Step |
Hyp |
Ref |
Expression |
1 |
|
nn0uz |
|
2 |
|
0zd |
|
3 |
|
eqeq1 |
|
4 |
|
oveq2 |
|
5 |
3 4
|
ifbieq2d |
|
6 |
|
oveq2 |
|
7 |
5 6
|
oveq12d |
|
8 |
|
eqid |
|
9 |
|
ovex |
|
10 |
7 8 9
|
fvmpt |
|
11 |
10
|
adantl |
|
12 |
|
0cnd |
|
13 |
|
simpr |
|
14 |
|
elnn0 |
|
15 |
13 14
|
sylib |
|
16 |
15
|
ord |
|
17 |
16
|
con1d |
|
18 |
17
|
imp |
|
19 |
18
|
nnrecred |
|
20 |
19
|
recnd |
|
21 |
12 20
|
ifclda |
|
22 |
|
expcl |
|
23 |
22
|
adantlr |
|
24 |
21 23
|
mulcld |
|
25 |
|
logtayllem |
|
26 |
1 2 11 24 25
|
isumclim2 |
|
27 |
|
simpl |
|
28 |
|
0cn |
|
29 |
|
eqid |
|
30 |
29
|
cnmetdval |
|
31 |
27 28 30
|
sylancl |
|
32 |
|
subid1 |
|
33 |
32
|
adantr |
|
34 |
33
|
fveq2d |
|
35 |
31 34
|
eqtrd |
|
36 |
|
simpr |
|
37 |
35 36
|
eqbrtrd |
|
38 |
|
cnxmet |
|
39 |
|
1xr |
|
40 |
|
elbl3 |
|
41 |
38 39 40
|
mpanl12 |
|
42 |
28 27 41
|
sylancr |
|
43 |
37 42
|
mpbird |
|
44 |
|
tru |
|
45 |
|
eqid |
|
46 |
|
0cnd |
|
47 |
39
|
a1i |
|
48 |
|
ax-1cn |
|
49 |
|
blssm |
|
50 |
38 28 39 49
|
mp3an |
|
51 |
50
|
sseli |
|
52 |
|
subcl |
|
53 |
48 51 52
|
sylancr |
|
54 |
51
|
abscld |
|
55 |
29
|
cnmetdval |
|
56 |
51 28 55
|
sylancl |
|
57 |
51
|
subid1d |
|
58 |
57
|
fveq2d |
|
59 |
56 58
|
eqtrd |
|
60 |
|
elbl3 |
|
61 |
38 39 60
|
mpanl12 |
|
62 |
28 51 61
|
sylancr |
|
63 |
62
|
ibi |
|
64 |
59 63
|
eqbrtrrd |
|
65 |
54 64
|
gtned |
|
66 |
|
abs1 |
|
67 |
|
fveq2 |
|
68 |
66 67
|
syl5eqr |
|
69 |
68
|
necon3i |
|
70 |
65 69
|
syl |
|
71 |
|
subeq0 |
|
72 |
71
|
necon3bid |
|
73 |
48 51 72
|
sylancr |
|
74 |
70 73
|
mpbird |
|
75 |
53 74
|
logcld |
|
76 |
75
|
negcld |
|
77 |
76
|
adantl |
|
78 |
77
|
fmpttd |
|
79 |
51
|
absge0d |
|
80 |
54
|
rexrd |
|
81 |
|
peano2re |
|
82 |
54 81
|
syl |
|
83 |
82
|
rehalfcld |
|
84 |
83
|
rexrd |
|
85 |
|
iccssxr |
|
86 |
|
eqeq1 |
|
87 |
|
oveq2 |
|
88 |
86 87
|
ifbieq2d |
|
89 |
|
eqid |
|
90 |
|
c0ex |
|
91 |
|
ovex |
|
92 |
90 91
|
ifex |
|
93 |
88 89 92
|
fvmpt |
|
94 |
93
|
eqcomd |
|
95 |
94
|
oveq1d |
|
96 |
95
|
mpteq2ia |
|
97 |
96
|
mpteq2i |
|
98 |
|
0cnd |
|
99 |
|
nn0cn |
|
100 |
99
|
adantl |
|
101 |
|
neqne |
|
102 |
|
reccl |
|
103 |
100 101 102
|
syl2an |
