Step |
Hyp |
Ref |
Expression |
1 |
|
4nn0 |
|
2 |
|
bpolyval |
|
3 |
1 2
|
mpan |
|
4 |
|
4m1e3 |
|
5 |
|
df-3 |
|
6 |
4 5
|
eqtri |
|
7 |
6
|
oveq2i |
|
8 |
7
|
sumeq1i |
|
9 |
|
2eluzge0 |
|
10 |
9
|
a1i |
|
11 |
|
elfzelz |
|
12 |
|
bccl |
|
13 |
1 11 12
|
sylancr |
|
14 |
13
|
nn0cnd |
|
15 |
14
|
adantl |
|
16 |
|
elfznn0 |
|
17 |
|
bpolycl |
|
18 |
16 17
|
sylan |
|
19 |
18
|
ancoms |
|
20 |
|
4re |
|
21 |
20
|
a1i |
|
22 |
11
|
zred |
|
23 |
21 22
|
resubcld |
|
24 |
|
peano2re |
|
25 |
23 24
|
syl |
|
26 |
25
|
recnd |
|
27 |
26
|
adantl |
|
28 |
|
1red |
|
29 |
5
|
oveq2i |
|
30 |
29
|
eleq2i |
|
31 |
|
elfzelz |
|
32 |
31
|
zred |
|
33 |
|
3re |
|
34 |
33
|
a1i |
|
35 |
20
|
a1i |
|
36 |
|
elfzle2 |
|
37 |
|
3lt4 |
|
38 |
37
|
a1i |
|
39 |
32 34 35 36 38
|
lelttrd |
|
40 |
30 39
|
sylbir |
|
41 |
22 21
|
posdifd |
|
42 |
40 41
|
mpbid |
|
43 |
|
0lt1 |
|
44 |
43
|
a1i |
|
45 |
23 28 42 44
|
addgt0d |
|
46 |
45
|
gt0ne0d |
|
47 |
46
|
adantl |
|
48 |
19 27 47
|
divcld |
|
49 |
15 48
|
mulcld |
|
50 |
5
|
eqeq2i |
|
51 |
|
oveq2 |
|
52 |
|
4bc3eq4 |
|
53 |
51 52
|
eqtrdi |
|
54 |
|
oveq1 |
|
55 |
|
oveq2 |
|
56 |
55
|
oveq1d |
|
57 |
|
4cn |
|
58 |
|
3cn |
|
59 |
|
ax-1cn |
|
60 |
|
3p1e4 |
|
61 |
57 58 59 60
|
subaddrii |
|
62 |
61
|
oveq1i |
|
63 |
|
df-2 |
|
64 |
62 63
|
eqtr4i |
|
65 |
56 64
|
eqtrdi |
|
66 |
54 65
|
oveq12d |
|
67 |
53 66
|
oveq12d |
|
68 |
50 67
|
sylbir |
|
69 |
10 49 68
|
fsump1 |
|
70 |
63
|
oveq2i |
|
71 |
70
|
sumeq1i |
|
72 |
|
1eluzge0 |
|
73 |
72
|
a1i |
|
74 |
|
fzssp1 |
|
75 |
63
|
oveq1i |
|
76 |
75
|
oveq2i |
|
77 |
74 76
|
sseqtrri |
|
78 |
77
|
sseli |
|
79 |
78 49
|
sylan2 |
|
80 |
63
|
eqeq2i |
|
81 |
|
oveq2 |
|
82 |
|
4bc2eq6 |
|
83 |
81 82
|
eqtrdi |
|
84 |
|
oveq1 |
|
85 |
|
oveq2 |
|
86 |
85
|
oveq1d |
|
87 |
|
2cn |
|
88 |
|
2p2e4 |
|
89 |
57 87 87 88
|
subaddrii |
|
90 |
89
|
oveq1i |
|
91 |
90 5
|
eqtr4i |
|
92 |
86 91
|
eqtrdi |
|
93 |
84 92
|
oveq12d |
|
94 |
83 93
|
oveq12d |
|
95 |
80 94
|
sylbir |
|
96 |
73 79 95
|
fsump1 |
|
97 |
|
0p1e1 |
|
98 |
97
|
oveq2i |
|
99 |
98
|
sumeq1i |
|
100 |
|
0nn0 |
|
101 |
|
nn0uz |
|
102 |
100 101
|
eleqtri |
|
