Step |
Hyp |
Ref |
Expression |
1 |
|
efgval.w |
|
2 |
|
efgval.r |
|
3 |
|
efgval2.m |
|
4 |
|
efgval2.t |
|
5 |
|
efgred.d |
|
6 |
|
efgred.s |
|
7 |
|
efgredlem.1 |
|
8 |
|
efgredlem.2 |
|
9 |
|
efgredlem.3 |
|
10 |
|
efgredlem.4 |
|
11 |
|
efgredlem.5 |
|
12 |
|
efgredlemb.k |
|
13 |
|
efgredlemb.l |
|
14 |
|
efgredlemb.p |
|
15 |
|
efgredlemb.q |
|
16 |
|
efgredlemb.u |
|
17 |
|
efgredlemb.v |
|
18 |
|
efgredlemb.6 |
|
19 |
|
efgredlemb.7 |
|
20 |
|
efgredlemb.8 |
|
21 |
|
efgredlemd.9 |
|
22 |
|
efgredlemd.c |
|
23 |
|
efgredlemd.sc |
|
24 |
1 2 3 4 5 6
|
efgsf |
|
25 |
24
|
fdmi |
|
26 |
25
|
feq2i |
|
27 |
24 26
|
mpbir |
|
28 |
27
|
ffvelrni |
|
29 |
22 28
|
syl |
|
30 |
|
elfzuz |
|
31 |
15 30
|
syl |
|
32 |
23
|
fveq2d |
|
33 |
|
fviss |
|
34 |
1 33
|
eqsstri |
|
35 |
1 2 3 4 5 6 7 8 9 10 11 12 13
|
efgredlemf |
|
36 |
35
|
simprd |
|
37 |
34 36
|
sseldi |
|
38 |
|
pfxcl |
|
39 |
37 38
|
syl |
|
40 |
35
|
simpld |
|
41 |
34 40
|
sseldi |
|
42 |
|
swrdcl |
|
43 |
41 42
|
syl |
|
44 |
|
ccatlen |
|
45 |
39 43 44
|
syl2anc |
|
46 |
|
pfxlen |
|
47 |
37 15 46
|
syl2anc |
|
48 |
|
2nn0 |
|
49 |
|
uzaddcl |
|
50 |
31 48 49
|
sylancl |
|
51 |
|
elfzuz3 |
|
52 |
14 51
|
syl |
|
53 |
|
uztrn |
|
54 |
52 21 53
|
syl2anc |
|
55 |
|
elfzuzb |
|
56 |
50 54 55
|
sylanbrc |
|
57 |
|
lencl |
|
58 |
41 57
|
syl |
|
59 |
|
nn0uz |
|
60 |
58 59
|
eleqtrdi |
|
61 |
|
eluzfz2 |
|
62 |
60 61
|
syl |
|
63 |
|
swrdlen |
|
64 |
41 56 62 63
|
syl3anc |
|
65 |
47 64
|
oveq12d |
|
66 |
15
|
elfzelzd |
|
67 |
66
|
zcnd |
|
68 |
58
|
nn0cnd |
|
69 |
|
2z |
|
70 |
|
zaddcl |
|
71 |
66 69 70
|
sylancl |
|
72 |
71
|
zcnd |
|
73 |
67 68 72
|
addsubassd |
|
74 |
|
2cn |
|
75 |
74
|
a1i |
|
76 |
67 68 75
|
pnpcand |
|
77 |
65 73 76
|
3eqtr2d |
|
78 |
32 45 77
|
3eqtrd |
|
79 |
14
|
elfzelzd |
|
80 |
|
zsubcl |
|
81 |
79 69 80
|
sylancl |
|
82 |
69
|
a1i |
|
83 |
79
|
zcnd |
|
84 |
|
npcan |
|
85 |
83 74 84
|
sylancl |
|
86 |
85
|
fveq2d |
|
87 |
52 86
|
eleqtrrd |
|
88 |
|
eluzsub |
|
89 |
81 82 87 88
|
syl3anc |
|
90 |
78 89
|
eqeltrd |
|
91 |
|
eluzsub |
|
92 |
66 82 21 91
|
syl3anc |
|
93 |
|
uztrn |
|
94 |
90 92 93
|
syl2anc |
|
95 |
|
elfzuzb |
|
96 |
31 94 95
|
sylanbrc |
|
97 |
1 2 3 4
|
efgtval |
|
98 |
29 96 17 97
|
syl3anc |
|
99 |
|
pfxcl |
|
100 |
41 99
|
syl |
|
101 |
|
wrd0 |
|
102 |
101
|
a1i |
|
103 |
3
|
efgmf |
|
104 |
103
|
ffvelrni |
|
105 |
17 104
|
syl |
|
106 |
17 105
|
s2cld |
|
107 |
66
|
zred |
|
108 |
|
nn0addge1 |
|
109 |
107 48 108
|
sylancl |
|
110 |
|
eluz2 |
|
111 |