|
104 |
98 103
|
ifclda |
|
105 |
104
|
fmpttd |
|
106 |
|
recn |
|
107 |
|
oveq1 |
|
108 |
107
|
oveq2d |
|
109 |
108
|
mpteq2dv |
|
110 |
|
eqid |
|
111 |
|
nn0ex |
|
112 |
111
|
mptex |
|
113 |
109 110 112
|
fvmpt |
|
114 |
106 113
|
syl |
|
115 |
114
|
eqcomd |
|
116 |
115
|
seqeq3d |
|
117 |
116
|
eleq1d |
|
118 |
117
|
rabbiia |
|
119 |
118
|
supeq1i |
|
120 |
97 105 119
|
radcnvcl |
|
121 |
85 120
|
sseldi |
|
122 |
44 121
|
mp1i |
|
123 |
|
1re |
|
124 |
|
avglt1 |
|
125 |
54 123 124
|
sylancl |
|
126 |
64 125
|
mpbid |
|
127 |
|
0red |
|
128 |
127 54 83 79 126
|
lelttrd |
|
129 |
127 83 128
|
ltled |
|
130 |
83 129
|
absidd |
|
131 |
44 105
|
mp1i |
|
132 |
83
|
recnd |
|
133 |
|
oveq1 |
|
134 |
133
|
oveq2d |
|
135 |
134
|
mpteq2dv |
|
136 |
111
|
mptex |
|
137 |
135 110 136
|
fvmpt |
|
138 |
132 137
|
syl |
|
139 |
138
|
seqeq3d |
|
140 |
|
avglt2 |
|
141 |
54 123 140
|
sylancl |
|
142 |
64 141
|
mpbid |
|
143 |
130 142
|
eqbrtrd |
|
144 |
|
logtayllem |
|
145 |
132 143 144
|
syl2anc |
|
146 |
139 145
|
eqeltrd |
|
147 |
97 131 119 132 146
|
radcnvle |
|
148 |
130 147
|
eqbrtrrd |
|
149 |
80 84 122 126 148
|
xrltletrd |
|
150 |
|
0re |
|
151 |
|
elico2 |
|
152 |
150 122 151
|
sylancr |
|
153 |
54 79 149 152
|
mpbir3and |
|
154 |
|
absf |
|
155 |
|
ffn |
|
156 |
|
elpreima |
|
157 |
154 155 156
|
mp2b |
|
158 |
51 153 157
|
sylanbrc |
|
159 |
|
cnvimass |
|
160 |
154
|
fdmi |
|
161 |
159 160
|
sseqtri |
|
162 |
161
|
sseli |
|
163 |
|
oveq1 |
|
164 |
163
|
oveq2d |
|
165 |
164
|
mpteq2dv |
|
166 |
111
|
mptex |
|
167 |
165 110 166
|
fvmpt |
|
168 |
167
|
adantr |
|
169 |
168
|
fveq1d |
|
170 |
|
eqeq1 |
|
171 |
|
oveq2 |
|
172 |
170 171
|
ifbieq2d |
|
173 |
|
oveq2 |
|
174 |
172 173
|
oveq12d |
|
175 |
|
eqid |
|
176 |
|
ovex |
|
177 |
174 175 176
|
fvmpt |
|
178 |
177
|
adantl |
|
179 |
169 178
|
eqtr2d |
|
180 |
179
|
sumeq2dv |
|
181 |
162 180
|
syl |
|
182 |
181
|
mpteq2ia |
|
183 |
|
eqid |
|
184 |
|
eqid |
|
185 |
97 182 105 119 183 184
|
psercn |
|
186 |
|
cncff |
|
187 |
185 186
|
syl |
|
188 |
187
|
fvmptelrn |
|
189 |
158 188
|
sylan2 |
|
190 |
189
|
fmpttd |
|
191 |
|
cnelprrecn |
|
192 |
191
|
a1i |
|