103 |
102
|
a1i |
|
104 |
|
3nn |
|
105 |
|
nnuz |
|
106 |
104 105
|
eleqtri |
|
107 |
|
fzss2 |
|
108 |
106 107
|
ax-mp |
|
109 |
|
2p1e3 |
|
110 |
109
|
oveq2i |
|
111 |
108 98 110
|
3sstr4i |
|
112 |
111
|
sseli |
|
113 |
112 49
|
sylan2 |
|
114 |
97
|
eqeq2i |
|
115 |
|
oveq2 |
|
116 |
|
bcn1 |
|
117 |
1 116
|
ax-mp |
|
118 |
115 117
|
eqtrdi |
|
119 |
|
oveq1 |
|
120 |
|
oveq2 |
|
121 |
120
|
oveq1d |
|
122 |
4
|
oveq1i |
|
123 |
|
df-4 |
|
124 |
122 123
|
eqtr4i |
|
125 |
121 124
|
eqtrdi |
|
126 |
119 125
|
oveq12d |
|
127 |
118 126
|
oveq12d |
|
128 |
114 127
|
sylbi |
|
129 |
103 113 128
|
fsump1 |
|
130 |
|
0z |
|
131 |
59
|
a1i |
|
132 |
|
bpolycl |
|
133 |
100 132
|
mpan |
|
134 |
|
5cn |
|
135 |
134
|
a1i |
|
136 |
|
0re |
|
137 |
|
5pos |
|
138 |
136 137
|
gtneii |
|
139 |
138
|
a1i |
|
140 |
133 135 139
|
divcld |
|
141 |
131 140
|
mulcld |
|
142 |
|
oveq2 |
|
143 |
|
bcn0 |
|
144 |
1 143
|
ax-mp |
|
145 |
142 144
|
eqtrdi |
|
146 |
|
oveq1 |
|
147 |
|
oveq2 |
|
148 |
147
|
oveq1d |
|
149 |
57
|
subid1i |
|
150 |
149
|
oveq1i |
|
151 |
|
4p1e5 |
|
152 |
150 151
|
eqtri |
|
153 |
148 152
|
eqtrdi |
|
154 |
146 153
|
oveq12d |
|
155 |
145 154
|
oveq12d |
|
156 |
155
|
fsum1 |
|
157 |
130 141 156
|
sylancr |
|
158 |
|
bpoly0 |
|
159 |
158
|
oveq1d |
|
160 |
159
|
oveq2d |
|
161 |
134 138
|
reccli |
|
162 |
161
|
mulid2i |
|
163 |
160 162
|
eqtrdi |
|
164 |
157 163
|
eqtrd |
|
165 |
|
1nn0 |
|
166 |
|
bpolycl |
|
167 |
165 166
|
mpan |
|
168 |
|
nn0cn |
|
169 |
1 168
|
mp1i |
|
170 |
|
4ne0 |
|
171 |
170
|
a1i |
|
172 |
167 169 171
|
divcan2d |
|
173 |
|
bpoly1 |
|
174 |
172 173
|
eqtrd |
|
175 |
164 174
|
oveq12d |
|
176 |
129 175
|
eqtrd |
|
177 |
99 176
|
syl5eqr |
|
178 |
|
6cn |
|
179 |
178
|
a1i |
|
180 |
|
2nn0 |
|
181 |
|
bpolycl |
|
182 |
180 181
|
mpan |
|
183 |
58
|
a1i |
|
184 |
|
3ne0 |
|
185 |
184
|
a1i |
|
186 |
179 182 183 185
|
div12d |
|
187 |
|
3t2e6 |
|
188 |
178 58 87 184
|
divmuli |
|
189 |
187 188
|
mpbir |
|
190 |
189
|
oveq2i |
|
191 |
87
|
a1i |
|
192 |
182 191
|
mulcomd |
|
193 |
|
bpoly2 |
|
194 |
193
|
oveq2d |
|
195 |
192 194
|
eqtrd |
|
196 |
190 195
|
syl5eq |
|
