Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimirlem22.s |
|
3 |
|
poimirlem9.1 |
|
4 |
|
poimirlem9.2 |
|
5 |
|
poimirlem7.3 |
|
6 |
|
elrabi |
|
7 |
6 2
|
eleq2s |
|
8 |
3 7
|
syl |
|
9 |
|
xp1st |
|
10 |
8 9
|
syl |
|
11 |
|
xp2nd |
|
12 |
10 11
|
syl |
|
13 |
|
fvex |
|
14 |
|
f1oeq1 |
|
15 |
13 14
|
elab |
|
16 |
12 15
|
sylib |
|
17 |
|
f1of |
|
18 |
16 17
|
syl |
|
19 |
|
elfznn |
|
20 |
4 19
|
syl |
|
21 |
20
|
peano2nnd |
|
22 |
21
|
peano2nnd |
|
23 |
|
nnuz |
|
24 |
22 23
|
eleqtrdi |
|
25 |
|
fzss1 |
|
26 |
24 25
|
syl |
|
27 |
26 5
|
sseldd |
|
28 |
18 27
|
ffvelrnd |
|
29 |
|
xp1st |
|
30 |
10 29
|
syl |
|
31 |
|
elmapfn |
|
32 |
30 31
|
syl |
|
33 |
32
|
adantr |
|
34 |
|
1ex |
|
35 |
|
fnconstg |
|
36 |
34 35
|
ax-mp |
|
37 |
|
c0ex |
|
38 |
|
fnconstg |
|
39 |
37 38
|
ax-mp |
|
40 |
36 39
|
pm3.2i |
|
41 |
|
dff1o3 |
|
42 |
41
|
simprbi |
|
43 |
16 42
|
syl |
|
44 |
|
imain |
|
45 |
43 44
|
syl |
|
46 |
5
|
elfzelzd |
|
47 |
46
|
zred |
|
48 |
47
|
ltm1d |
|
49 |
|
fzdisj |
|
50 |
48 49
|
syl |
|
51 |
50
|
imaeq2d |
|
52 |
|
ima0 |
|
53 |
51 52
|
eqtrdi |
|
54 |
45 53
|
eqtr3d |
|
55 |
|
fnun |
|
56 |
40 54 55
|
sylancr |
|
57 |
46
|
zcnd |
|
58 |
|
npcan1 |
|
59 |
57 58
|
syl |
|
60 |
|
1red |
|
61 |
22
|
nnred |
|
62 |
21
|
nnred |
|
63 |
21
|
nnge1d |
|
64 |
62
|
ltp1d |
|
65 |
60 62 61 63 64
|
lelttrd |
|
66 |
|
elfzle1 |
|
67 |
5 66
|
syl |
|
68 |
60 61 47 65 67
|
ltletrd |
|
69 |
60 47 68
|
ltled |
|
70 |
|
elnnz1 |
|
71 |
46 69 70
|
sylanbrc |
|
72 |
71 23
|
eleqtrdi |
|
73 |
59 72
|
eqeltrd |
|
74 |
|
peano2zm |
|
75 |
46 74
|
syl |
|
76 |
|
uzid |
|
77 |
|
peano2uz |
|
78 |
75 76 77
|
3syl |
|
79 |
59 78
|
eqeltrrd |
|
80 |
|
uzss |
|
81 |
79 80
|
syl |
|
82 |
|
elfzuz3 |
|
83 |
5 82
|
syl |
|
84 |
81 83
|
sseldd |
|
85 |
|
fzsplit2 |
|
86 |
73 84 85
|
syl2anc |
|
87 |
59
|
oveq1d |
|
88 |
87
|
uneq2d |
|
89 |
86 88
|
eqtrd |
|
90 |
89
|
imaeq2d |
|
91 |
|
imaundi |
|
92 |
90 91
|
eqtrdi |
|
93 |
|
f1ofo |
|
94 |
16 93
|
syl |
|
95 |
|
foima |
|
96 |
94 95
|
syl |
|
97 |
92 96
|
eqtr3d |
|
98 |
97
|
fneq2d |
|
99 |
56 98
|
mpbid |
|
100 |
99
|
adantr |
|
101 |
|
ovexd |
|
102 |
|
inidm |
|
103 |
|
eqidd |
|
104 |
|
imaundi |
|
105 |
|
fzpred |
|
106 |
83 105
|
syl |
|
107 |
106
|
imaeq2d |
|
108 |
|
f1ofn |
|
109 |
16 108
|
syl |
|
110 |
|
fnsnfv |
|
111 |
109 27 110
|
syl2anc |
|
112 |
111
|
uneq1d |
|
113 |
104 107 112
|
3eqtr4a |
|
114 |
113
|
xpeq1d |
|
115 |
|