193 |
75
|
adantl |
|
194 |
|
ovexd |
|
195 |
29
|
cnmetdval |
|
196 |
48 53 195
|
sylancr |
|
197 |
|
nncan |
|
198 |
48 51 197
|
sylancr |
|
199 |
198
|
fveq2d |
|
200 |
196 199
|
eqtrd |
|
201 |
200 64
|
eqbrtrd |
|
202 |
|
elbl |
|
203 |
38 48 39 202
|
mp3an |
|
204 |
53 201 203
|
sylanbrc |
|
205 |
204
|
adantl |
|
206 |
|
neg1cn |
|
207 |
206
|
a1i |
|
208 |
|
eqid |
|
209 |
208
|
dvlog2lem |
|
210 |
209
|
sseli |
|
211 |
210
|
eldifad |
|
212 |
|
eqid |
|
213 |
212
|
logdmn0 |
|
214 |
210 213
|
syl |
|
215 |
211 214
|
logcld |
|
216 |
215
|
adantl |
|
217 |
|
ovexd |
|
218 |
|
simpr |
|
219 |
48 218 52
|
sylancr |
|
220 |
206
|
a1i |
|
221 |
|
1cnd |
|
222 |
|
0cnd |
|
223 |
|
1cnd |
|
224 |
192 223
|
dvmptc |
|
225 |
192
|
dvmptid |
|
226 |
192 221 222 224 218 221 225
|
dvmptsub |
|
227 |
|
df-neg |
|
228 |
227
|
mpteq2i |
|
229 |
226 228
|
eqtr4di |
|
230 |
50
|
a1i |
|
231 |
|
eqid |
|
232 |
231
|
cnfldtopon |
|
233 |
232
|
toponrestid |
|
234 |
231
|
cnfldtopn |
|
235 |
234
|
blopn |
|
236 |
38 28 39 235
|
mp3an |
|
237 |
236
|
a1i |
|
238 |
192 219 220 229 230 233 231 237
|
dvmptres |
|
239 |
208
|
dvlog2 |
|
240 |
|
logf1o |
|
241 |
|
f1of |
|
242 |
240 241
|
ax-mp |
|
243 |
212
|
logdmss |
|
244 |
209 243
|
sstri |
|
245 |
|
fssres |
|
246 |
242 244 245
|
mp2an |
|
247 |
246
|
a1i |
|
248 |
247
|
feqmptd |
|
249 |
|
fvres |
|
250 |
249
|
mpteq2ia |
|
251 |
248 250
|
eqtrdi |
|
252 |
251
|
oveq2d |
|
253 |
239 252
|
syl5reqr |
|
254 |
|
fveq2 |
|
255 |
|
oveq2 |
|
256 |
192 192 205 207 216 217 238 253 254 255
|
dvmptco |
|
257 |
192 193 194 256
|
dvmptneg |
|
258 |
53 74
|
reccld |
|
259 |
|
mulcom |
|
260 |
258 206 259
|
sylancl |
|
261 |
258
|
mulm1d |
|
262 |
260 261
|
eqtrd |
|
263 |
262
|
negeqd |
|
264 |
258
|
negnegd |
|
265 |
263 264
|
eqtrd |
|
266 |
265
|
mpteq2ia |
|
267 |
257 266
|
eqtrdi |
|
268 |
267
|
dmeqd |
|
269 |
|
dmmptg |
|
270 |
|
ovexd |
|
271 |
269 270
|
mprg |
|
272 |
268 271
|
eqtrdi |
|
273 |
|
sumex |
|
274 |
273
|
a1i |
|
275 |
|
fveq2 |
|
276 |
275
|
cbvsumv |
|
277 |
181 276
|
eqtrdi |
|
278 |
277
|
mpteq2ia |
|
279 |
|
eqid |
|
280 |
97 278 105 119 183 184 279
|
pserdv2 |
|
281 |
158