197 |
186 196
|
eqtrd |
|
198 |
177 197
|
oveq12d |
|
199 |
96 198
|
eqtrd |
|
200 |
71 199
|
syl5eq |
|
201 |
|
3nn0 |
|
202 |
|
bpolycl |
|
203 |
201 202
|
mpan |
|
204 |
|
2ne0 |
|
205 |
204
|
a1i |
|
206 |
169 203 191 205
|
div12d |
|
207 |
|
4d2e2 |
|
208 |
207
|
oveq2i |
|
209 |
203 191
|
mulcomd |
|
210 |
|
bpoly3 |
|
211 |
210
|
oveq2d |
|
212 |
209 211
|
eqtrd |
|
213 |
208 212
|
syl5eq |
|
214 |
206 213
|
eqtrd |
|
215 |
200 214
|
oveq12d |
|
216 |
69 215
|
eqtrd |
|
217 |
8 216
|
syl5eq |
|
218 |
217
|
oveq2d |
|
219 |
|
expcl |
|
220 |
1 219
|
mpan2 |
|
221 |
|
expcl |
|
222 |
201 221
|
mpan2 |
|
223 |
191 222
|
mulcld |
|
224 |
|
sqcl |
|
225 |
201 100
|
deccl |
|
226 |
225
|
nn0cni |
|
227 |
|
dfdec10 |
|
228 |
|
10re |
|
229 |
228
|
recni |
|
230 |
229 58
|
mulcli |
|
231 |
230
|
addid1i |
|
232 |
227 231
|
eqtri |
|
233 |
|
10pos |
|
234 |
136 233
|
gtneii |
|
235 |
229 58 234 184
|
mulne0i |
|
236 |
232 235
|
eqnetri |
|
237 |
226 236
|
reccli |
|
238 |
237
|
a1i |
|
239 |
224 238
|
subcld |
|
240 |
220 223 239
|
subsubd |
|
241 |
161
|
a1i |
|
242 |
|
id |
|
243 |
87 204
|
reccli |
|
244 |
243
|
a1i |
|
245 |
242 244
|
subcld |
|
246 |
241 245
|
addcld |
|
247 |
224 242
|
subcld |
|
248 |
|
6pos |
|
249 |
136 248
|
gtneii |
|
250 |
178 249
|
reccli |
|
251 |
250
|
a1i |
|
252 |
247 251
|
addcld |
|
253 |
191 252
|
mulcld |
|
254 |
246 253
|
addcld |
|
255 |
58 87 204
|
divcli |
|
256 |
255
|
a1i |
|
257 |
256 224
|
mulcld |
|
258 |
222 257
|
subcld |
|
259 |
244 242
|
mulcld |
|
260 |
258 259
|
addcld |
|
261 |
191 260
|
mulcld |
|
262 |
254 261
|
addcomd |
|
263 |
191 258 259
|
adddid |
|
264 |
191 222 257
|
subdid |
|
265 |
87 204
|
recidi |
|
266 |
265
|
oveq1i |
|
267 |
191 244 242
|
mulassd |
|
268 |
|
mulid2 |
|
269 |
266 267 268
|
3eqtr3a |
|
270 |
264 269
|
oveq12d |
|
271 |
263 270
|
eqtrd |
|
272 |
271
|
oveq1d |
|
273 |
191 257
|
mulcld |
|
274 |
223 273
|
subcld |
|
275 |
274 242 254
|
addassd |
|
276 |
242 254
|
addcld |
|
277 |
223 273 276
|
subsubd |
|
278 |
58 87 204
|
divcan2i |
|
279 |
278
|
oveq1i |
|
280 |
191 256 224
|
mulassd |
|
281 |
279 280
|
syl5reqr |
|
282 |
281