xpundir |
|
116 |
114 115
|
eqtrdi |
|
117 |
116
|
uneq2d |
|
118 |
|
un12 |
|
119 |
117 118
|
eqtrdi |
|
120 |
119
|
fveq1d |
|
121 |
120
|
ad2antrr |
|
122 |
|
fnconstg |
|
123 |
37 122
|
ax-mp |
|
124 |
36 123
|
pm3.2i |
|
125 |
|
imain |
|
126 |
43 125
|
syl |
|
127 |
75
|
zred |
|
128 |
|
peano2re |
|
129 |
47 128
|
syl |
|
130 |
47
|
ltp1d |
|
131 |
127 47 129 48 130
|
lttrd |
|
132 |
|
fzdisj |
|
133 |
131 132
|
syl |
|
134 |
133
|
imaeq2d |
|
135 |
134 52
|
eqtrdi |
|
136 |
126 135
|
eqtr3d |
|
137 |
|
fnun |
|
138 |
124 136 137
|
sylancr |
|
139 |
|
imaundi |
|
140 |
|
imadif |
|
141 |
43 140
|
syl |
|
142 |
|
fzsplit |
|
143 |
27 142
|
syl |
|
144 |
143
|
difeq1d |
|
145 |
|
difundir |
|
146 |
|
fzsplit2 |
|
147 |
73 79 146
|
syl2anc |
|
148 |
59
|
oveq1d |
|
149 |
|
fzsn |
|
150 |
46 149
|
syl |
|
151 |
148 150
|
eqtrd |
|
152 |
151
|
uneq2d |
|
153 |
147 152
|
eqtrd |
|
154 |
153
|
difeq1d |
|
155 |
|
difun2 |
|
156 |
127 47
|
ltnled |
|
157 |
48 156
|
mpbid |
|
158 |
|
elfzle2 |
|
159 |
157 158
|
nsyl |
|
160 |
|
difsn |
|
161 |
159 160
|
syl |
|
162 |
155 161
|
syl5eq |
|
163 |
154 162
|
eqtrd |
|
164 |
47 129
|
ltnled |
|
165 |
130 164
|
mpbid |
|
166 |
|
elfzle1 |
|
167 |
165 166
|
nsyl |
|
168 |
|
difsn |
|
169 |
167 168
|
syl |
|
170 |
163 169
|
uneq12d |
|
171 |
145 170
|
syl5eq |
|
172 |
144 171
|
eqtrd |
|
173 |
172
|
imaeq2d |
|
174 |
111
|
eqcomd |
|
175 |
96 174
|
difeq12d |
|
176 |
141 173 175
|
3eqtr3d |
|
177 |
139 176
|
eqtr3id |
|
178 |
177
|
fneq2d |
|
179 |
138 178
|
mpbid |
|
180 |
|
eldifsn |
|
181 |
180
|
biimpri |
|
182 |
181
|
ancoms |
|
183 |
|
disjdif |
|
184 |
|
fnconstg |
|
185 |
37 184
|
ax-mp |
|
186 |
|
fvun2 |
|
187 |
185 186
|
mp3an1 |
|
188 |
183 187
|
mpanr1 |
|
189 |
179 182 188
|
syl2an |
|
190 |
189
|
anassrs |
|
191 |
121 190
|
eqtrd |
|
192 |
33 100 101 101 102 103 191
|
ofval |
|
193 |
|
fnconstg |
|
194 |
34 193
|
ax-mp |
|
195 |
194 123
|
pm3.2i |
|
196 |
|
imain |
|
197 |
43 196
|
syl |
|
198 |
|
fzdisj |
|
199 |
130 198
|
syl |
|
200 |
199
|
imaeq2d |
|
201 |
200 52
|
eqtrdi |
|
202 |
197 201
|
eqtr3d |
|
203 |
|
fnun |
|
204 |
195 202 203
|
sylancr |
|
205 |
143
|
imaeq2d |
|
206 |
|
imaundi |
|
207 |
205 206
|
eqtrdi |
|
208 |
207 96
|
eqtr3d |
|
209 |
208
|
fneq2d |
|
210 |
204 209
|
mpbid |
|
211 |
210
|
adantr |
|
212 |
|
imaundi |
|
213 |
153
|
imaeq2d |
|
214 |
111
|
uneq2d |
|
215 |
212 213 214
|
3eqtr4a |
|
216 |
215
|
xpeq1d |
|
217 |
|
xpundir |
