|
274 |
240 273
|
expcld |
|
275 |
261 274
|
mulcld |
|
276 |
258 275
|
mulcld |
|
277 |
59
|
adantr |
|
278 |
|
ssidd |
|
279 |
|
fzssz |
|
280 |
|
simpr |
|
281 |
279 280
|
sseldi |
|
282 |
|
simplr |
|
283 |
119 282
|
sseldi |
|
284 |
281 283
|
zsubcld |
|
285 |
5
|
ad2antrr |
|
286 |
27
|
ad2antrr |
|
287 |
277
|
nn0red |
|
288 |
286 287
|
remulcld |
|
289 |
283
|
zred |
|
290 |
221
|
adantr |
|
291 |
290 75
|
nn0addcld |
|
292 |
186
|
a1i |
|
293 |
291 292
|
nn0addcld |
|
294 |
|
fz2ssnn0 |
|
295 |
293 294
|
syl |
|
296 |
295
|
sselda |
|
297 |
296
|
nn0red |
|
298 |
25
|
ad2antrr |
|
299 |
277
|
nn0zd |
|
300 |
298 299
|
zmulcld |
|
301 |
300 283
|
zaddcld |
|
302 |
|
elfzle1 |
|
303 |
280 302
|
syl |
|
304 |
|
zltp1le |
|
305 |
304
|
biimpar |
|
306 |
301 281 303 305
|
syl21anc |
|
307 |
|
ltaddsub |
|
308 |
307
|
biimpa |
|
309 |
288 289 297 306 308
|
syl31anc |
|
310 |
277 278 284 285 309
|
reprgt |
|
311 |
310
|
sumeq1d |
|
312 |
|
sum0 |
|
313 |
311 312
|
eqtrdi |
|
314 |
313
|
oveq1d |
|
315 |
74
|
adantr |
|
316 |
61
|
adantr |
|
317 |
281
|
zcnd |
|
318 |
283
|
zcnd |
|
319 |
317 318
|
npcand |
|
320 |
319 296
|
eqeltrd |
|
321 |
316 320
|
expcld |
|
322 |
315 321
|
mulcld |
|
323 |
322
|
mul02d |
|
324 |
314 323
|
eqtrd |
|
325 |
40
|
a1i |
|
326 |
|
fzossfz |
|
327 |
|
fzssz |
|
328 |
326 327
|
sstri |
|
329 |
|
simpr |
|
330 |
328 329
|
sseldi |
|
331 |
|
simplr |
|
332 |
119 331
|
sseldi |
|
333 |
330 332
|
zsubcld |
|
334 |
5
|
ad2antrr |
|
335 |
333
|
zred |
|
336 |
|
0red |
|
337 |
27
|
ad2antrr |
|
338 |
|
elfzolt2 |
|
339 |
338
|
adantl |
|
340 |
330
|
zred |
|
341 |
332
|
zred |
|
342 |
340 341
|
sublt0d |
|
343 |
339 342
|
mpbird |
|
344 |
63
|
ad2antrr |
|
345 |
335 336 337 343 344
|
ltletrd |
|
346 |
325 333 334 345
|
reprlt |
|
347 |
346
|
sumeq1d |
|
348 |
347 312
|
eqtrdi |
|
349 |
348
|
oveq1d |
|
350 |
74
|
adantr |
|
351 |
61
|
adantr |
|
352 |
340
|
recnd |
|
353 |
341
|
recnd |
|
354 |
352 353
|
npcand |
|
355 |
|
fzo0ssnn0 |
|
356 |
355 329
|
sseldi |
|
357 |
354 356
|
eqeltrd |
|
358 |
351 357
|
expcld |
|
359 |
350 358
|
mulcld |
|
360 |
359
|
mul02d |
|
361 |
349 360
|
eqtrd |
|
362 |
221 1 227 276 324 361
|
fsum2dsub |
|
363 |
|
nn0sscn |
|
364 |
363 5
|
sseldi |
|
365 |
363 1
|
sseldi |
|
366 |
364 365
|
adddirp1d |
|
367 |
366
|
oveq2d |
|
368 |
130 363
|
sstri |
|
369 |
|
simplr |
|
370 |
368 369
|
sseldi |
|
371 |
45 363
|
sstri |
|
372 |
|
simpr |
|
373 |
371 372
|
sseldi |
|
374 |
370 373
|
npcand |
|
375 |
374
|
eqcomd |
|
376 |
375
|
oveq2d |
|
377 |
376
|
oveq2d |
|
378 |
377
|
oveq2d |
|
379 |
378
|
sumeq2dv |
|
380 |
367 379
|
sumeq12dv |
|
381 |
362 380
|
eqtr4d |
|
382 |
107
|
adantlr |
|
383 |
110
|
adantlr |
|
384 |
77
|
adantlr |
|
385 |
384
|
adantr |
|
386 |
382 383 385
|
mulassd |
|
387 |
74
|
ad4ant13 |
|
388 |
76
|
ad4ant13 |
|
389 |
383 387 388
|
mulassd |
|
390 |
387 383 388
|
mulassd |
|
391 |
383 387
|
mulcomd |
|
392 |
391
|
oveq1d |
|
393 |
108
|
adantlr |
|
394 |
75
|
ad4ant13 |
|
395 |
109
|
adantlr |
|
396 |
393 394 395
|
expaddd |
|
397 |
396
|
oveq2d |
|
398 |
390 392 397
|
3eqtr4d |
|
399 |
389 398
|
eqtr3d |
|
400 |
399
|
oveq2d |
|
401 |
386 400
|
eqtrd |
|
402 |
401
|
sumeq2dv |
|
403 |
89
|
adantr |
|
404 |
111
|
adantlr |
|
405 |
403 384 404
|
fsummulc1 |
|
406 |
74
|
adantlr |
|
407 |
61
|
adantlr |
|
408 |
85
|
adantr |
|
409 |
75
|
adantlr |
|
410 |
408 409
|
nn0addcld |
|
411 |
407 410
|
expcld |
|
412 |
406 411
|
mulcld |
|
413 |
403 412 382
|
fsummulc1 |
|
414 |
402 405 413
|
3eqtr4rd |
|
415 |
414
|
sumeq2dv |
|
416 |
415
|
sumeq2dv |
|
417 |
220 381 416
|
3eqtr2rd |
|
418 |
80 113 417
|
3eqtr2d |
|
419 |
12 79 418
|
3eqtrd |
|