|
oveq1d |
|
283 |
242 246 253
|
add12d |
|
284 |
191 247 251
|
adddid |
|
285 |
191 224 242
|
subdid |
|
286 |
187
|
oveq2i |
|
287 |
58 184
|
reccli |
|
288 |
58 87 287
|
mul32i |
|
289 |
58 184
|
recidi |
|
290 |
289
|
oveq1i |
|
291 |
87
|
mulid2i |
|
292 |
290 291
|
eqtri |
|
293 |
288 292
|
eqtri |
|
294 |
187 178
|
eqeltri |
|
295 |
187 249
|
eqnetri |
|
296 |
87 294 287 295
|
divmuli |
|
297 |
293 296
|
mpbir |
|
298 |
87 178 249
|
divreci |
|
299 |
286 297 298
|
3eqtr3ri |
|
300 |
299
|
a1i |
|
301 |
285 300
|
oveq12d |
|
302 |
284 301
|
eqtrd |
|
303 |
302
|
oveq2d |
|
304 |
191 224
|
mulcld |
|
305 |
191 242
|
mulcld |
|
306 |
304 305
|
subcld |
|
307 |
287
|
a1i |
|
308 |
242 306 307
|
addassd |
|
309 |
242 304 305
|
addsub12d |
|
310 |
309
|
oveq1d |
|
311 |
303 308 310
|
3eqtr2d |
|
312 |
311
|
oveq2d |
|
313 |
283 312
|
eqtrd |
|
314 |
313
|
oveq2d |
|
315 |
242 305
|
subcld |
|
316 |
304 315
|
addcld |
|
317 |
241 245 316 307
|
add4d |
|
318 |
241 304 315
|
add12d |
|
319 |
318
|
oveq1d |
|
320 |
241 315
|
addcld |
|
321 |
245 307
|
addcld |
|
322 |
304 320 321
|
addassd |
|
323 |
317 319 322
|
3eqtrd |
|
324 |
323
|
oveq2d |
|
325 |
183 224
|
mulcld |
|
326 |
320 321
|
addcld |
|
327 |
325 304 326
|
subsub4d |
|
328 |
58 87 59 109
|
subaddrii |
|
329 |
328
|
oveq1i |
|
330 |
183 191 224
|
subdird |
|
331 |
224
|
mulid2d |
|
332 |
329 330 331
|
3eqtr3a |
|
333 |
241 305 242
|
subsubd |
|
334 |
|
2txmxeqx |
|
335 |
334
|
oveq2d |
|
336 |
241 305 242
|
subadd23d |
|
337 |
333 335 336
|
3eqtr3d |
|
338 |
242 244 307
|
subsubd |
|
339 |
337 338
|
oveq12d |
|
340 |
243 287
|
subcli |
|
341 |
340
|
a1i |
|
342 |
241 242 341
|
npncand |
|
343 |
|
halfthird |
|
344 |
343
|
oveq2i |
|
345 |
|
5recm6rec |
|
346 |
344 345
|
eqtri |
|
347 |
342 346
|
eqtrdi |
|
348 |
339 347
|
eqtr3d |
|
349 |
332 348
|
oveq12d |
|
350 |
324 327 349
|
3eqtr2d |
|
351 |
282 314 350
|
3eqtrd |
|
352 |
351
|
oveq2d |
|
353 |
275 277 352
|
3eqtr2d |
|
354 |
262 272 353
|
3eqtrd |
|
355 |
354
|
oveq2d |
|
356 |
220 223
|
subcld |
|
357 |
356 224 238
|
addsubassd |
|
358 |
240 355 357
|
3eqtr4d |
|
359 |
3 218 358
|
3eqtrd |
|