|
218 |
216 217
|
eqtrdi |
|
219 |
218
|
uneq1d |
|
220 |
|
un23 |
|
221 |
220
|
equncomi |
|
222 |
219 221
|
eqtrdi |
|
223 |
222
|
fveq1d |
|
224 |
223
|
ad2antrr |
|
225 |
|
fnconstg |
|
226 |
34 225
|
ax-mp |
|
227 |
|
fvun2 |
|
228 |
226 227
|
mp3an1 |
|
229 |
183 228
|
mpanr1 |
|
230 |
179 182 229
|
syl2an |
|
231 |
230
|
anassrs |
|
232 |
224 231
|
eqtrd |
|
233 |
33 211 101 101 102 103 232
|
ofval |
|
234 |
192 233
|
eqtr4d |
|
235 |
234
|
an32s |
|
236 |
235
|
anasss |
|
237 |
|
fveq2 |
|
238 |
237
|
breq2d |
|
239 |
238
|
ifbid |
|
240 |
239
|
csbeq1d |
|
241 |
|
2fveq3 |
|
242 |
|
2fveq3 |
|
243 |
242
|
imaeq1d |
|
244 |
243
|
xpeq1d |
|
245 |
242
|
imaeq1d |
|
246 |
245
|
xpeq1d |
|
247 |
244 246
|
uneq12d |
|
248 |
241 247
|
oveq12d |
|
249 |
248
|
csbeq2dv |
|
250 |
240 249
|
eqtrd |
|
251 |
250
|
mpteq2dv |
|
252 |
251
|
eqeq2d |
|
253 |
252 2
|
elrab2 |
|
254 |
253
|
simprbi |
|
255 |
3 254
|
syl |
|
256 |
|
breq1 |
|
257 |
256
|
adantl |
|
258 |
|
oveq1 |
|
259 |
|
sub1m1 |
|
260 |
57 259
|
syl |
|
261 |
260
|
oveq1d |
|
262 |
75
|
zcnd |
|
263 |
|
npcan1 |
|
264 |
262 263
|
syl |
|
265 |
261 264
|
eqtr3d |
|
266 |
258 265
|
sylan9eqr |
|
267 |
257 266
|
ifbieq2d |
|
268 |
20
|
nncnd |
|
269 |
|
add1p1 |
|
270 |
268 269
|
syl |
|
271 |
270 67
|
eqbrtrrd |
|
272 |
20
|
nnred |
|
273 |
|
2re |
|
274 |
|
leaddsub |
|
275 |
273 274
|
mp3an2 |
|
276 |
272 47 275
|
syl2anc |
|
277 |
60 47
|
posdifd |
|
278 |
68 277
|
mpbid |
|
279 |
|
elnnz |
|
280 |
75 278 279
|
sylanbrc |
|
281 |
|
nnm1nn0 |
|
282 |
280 281
|
syl |
|
283 |
260 282
|
eqeltrrd |
|
284 |
283
|
nn0red |
|
285 |
272 284
|
lenltd |
|
286 |
276 285
|
bitrd |
|
287 |
271 286
|
mpbid |
|
288 |
287
|
iffalsed |
|
289 |
288
|
adantr |
|
290 |
267 289
|
eqtrd |
|
291 |
290
|
csbeq1d |
|
292 |
|
oveq2 |
|
293 |
292
|
imaeq2d |
|
294 |
293
|
xpeq1d |
|
295 |
294
|
adantl |
|
296 |
|
oveq1 |
|
297 |
296 59
|
sylan9eqr |
|
298 |
297
|
oveq1d |
|
299 |
298
|
imaeq2d |
|
300 |
299
|
xpeq1d |
|
301 |
295 300
|
uneq12d |
|
302 |
301
|
oveq2d |
|
303 |
75 302
|
csbied |
|
304 |
303
|
adantr |
|
305 |
291 304
|
eqtrd |
|
306 |
|
nnm1nn0 |
|
307 |
1 306
|
syl |
|
308 |
1
|
nnred |
|
309 |
47
|
lem1d |
|
310 |
|
elfzle2 |
|
311 |
5 310
|
syl |
|
312 |
127 47 308 309 311
|
letrd |
|
313 |
127 308 60 312
|
lesub1dd |
|
314 |
260 313
|
eqbrtrrd |
|
315 |
|
elfz2nn0 |
|
316 |
283 307 314 315
|
syl3anbrc |
|
317 |
|
ovexd |
|
318 |
255 305 316 317