|
ssriv |
|
282 |
281
|
a1i |
|
283 |
192 188 274 280 282 233 231 237
|
dvmptres |
|
284 |
|
nnnn0 |
|
285 |
284
|
adantl |
|
286 |
|
eqeq1 |
|
287 |
|
oveq2 |
|
288 |
286 287
|
ifbieq2d |
|
289 |
|
ovex |
|
290 |
90 289
|
ifex |
|
291 |
288 89 290
|
fvmpt |
|
292 |
285 291
|
syl |
|
293 |
|
nnne0 |
|
294 |
293
|
adantl |
|
295 |
294
|
neneqd |
|
296 |
295
|
iffalsed |
|
297 |
292 296
|
eqtrd |
|
298 |
297
|
oveq2d |
|
299 |
|
nncn |
|
300 |
299
|
adantl |
|
301 |
300 294
|
recidd |
|
302 |
298 301
|
eqtrd |
|
303 |
302
|
oveq1d |
|
304 |
|
nnm1nn0 |
|
305 |
|
expcl |
|
306 |
51 304 305
|
syl2an |
|
307 |
306
|
mulid2d |
|
308 |
303 307
|
eqtrd |
|
309 |
308
|
sumeq2dv |
|
310 |
|
nnuz |
|
311 |
|
1e0p1 |
|
312 |
311
|
fveq2i |
|
313 |
310 312
|
eqtri |
|
314 |
|
oveq1 |
|
315 |
314
|
oveq2d |
|
316 |
|
1zzd |
|
317 |
|
0zd |
|
318 |
1 313 315 316 317 306
|
isumshft |
|
319 |
|
pncan2 |
|
320 |
48 99 319
|
sylancr |
|
321 |
320
|
oveq2d |
|
322 |
321
|
sumeq2i |
|
323 |
318 322
|
eqtrdi |
|
324 |
|
geoisum |
|
325 |
51 64 324
|
syl2anc |
|
326 |
309 323 325
|
3eqtrd |
|
327 |
326
|
mpteq2ia |
|
328 |
283 327
|
eqtrdi |
|
329 |
267 328
|
eqtr4d |
|
330 |
|
1rp |
|
331 |
|
blcntr |
|
332 |
38 28 330 331
|
mp3an |
|
333 |
332
|
a1i |
|
334 |
|
oveq2 |
|
335 |
|
1m0e1 |
|
336 |
334 335
|
eqtrdi |
|
337 |
336
|
fveq2d |
|
338 |
|
log1 |
|
339 |
337 338
|
eqtrdi |
|
340 |
339
|
negeqd |
|
341 |
|
neg0 |
|
342 |
340 341
|
eqtrdi |
|
343 |
|
eqid |
|
344 |
342 343 90
|
fvmpt |
|
345 |
332 344
|
mp1i |
|
346 |
|
oveq1 |
|
347 |
346
|
eqeq1d |
|
348 |
|
oveq1 |
|
349 |
348
|
eqeq1d |
|
350 |
|
simpll |
|
351 |
350 28
|
eqeltrdi |
|
352 |
|
simplr |
|
353 |
351 352
|
expcld |
|
354 |
353
|
mul02d |
|
355 |
|
simpll |
|
356 |
355
|
oveq1d |
|
357 |
|
simpr |
|
358 |
357 14
|
sylib |
|
359 |
358
|
ord |
|
360 |
359
|
con1d |
|
361 |
360
|
imp |
|
362 |
361
|
0expd |
|
363 |
356 362
|
eqtrd |
|
364 |
363
|
oveq2d |
|
365 |
361
|
nnrecred |
|
366 |
365
|
recnd |
|
367 |
366
|
mul01d |
|
368 |
364 367
|
eqtrd |
|
369 |
347 349 354 368
|
ifbothda |
|
370 |
369
|
sumeq2dv |
|
371 |
1
|
eqimssi |
|
372 |
371
|
orci |
|
373 |
|
sumz |
|
374 |
