Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimirlem22.s |
|
3 |
|
poimirlem9.1 |
|
4 |
|
poimirlem9.2 |
|
5 |
|
poimirlem6.3 |
|
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
|
nnzd |
|
22 |
|
peano2zm |
|
23 |
21 22
|
syl |
|
24 |
1
|
nnzd |
|
25 |
23
|
zred |
|
26 |
20
|
nnred |
|
27 |
1
|
nnred |
|
28 |
26
|
lem1d |
|
29 |
|
nnm1nn0 |
|
30 |
1 29
|
syl |
|
31 |
30
|
nn0red |
|
32 |
|
elfzle2 |
|
33 |
4 32
|
syl |
|
34 |
27
|
lem1d |
|
35 |
26 31 27 33 34
|
letrd |
|
36 |
25 26 27 28 35
|
letrd |
|
37 |
|
eluz2 |
|
38 |
23 24 36 37
|
syl3anbrc |
|
39 |
|
fzss2 |
|
40 |
38 39
|
syl |
|
41 |
40 5
|
sseldd |
|
42 |
18 41
|
ffvelrnd |
|
43 |
|
xp1st |
|
44 |
10 43
|
syl |
|
45 |
|
elmapfn |
|
46 |
44 45
|
syl |
|
47 |
46
|
adantr |
|
48 |
|
1ex |
|
49 |
|
fnconstg |
|
50 |
48 49
|
ax-mp |
|
51 |
|
c0ex |
|
52 |
|
fnconstg |
|
53 |
51 52
|
ax-mp |
|
54 |
50 53
|
pm3.2i |
|
55 |
|
dff1o3 |
|
56 |
55
|
simprbi |
|
57 |
16 56
|
syl |
|
58 |
|
imain |
|
59 |
57 58
|
syl |
|
60 |
|
elfznn |
|
61 |
5 60
|
syl |
|
62 |
61
|
nnred |
|
63 |
62
|
ltm1d |
|
64 |
|
fzdisj |
|
65 |
63 64
|
syl |
|
66 |
65
|
imaeq2d |
|
67 |
|
ima0 |
|
68 |
66 67
|
eqtrdi |
|
69 |
59 68
|
eqtr3d |
|
70 |
|
fnun |
|
71 |
54 69 70
|
sylancr |
|
72 |
61
|
nncnd |
|
73 |
|
npcan1 |
|
74 |
72 73
|
syl |
|
75 |
|
nnuz |
|
76 |
61 75
|
eleqtrdi |
|
77 |
74 76
|
eqeltrd |
|
78 |
|
nnm1nn0 |
|
79 |
61 78
|
syl |
|
80 |
79
|
nn0zd |
|
81 |
|
uzid |
|
82 |
80 81
|
syl |
|
83 |
|
peano2uz |
|
84 |
82 83
|
syl |
|
85 |
74 84
|
eqeltrrd |
|
86 |
|
uzss |
|
87 |
85 86
|
syl |
|
88 |
61
|
nnzd |
|
89 |
|
elfzle2 |
|
90 |
5 89
|
syl |
|
91 |
62 25 27 90 36
|
letrd |
|
92 |
|
eluz2 |
|
93 |
88 24 91 92
|
syl3anbrc |
|
94 |
87 93
|
sseldd |
|
95 |
|
fzsplit2 |
|
96 |
77 94 95
|
syl2anc |
|
97 |
74
|
oveq1d |
|
98 |
97
|
uneq2d |
|
99 |
96 98
|
eqtrd |
|
100 |
99
|
imaeq2d |
|
101 |
|
imaundi |
|
102 |
100 101
|
eqtrdi |
|
103 |
|
f1ofo |
|
104 |
16 103
|
syl |
|
105 |
|
foima |
|
106 |
104 105
|
syl |
|
107 |
102 106
|
eqtr3d |
|
108 |
107
|
fneq2d |
|
109 |
71 108
|
mpbid |
|
110 |
109
|
adantr |
|
111 |
|
ovexd |
|
112 |
|
inidm |
|
113 |
|
eqidd |
|
114 |
|
imaundi |
|
115 |
|
fzpred |