|
fvmptd |
|
319 |
318
|
fveq1d |
|
320 |
319
|
adantr |
|
321 |
|
breq1 |
|
322 |
321
|
adantl |
|
323 |
|
oveq1 |
|
324 |
323 59
|
sylan9eqr |
|
325 |
322 324
|
ifbieq2d |
|
326 |
62
|
lep1d |
|
327 |
62 61 47 326 67
|
letrd |
|
328 |
|
1re |
|
329 |
|
leaddsub |
|
330 |
328 329
|
mp3an2 |
|
331 |
272 47 330
|
syl2anc |
|
332 |
272 127
|
lenltd |
|
333 |
331 332
|
bitrd |
|
334 |
327 333
|
mpbid |
|
335 |
334
|
iffalsed |
|
336 |
335
|
adantr |
|
337 |
325 336
|
eqtrd |
|
338 |
337
|
csbeq1d |
|
339 |
|
oveq2 |
|
340 |
339
|
imaeq2d |
|
341 |
340
|
xpeq1d |
|
342 |
|
oveq1 |
|
343 |
342
|
oveq1d |
|
344 |
343
|
imaeq2d |
|
345 |
344
|
xpeq1d |
|
346 |
341 345
|
uneq12d |
|
347 |
346
|
oveq2d |
|
348 |
347
|
adantl |
|
349 |
5 348
|
csbied |
|
350 |
349
|
adantr |
|
351 |
338 350
|
eqtrd |
|
352 |
280
|
nnnn0d |
|
353 |
47 308 60 311
|
lesub1dd |
|
354 |
|
elfz2nn0 |
|
355 |
352 307 353 354
|
syl3anbrc |
|
356 |
|
ovexd |
|
357 |
255 351 355 356
|
fvmptd |
|
358 |
357
|
fveq1d |
|
359 |
358
|
adantr |
|
360 |
236 320 359
|
3eqtr4d |
|
361 |
360
|
expr |
|
362 |
361
|
necon1d |
|
363 |
|
elmapi |
|
364 |
30 363
|
syl |
|
365 |
364 28
|
ffvelrnd |
|
366 |
|
elfzonn0 |
|
367 |
365 366
|
syl |
|
368 |
367
|
nn0red |
|
369 |
368
|
ltp1d |
|
370 |
368 369
|
ltned |
|
371 |
318
|
fveq1d |
|
372 |
|
ovexd |
|
373 |
|
eqidd |
|
374 |
|
fzss1 |
|
375 |
72 374
|
syl |
|
376 |
|
eluzfz1 |
|
377 |
83 376
|
syl |
|
378 |
|
fnfvima |
|
379 |
109 375 377 378
|
syl3anc |
|
380 |
|
fvun2 |
|
381 |
36 39 380
|
mp3an12 |
|
382 |
54 379 381
|
syl2anc |
|
383 |
37
|
fvconst2 |
|
384 |
379 383
|
syl |
|
385 |
382 384
|
eqtrd |
|
386 |
385
|
adantr |
|
387 |
32 99 372 372 102 373 386
|
ofval |
|
388 |
28 387
|
mpdan |
|
389 |
367
|
nn0cnd |
|
390 |
389
|
addid1d |
|
391 |
371 388 390
|
3eqtrd |
|
392 |
357
|
fveq1d |
|
393 |
|
fzss2 |
|
394 |
83 393
|
syl |
|
395 |
|
elfz1end |
|
396 |
71 395
|
sylib |
|
397 |
|
fnfvima |
|
398 |
109 394 396 397
|
syl3anc |
|
399 |
|
fvun1 |
|
400 |
194 123 399
|
mp3an12 |
|
401 |
202 398 400
|
syl2anc |
|
402 |
34
|
fvconst2 |
|
403 |
398 402
|
syl |
|
404 |
401 403
|
eqtrd |
|
405 |
404
|
adantr |
|
406 |
32 210 372 372 102 373 405
|
ofval |
|
407 |
28 406
|
mpdan |
|
408 |
392 407
|
eqtrd |
|
409 |
370 391 408
|
3netr4d |
|
410 |
|
fveq2 |
|
411 |
|
fveq2 |
|
412 |
410 411
|
neeq12d |
|
413 |
409 412
|
syl5ibrcom |
|
414 |
413
|
adantr |
|
415 |
362 414
|
impbid |
|
416 |
28 415
|
riota5 |
|