372 373
|
ax-mp |
|
375 |
370 374
|
eqtrdi |
|
376 |
|
eqid |
|
377 |
375 376 90
|
fvmpt |
|
378 |
332 377
|
mp1i |
|
379 |
345 378
|
eqtr4d |
|
380 |
45 46 47 78 190 272 329 333 379
|
dv11cn |
|
381 |
380
|
fveq1d |
|
382 |
44 381
|
mp1i |
|
383 |
|
oveq2 |
|
384 |
383
|
fveq2d |
|
385 |
384
|
negeqd |
|
386 |
|
negex |
|
387 |
385 343 386
|
fvmpt |
|
388 |
|
oveq1 |
|
389 |
388
|
oveq2d |
|
390 |
389
|
sumeq2sdv |
|
391 |
|
sumex |
|
392 |
390 376 391
|
fvmpt |
|
393 |
382 387 392
|
3eqtr3d |
|
394 |
43 393
|
syl |
|
395 |
26 394
|
breqtrrd |
|
396 |
|
seqex |
|
397 |
396
|
a1i |
|
398 |
|
seqex |
|
399 |
398
|
a1i |
|
400 |
|
1zzd |
|
401 |
|
elnnuz |
|
402 |
|
fvres |
|
403 |
401 402
|
sylbi |
|
404 |
403
|
eqcomd |
|
405 |
|
addid2 |
|
406 |
405
|
adantl |
|
407 |
|
0cnd |
|
408 |
|
1eluzge0 |
|
409 |
408
|
a1i |
|
410 |
|
0cnd |
|
411 |
|
nn0cn |
|
412 |
411
|
adantl |
|
413 |
|
neqne |
|
414 |
|
reccl |
|
415 |
412 413 414
|
syl2an |
|
416 |
410 415
|
ifclda |
|
417 |
|
expcl |
|
418 |
417
|
adantlr |
|
419 |
416 418
|
mulcld |
|
420 |
419
|
fmpttd |
|
421 |
|
1nn0 |
|
422 |
|
ffvelrn |
|
423 |
420 421 422
|
sylancl |
|
424 |
|
elfz1eq |
|
425 |
|
1m1e0 |
|
426 |
425
|
oveq2i |
|
427 |
424 426
|
eleq2s |
|
428 |
427
|
fveq2d |
|
429 |
|
0nn0 |
|
430 |
|
iftrue |
|
431 |
|
oveq2 |
|
432 |
430 431
|
oveq12d |
|
433 |
|
ovex |
|
434 |
432 8 433
|
fvmpt |
|
435 |
429 434
|
ax-mp |
|
436 |
|
expcl |
|
437 |
27 429 436
|
sylancl |
|
438 |
437
|
mul02d |
|
439 |
435 438
|
syl5eq |
|
440 |
428 439
|
sylan9eqr |
|
441 |
406 407 409 423 440
|
seqid |
|
442 |
293
|
adantl |
|
443 |
442
|
neneqd |
|
444 |
443
|
iffalsed |
|
445 |
444
|
oveq1d |
|
446 |
284 23
|
sylan2 |
|
447 |
299
|
adantl |
|
448 |
446 447 442
|
divrec2d |
|
449 |
445 448
|
eqtr4d |
|
450 |
284 11
|
sylan2 |
|
451 |
|
id |
|
452 |
6 451
|
oveq12d |
|
453 |
|
eqid |
|
454 |
|
ovex |
|
455 |
452 453 454
|
fvmpt |
|
456 |
455
|
adantl |
|
457 |
449 450 456
|
3eqtr4d |
|
458 |
401 457
|
sylan2br |
|
459 |
400 458
|
seqfeq |
|
460 |
441 459
|
eqtrd |
|
461 |
460
|
fveq1d |
|
462 |
404 461
|
sylan9eqr |
|
463 |
310 397 399 400 462
|
climeq |
|
464 |
395 463
|
mpbid |
|