|
116 |
93 115
|
syl |
|
117 |
116
|
imaeq2d |
|
118 |
|
f1ofn |
|
119 |
16 118
|
syl |
|
120 |
|
fnsnfv |
|
121 |
119 41 120
|
syl2anc |
|
122 |
121
|
uneq1d |
|
123 |
114 117 122
|
3eqtr4a |
|
124 |
123
|
xpeq1d |
|
125 |
|
xpundir |
|
126 |
124 125
|
eqtrdi |
|
127 |
126
|
uneq2d |
|
128 |
|
un12 |
|
129 |
127 128
|
eqtrdi |
|
130 |
129
|
fveq1d |
|
131 |
130
|
ad2antrr |
|
132 |
|
fnconstg |
|
133 |
51 132
|
ax-mp |
|
134 |
50 133
|
pm3.2i |
|
135 |
|
imain |
|
136 |
57 135
|
syl |
|
137 |
79
|
nn0red |
|
138 |
|
peano2re |
|
139 |
62 138
|
syl |
|
140 |
62
|
ltp1d |
|
141 |
137 62 139 63 140
|
lttrd |
|
142 |
|
fzdisj |
|
143 |
141 142
|
syl |
|
144 |
143
|
imaeq2d |
|
145 |
144 67
|
eqtrdi |
|
146 |
136 145
|
eqtr3d |
|
147 |
|
fnun |
|
148 |
134 146 147
|
sylancr |
|
149 |
|
imaundi |
|
150 |
|
imadif |
|
151 |
57 150
|
syl |
|
152 |
|
fzsplit |
|
153 |
41 152
|
syl |
|
154 |
153
|
difeq1d |
|
155 |
|
difundir |
|
156 |
|
fzsplit2 |
|
157 |
77 85 156
|
syl2anc |
|
158 |
74
|
oveq1d |
|
159 |
|
fzsn |
|
160 |
88 159
|
syl |
|
161 |
158 160
|
eqtrd |
|
162 |
161
|
uneq2d |
|
163 |
157 162
|
eqtrd |
|
164 |
163
|
difeq1d |
|
165 |
|
difun2 |
|
166 |
137 62
|
ltnled |
|
167 |
63 166
|
mpbid |
|
168 |
|
elfzle2 |
|
169 |
167 168
|
nsyl |
|
170 |
|
difsn |
|
171 |
169 170
|
syl |
|
172 |
165 171
|
syl5eq |
|
173 |
164 172
|
eqtrd |
|
174 |
62 139
|
ltnled |
|
175 |
140 174
|
mpbid |
|
176 |
|
elfzle1 |
|
177 |
175 176
|
nsyl |
|
178 |
|
difsn |
|
179 |
177 178
|
syl |
|
180 |
173 179
|
uneq12d |
|
181 |
155 180
|
syl5eq |
|
182 |
154 181
|
eqtrd |
|
183 |
182
|
imaeq2d |
|
184 |
121
|
eqcomd |
|
185 |
106 184
|
difeq12d |
|
186 |
151 183 185
|
3eqtr3d |
|
187 |
149 186
|
syl5eqr |
|
188 |
187
|
fneq2d |
|
189 |
148 188
|
mpbid |
|
190 |
|
eldifsn |
|
191 |
190
|
biimpri |
|
192 |
191
|
ancoms |
|
193 |
|
disjdif |
|
194 |
|
fnconstg |
|
195 |
51 194
|
ax-mp |
|
196 |
|
fvun2 |
|
197 |
195 196
|
mp3an1 |
|
198 |
193 197
|
mpanr1 |
|
199 |
189 192 198
|
syl2an |
|
200 |
199
|
anassrs |
|
201 |
131 200
|
eqtrd |
|
202 |
47 110 111 111 112 113 201
|
ofval |
|
203 |
|
fnconstg |
|
204 |
48 203
|
ax-mp |
|
205 |
204 133
|
pm3.2i |
|
206 |
|
imain |
|
207 |
57 206
