Step |
Hyp |
Ref |
Expression |
1 |
|
seqf1o.1 |
|
2 |
|
seqf1o.2 |
|
3 |
|
seqf1o.3 |
|
4 |
|
seqf1o.4 |
|
5 |
|
seqf1o.5 |
|
6 |
|
seqf1olem.5 |
|
7 |
|
seqf1olem.6 |
|
8 |
|
seqf1olem.7 |
|
9 |
|
seqf1olem.8 |
|
10 |
|
seqf1olem.9 |
|
11 |
7
|
ffnd |
|
12 |
|
fzssp1 |
|
13 |
|
fnssres |
|
14 |
11 12 13
|
sylancl |
|
15 |
|
fzfid |
|
16 |
|
fnfi |
|
17 |
14 15 16
|
syl2anc |
|
18 |
17
|
elexd |
|
19 |
1 2 3 4 5 6 7 8 9
|
seqf1olem1 |
|
20 |
|
f1of |
|
21 |
19 20
|
syl |
|
22 |
|
fex2 |
|
23 |
21 15 15 22
|
syl3anc |
|
24 |
18 23
|
jca |
|
25 |
|
fssres |
|
26 |
7 12 25
|
sylancl |
|
27 |
19 26
|
jca |
|
28 |
|
f1oeq1 |
|
29 |
|
feq1 |
|
30 |
28 29
|
bi2anan9r |
|
31 |
|
coeq1 |
|
32 |
|
coeq2 |
|
33 |
31 32
|
sylan9eq |
|
34 |
33
|
seqeq3d |
|
35 |
34
|
fveq1d |
|
36 |
|
simpl |
|
37 |
36
|
seqeq3d |
|
38 |
37
|
fveq1d |
|
39 |
35 38
|
eqeq12d |
|
40 |
30 39
|
imbi12d |
|
41 |
40
|
spc2gv |
|
42 |
24 10 27 41
|
syl3c |
|
43 |
|
fvres |
|
44 |
43
|
adantl |
|
45 |
4 44
|
seqfveq |
|
46 |
42 45
|
eqtrd |
|
47 |
46
|
oveq1d |
|
48 |
1
|
adantlr |
|
49 |
3
|
adantlr |
|
50 |
|
elfzuz3 |
|
51 |
50
|
adantl |
|
52 |
|
eluzp1p1 |
|
53 |
51 52
|
syl |
|
54 |
|
elfzuz |
|
55 |
54
|
adantl |
|
56 |
|
f1of |
|
57 |
6 56
|
syl |
|
58 |
|
fco |
|
59 |
7 57 58
|
syl2anc |
|
60 |
59 5
|
fssd |
|
61 |
60
|
ffvelrnda |
|
62 |
61
|
adantlr |
|
63 |
48 49 53 55 62
|
seqsplit |
|
64 |
|
elfzp12 |
|
65 |
64
|
biimpa |
|
66 |
4 65
|
sylan |
|
67 |
|
seqeq1 |
|
68 |
67
|
eqcomd |
|
69 |
68
|
fveq1d |
|
70 |
|
f1ocnv |
|
71 |
|
f1of |
|
72 |
6 70 71
|
3syl |
|
73 |
|
peano2uz |
|
74 |
|
eluzfz2 |
|
75 |
4 73 74
|
3syl |
|
76 |
72 75
|
ffvelrnd |
|
77 |
9 76
|
eqeltrid |
|
78 |
|
elfzelz |
|
79 |
|
seq1 |
|
80 |
77 78 79
|
3syl |
|
81 |
69 80
|
sylan9eqr |
|
82 |
81
|
oveq1d |
|
83 |
|
simpr |
|
84 |
|
eluzfz1 |
|
85 |
4 84
|
syl |
|
86 |
85
|
adantr |
|
87 |
83 86
|
eqeltrd |
|
88 |
2
|
adantlr |
|
89 |
5
|
adantr |
|
90 |
59
|
adantr |
|
91 |
77
|
adantr |
|
92 |
|
peano2uz |
|
93 |
|
fzss1 |
|
94 |
55 92 93
|
3syl |
|
95 |
48 88 49 53 89 90 91 94
|
seqf1olem2a |
|
96 |
|
1zzd |
|
97 |
|
elfzuz |
|
98 |
|
fzss1 |
|
99 |
77 97 98
|
3syl |
|
100 |
99
|
sselda |
|
101 |
21
|
ffvelrnda |
|
102 |
100 101
|
syldan |
|
103 |
102
|
fvresd |
|
104 |
|
breq1 |
|
105 |
|
id |
|
106 |
|
oveq1 |
|
107 |
104 105 106
|
ifbieq12d |
|
108 |
107
|
fveq2d |
|
109 |
|
fvex |
|
110 |
108 8 109
|
fvmpt |
|
111 |
100 110
|
syl |
|
112 |
77 78
|
syl |
|
113 |
112
|
zred |
|
114 |
113
|
adantr |
|
115 |
|
elfzelz |
|
116 |
115
|
adantl |
|
117 |
116
|
zred |
|
118 |
|
elfzle1 |
|
119 |