|
syl |
|
208 |
|
fzdisj |
|
209 |
140 208
|
syl |
|
210 |
209
|
imaeq2d |
|
211 |
210 67
|
eqtrdi |
|
212 |
207 211
|
eqtr3d |
|
213 |
|
fnun |
|
214 |
205 212 213
|
sylancr |
|
215 |
153
|
imaeq2d |
|
216 |
|
imaundi |
|
217 |
215 216
|
eqtrdi |
|
218 |
217 106
|
eqtr3d |
|
219 |
218
|
fneq2d |
|
220 |
214 219
|
mpbid |
|
221 |
220
|
adantr |
|
222 |
|
imaundi |
|
223 |
163
|
imaeq2d |
|
224 |
121
|
uneq2d |
|
225 |
222 223 224
|
3eqtr4a |
|
226 |
225
|
xpeq1d |
|
227 |
|
xpundir |
|
228 |
226 227
|
eqtrdi |
|
229 |
228
|
uneq1d |
|
230 |
|
un23 |
|
231 |
230
|
equncomi |
|
232 |
229 231
|
eqtrdi |
|
233 |
232
|
fveq1d |
|
234 |
233
|
ad2antrr |
|
235 |
|
fnconstg |
|
236 |
48 235
|
ax-mp |
|
237 |
|
fvun2 |
|
238 |
236 237
|
mp3an1 |
|
239 |
193 238
|
mpanr1 |
|
240 |
189 192 239
|
syl2an |
|
241 |
240
|
anassrs |
|
242 |
234 241
|
eqtrd |
|
243 |
47 221 111 111 112 113 242
|
ofval |
|
244 |
202 243
|
eqtr4d |
|
245 |
244
|
an32s |
|
246 |
245
|
anasss |
|
247 |
|
fveq2 |
|
248 |
247
|
breq2d |
|
249 |
248
|
ifbid |
|
250 |
249
|
csbeq1d |
|
251 |
|
2fveq3 |
|
252 |
|
2fveq3 |
|
253 |
252
|
imaeq1d |
|
254 |
253
|
xpeq1d |
|
255 |
252
|
imaeq1d |
|
256 |
255
|
xpeq1d |
|
257 |
254 256
|
uneq12d |
|
258 |
251 257
|
oveq12d |
|
259 |
258
|
csbeq2dv |
|
260 |
250 259
|
eqtrd |
|
261 |
260
|
mpteq2dv |
|
262 |
261
|
eqeq2d |
|
263 |
262 2
|
elrab2 |
|
264 |
263
|
simprbi |
|
265 |
3 264
|
syl |
|
266 |
|
breq1 |
|
267 |
|
id |
|
268 |
266 267
|
ifbieq1d |
|
269 |
26
|
ltm1d |
|
270 |
62 25 26 90 269
|
lelttrd |
|
271 |
137 62 26 63 270
|
lttrd |
|
272 |
271
|
iftrued |
|
273 |
268 272
|
sylan9eqr |
|
274 |
273
|
csbeq1d |
|
275 |
|
oveq2 |
|
276 |
275
|
imaeq2d |
|
277 |
276
|
xpeq1d |
|
278 |
277
|
adantl |
|
279 |
|
oveq1 |
|
280 |
279 74
|
sylan9eqr |
|
281 |
280
|
oveq1d |
|
282 |
281
|
imaeq2d |
|
283 |
282
|
xpeq1d |
|
284 |
278 283
|
uneq12d |
|
285 |
284
|
oveq2d |
|
286 |
79 285
|
csbied |
|
287 |
286
|
adantr |
|
288 |
274 287
|
eqtrd |
|
289 |
|
1red |
|
290 |
62 27 289 91
|
lesub1dd |
|
291 |
|
elfz2nn0 |
|
292 |
79 30 290 291
|
syl3anbrc |
|
293 |
|
ovexd |
|
294 |
265 288 292 293
|
fvmptd |
|
295 |
294
|
fveq1d |
|
296 |
295
|
adantr |
|
297 |
|
breq1 |
|
298 |
|
id |
|
299 |
297 298
|
ifbieq1d |
|
300 |
270
|
iftrued |
|
301 |
299 300
|
sylan9eqr |
|
302 |
301
|
csbeq1d |
|
303 |
|
oveq2 |
|
304 |
303
|
imaeq2d |
|
305 |
304
|
xpeq1d |
|
306 |
|
oveq1 |
|
307 |
306
|
oveq1d |
|
308 |
307
|
imaeq2d |
|
309 |
308
|
xpeq1d |
|
310 |
305 309
|
uneq12d |
|
311 |
310
|
oveq2d |
|
312 |
311
|
adantl |
|
313 |
5 312
|
csbied |
|
314 |
313
|
adantr |
|
315 |
302 314
|
eqtrd |
|
316 |
30
|
nn0zd |
|
317 |
26 27 289 35
|
lesub1dd |
|
318 |
|
eluz2 |
|
319 |
23 316 317 318
|
syl3anbrc |
|
320 |
|
fzss2 |
|
321 |
319 320
|
syl |
|
322 |
|
fz1ssfz0 |
|
323 |
321 322
|
sstrdi |
|
324 |
323 5
|
sseldd |
|
325 |
|
ovexd |
|
326 |
265 315 324 325
|
fvmptd |
|
327 |
326
|
fveq1d |
|
328 |
327
|
adantr |
|
329 |
246 296 328
|
3eqtr4d |
|
330 |
329
|
expr |
|
331 |
330
|
necon1d |
|
332 |
|
elmapi |
|
333 |
44 332
|
syl |
|
334 |
333 42
|
ffvelrnd |
|
335 |
|
elfzonn0 |
|
336 |
334 335
|
syl |
|
337 |
336
|
nn0red |
|
338 |
337
|
ltp1d |
|
339 |
337 338
|
ltned |
|
340 |
294
|
fveq1d |
|
341 |
|
ovexd |
|
342 |
|
eqidd |
|
343 |
|
fzss1 |
|
344 |
76 343
|
syl |
|
345 |
|
eluzfz1 |
|
346 |
93 345
|
syl |
|
347 |
|
fnfvima |
|
348 |
119 344 346 347
|
syl3anc |
|
349 |
|
fvun2 |
|
350 |
50 53 349
|
mp3an12 |
|
351 |
69 348 350
|
syl2anc |
|
352 |
51
|
fvconst2 |
|
353 |
348 352
|
syl |
|
354 |
351 353
|
eqtrd |
|
355 |
354
|
adantr |
|
356 |
46 109 341 341 112 342 355
|
ofval |
|
357 |
42 356
|
mpdan |
|
358 |
336
|
nn0cnd |
|
359 |
358
|
addid1d |
|
360 |
340 357 359
|
3eqtrd |
|
361 |
326
|
fveq1d |
|
362 |
|
fzss2 |
|
363 |
93 362
|
syl |
|
364 |
|
elfz1end |
|
365 |
61 364
|
sylib |
|
366 |
|
fnfvima |
|
367 |
119 363 365 366
|
syl3anc |
|
368 |
|
fvun1 |
|
369 |
204 133 368
|
mp3an12 |
|
370 |
212 367 369
|
syl2anc |
|
371 |
48
|
fvconst2 |
|
372 |
367 371
|
syl |
|
373 |
370 372
|
eqtrd |
|
374 |
373
|
adantr |
|
375 |
46 220 341 341 112 342 374
|
ofval |
|
376 |
42 375
|
mpdan |
|
377 |
361 376
|
eqtrd |
|
378 |
339 360 377
|
3netr4d |
|
379 |
|
fveq2 |
|
380 |
|
fveq2 |
|
381 |
379 380
|
neeq12d |
|
382 |
378 381
|
syl5ibrcom |
|
383 |
382
|
adantr |
|
384 |
331 383
|
impbid |
|
385 |
42 384
|
riota5 |
|