118
|
adantl |
|
120 |
114 117 119
|
lensymd |
|
121 |
|
iffalse |
|
122 |
121
|
fveq2d |
|
123 |
120 122
|
syl |
|
124 |
111 123
|
eqtrd |
|
125 |
124
|
fveq2d |
|
126 |
103 125
|
eqtrd |
|
127 |
|
fvco3 |
|
128 |
21 127
|
sylan |
|
129 |
100 128
|
syldan |
|
130 |
|
fzp1elp1 |
|
131 |
100 130
|
syl |
|
132 |
|
fvco3 |
|
133 |
57 132
|
sylan |
|
134 |
131 133
|
syldan |
|
135 |
126 129 134
|
3eqtr4d |
|
136 |
135
|
adantlr |
|
137 |
51 96 136
|
seqshft2 |
|
138 |
|
fvco3 |
|
139 |
57 77 138
|
syl2anc |
|
140 |
9
|
fveq2i |
|
141 |
|
f1ocnvfv2 |
|
142 |
6 75 141
|
syl2anc |
|
143 |
140 142
|
eqtrid |
|
144 |
143
|
fveq2d |
|
145 |
139 144
|
eqtr2d |
|
146 |
145
|
adantr |
|
147 |
137 146
|
oveq12d |
|
148 |
95 147
|
eqtr4d |
|
149 |
87 148
|
syldan |
|
150 |
83
|
seqeq1d |
|
151 |
150
|
fveq1d |
|
152 |
151
|
oveq1d |
|
153 |
82 149 152
|
3eqtrd |
|
154 |
|
eluzel2 |
|
155 |
4 154
|
syl |
|
156 |
|
elfzuz |
|
157 |
|
eluzp1m1 |
|
158 |
155 156 157
|
syl2an |
|
159 |
|
eluzelz |
|
160 |
4 159
|
syl |
|
161 |
160
|
zcnd |
|
162 |
|
ax-1cn |
|
163 |
|
pncan |
|
164 |
161 162 163
|
sylancl |
|
165 |
|
peano2zm |
|
166 |
77 78 165
|
3syl |
|
167 |
|
elfzuz3 |
|
168 |
77 167
|
syl |
|
169 |
112
|
zcnd |
|
170 |
|
npcan |
|
171 |
169 162 170
|
sylancl |
|
172 |
171
|
fveq2d |
|
173 |
168 172
|
eleqtrrd |
|
174 |
|
eluzp1m1 |
|
175 |
166 173 174
|
syl2anc |
|
176 |
164 175
|
eqeltrrd |
|
177 |
|
fzss2 |
|
178 |
176 177
|
syl |
|
179 |
178
|
sselda |
|
180 |
179 101
|
syldan |
|
181 |
180
|
fvresd |
|
182 |
179 110
|
syl |
|
183 |
|
elfzm11 |
|
184 |
155 112 183
|
syl2anc |
|
185 |
184
|
biimpa |
|
186 |
185
|
simp3d |
|
187 |
|
iftrue |
|
188 |
187
|
fveq2d |
|
189 |
186 188
|
syl |
|
190 |
182 189
|
eqtrd |
|
191 |
190
|
fveq2d |
|
192 |
181 191
|
eqtr2d |
|
193 |
|
peano2uz |
|
194 |
|
fzss2 |
|
195 |
176 193 194
|
3syl |
|
196 |
195
|
sselda |
|
197 |
|
fvco3 |
|
198 |
57 197
|
sylan |
|
199 |
196 198
|
syldan |
|
200 |
179 128
|
syldan |
|
201 |
192 199 200
|
3eqtr4d |
|
202 |
201
|
adantlr |
|
203 |
158 202
|
seqfveq |
|
204 |
|
fzp1ss |
|
205 |
4 154 204
|
3syl |
|
206 |
205
|
sselda |
|
207 |
206 148
|
syldan |
|
208 |
203 207
|
oveq12d |
|
209 |
196 61
|
syldan |
|
210 |
209
|
adantlr |
|
211 |
1
|
adantlr |
|
212 |
158 210 211
|
seqcl |
|
213 |
59 77
|
ffvelrnd |
|
214 |
5 213
|
sseldd |
|
215 |
214
|
adantr |
|
216 |
94
|
sselda |
|
217 |
216 62
|
syldan |
|
218 |
53 217 48
|
seqcl |
|
219 |
206 218
|
syldan |
|
220 |
212 215 219
|
3jca |
|
221 |
3
|
caovassg |
|
222 |
220 221
|
syldan |
|
223 |
7 5
|
fssd |
|
224 |
|
fssres |
|
225 |
223 12 224
|
sylancl |
|
226 |
|
fco |
|
227 |
225 21 226
|
syl2anc |
|
228 |
227
|
ffvelrnda |
|
229 |
179 228
|
syldan |
|
230 |
229
|
adantlr |
|
231 |
158 230 211
|
seqcl |
|
232 |
|
elfzuz3 |
|
233 |
232
|
adantl |
|
234 |
100 228
|
syldan |
|
235 |
234
|
adantlr |
|
236 |
233 235 211
|
seqcl |
|
237 |
223 75
|
ffvelrnd |
|
238 |
237
|
adantr |
|
239 |
231 236 238
|
3jca |
|
240 |
3
|
caovassg |
|
241 |
239 240
|
syldan |
|
242 |
208 222 241
|
3eqtr4d |
|
243 |
|
seqm1 |
|
244 |
155 156 243
|
syl2an |
|
245 |
244
|
oveq1d |
|
246 |
3
|
adantlr |
|
247 |
|
elfzelz |
|
248 |
247
|
adantl |
|
249 |
248
|
zcnd |
|
250 |
249 162 170
|
sylancl |
|
251 |
250
|
fveq2d |
|
252 |
233 251
|
eleqtrrd |
|
253 |
228
|
adantlr |
|
254 |
211 246 252 158 253
|
seqsplit |
|
255 |
250
|
seqeq1d |
|
256 |
255
|
fveq1d |
|
257 |
256
|
oveq2d |
|
258 |
254 257
|
eqtrd |
|
259 |
258
|
oveq1d |
|
260 |
242 245 259
|
3eqtr4d |
|
261 |
153 260
|
jaodan |
|
262 |
66 261
|
syldan |
|
263 |
63 262
|
eqtrd |
|
264 |
4
|
adantr |
|
265 |
|
seqp1 |
|
266 |
264 265
|
syl |
|
267 |
110
|
adantl |
|
268 |
|
elfzelz |
|
269 |
268
|
zred |
|
270 |
269
|
adantl |
|
271 |
160
|
zred |
|
272 |
271
|
adantr |
|
273 |
|
peano2re |
|
274 |
272 273
|
syl |
|
275 |
|
elfzle2 |
|
276 |
275
|
adantl |
|
277 |
272
|
ltp1d |
|
278 |
270 272 274 276 277
|
lelttrd |
|
279 |
278
|
adantlr |
|
280 |
|
simplr |
|
281 |
279 280
|
breqtrrd |
|
282 |
281 188
|
syl |
|
283 |
267 282
|
eqtrd |
|
284 |
283
|
fveq2d |
|
285 |
269
|
adantl |
|
286 |
285 281
|
gtned |
|
287 |
57
|
ad2antrr |
|
288 |
|
fzelp1 |
|
289 |
288
|
adantl |
|
290 |
287 289
|
ffvelrnd |
|
291 |
4
|
ad2antrr |
|
292 |
|
elfzp1 |
|
293 |
291 292
|
syl |
|
294 |
290 293
|
mpbid |
|
295 |
294
|
ord |
|
296 |
6
|
ad2antrr |
|
297 |
|
f1ocnvfv |
|
298 |
296 289 297
|
syl2anc |
|
299 |
9
|
eqeq1i |
|
300 |
298 299
|
syl6ibr |
|
301 |
295 300
|
syld |
|
302 |
301
|
necon1ad |
|
303 |
286 302
|
mpd |
|
304 |
303
|
fvresd |
|
305 |
284 304
|
eqtr2d |
|
306 |
57 288 197
|
syl2an |
|
307 |
306
|
adantlr |
|
308 |
128
|
adantlr |
|
309 |
305 307 308
|
3eqtr4d |
|
310 |
264 309
|
seqfveq |
|
311 |
|
fvco3 |
|
312 |
57 75 311
|
syl2anc |
|
313 |
312
|
adantr |
|
314 |
|
simpr |
|
315 |
9 314
|
eqtr3id |
|
316 |
315
|
fveq2d |
|
317 |
142
|
adantr |
|
318 |
316 317
|
eqtr3d |
|
319 |
318
|
fveq2d |
|
320 |
313 319
|
eqtrd |
|
321 |
310 320
|
oveq12d |
|
322 |
266 321
|
eqtrd |
|
323 |
|
elfzp1 |
|
324 |
4 323
|
syl |
|
325 |
77 324
|
mpbid |
|
326 |
263 322 325
|
mpjaodan |
|
327 |
|
seqp1 |
|
328 |
4 327
|
syl |
|
329 |
47 326 328
|
3eqtr4d |
|