66 71 109 110
|
syl3anbrc |
|
112 |
|
uztrn |
|
113 |
21 111 112
|
syl2anc |
|
114 |
|
elfzuzb |
|
115 |
31 113 114
|
sylanbrc |
|
116 |
|
ccatpfx |
|
117 |
41 115 14 116
|
syl3anc |
|
118 |
117
|
oveq1d |
|
119 |
|
pfxcl |
|
120 |
41 119
|
syl |
|
121 |
103
|
ffvelrni |
|
122 |
16 121
|
syl |
|
123 |
16 122
|
s2cld |
|
124 |
|
swrdcl |
|
125 |
41 124
|
syl |
|
126 |
|
ccatass |
|
127 |
120 123 125 126
|
syl3anc |
|
128 |
1 2 3 4
|
efgtval |
|
129 |
40 14 16 128
|
syl3anc |
|
130 |
|
splval |
|
131 |
40 14 14 123 130
|
syl13anc |
|
132 |
18 129 131
|
3eqtrd |
|
133 |
1 2 3 4
|
efgtval |
|
134 |
36 15 17 133
|
syl3anc |
|
135 |
|
splval |
|
136 |
36 15 15 106 135
|
syl13anc |
|
137 |
19 134 136
|
3eqtrd |
|
138 |
10 132 137
|
3eqtr3d |
|
139 |
118 127 138
|
3eqtr2d |
|
140 |
|
swrdcl |
|
141 |
41 140
|
syl |
|
142 |
|
ccatcl |
|
143 |
123 125 142
|
syl2anc |
|
144 |
|
ccatass |
|
145 |
100 141 143 144
|
syl3anc |
|
146 |
|
swrdcl |
|
147 |
37 146
|
syl |
|
148 |
|
ccatass |
|
149 |
39 106 147 148
|
syl3anc |
|
150 |
139 145 149
|
3eqtr3d |
|
151 |
|
ccatcl |
|
152 |
141 143 151
|
syl2anc |
|
153 |
|
ccatcl |
|
154 |
106 147 153
|
syl2anc |
|
155 |
|
uztrn |
|
156 |
52 113 155
|
syl2anc |
|
157 |
|
elfzuzb |
|
158 |
31 156 157
|
sylanbrc |
|
159 |
|
pfxlen |
|
160 |
41 158 159
|
syl2anc |
|
161 |
160 47
|
eqtr4d |
|
162 |
|
ccatopth |
|
163 |
100 152 39 154 161 162
|
syl221anc |
|
164 |
150 163
|
mpbid |
|
165 |
164
|
simpld |
|
166 |
165
|
oveq1d |
|
167 |
|
ccatrid |
|
168 |
100 167
|
syl |
|
169 |
168
|
oveq1d |
|
170 |
166 169 23
|
3eqtr4rd |
|
171 |
160
|
eqcomd |
|
172 |
|
hash0 |
|
173 |
172
|
oveq2i |
|
174 |
67
|
addid1d |
|
175 |
173 174
|
eqtr2id |
|
176 |
100 102 43 106 170 171 175
|
splval2 |
|
177 |
|
elfzuzb |
|
178 |
31 111 177
|
sylanbrc |
|
179 |
|
elfzuzb |
|
180 |
50 21 179
|
sylanbrc |
|
181 |
|
ccatswrd |
|
182 |
41 178 180 14 181
|
syl13anc |
|
183 |
182
|
oveq1d |
|
184 |
|
swrdcl |
|
185 |
41 184
|
syl |
|
186 |
|
swrdcl |
|
187 |
41 186
|
syl |
|
188 |
|
ccatass |
|
189 |
185 187 143 188
|
syl3anc |
|
190 |
164
|
simprd |
|
191 |
183 189 190
|
3eqtr3d |
|
192 |
|
ccatcl |
|
193 |
187 143 192
|
syl2anc |
|
194 |
|
swrdlen |
|
195 |
41 178 56 194
|
syl3anc |
|
196 |
|
pncan2 |
|
197 |
67 74 196
|
sylancl |
|
198 |
195 197
|
eqtrd |
|
199 |
|
s2len |
|
200 |
198 199
|
eqtr4di |
|
201 |
|
ccatopth |
|
202 |
185 193 106 147 200 201
|
syl221anc |
|
203 |
191 202
|
mpbid |
|
204 |
203
|
simpld |
|
205 |
204
|
oveq2d |
|
206 |
|
ccatpfx |
|
207 |
41 178 56 206
|
syl3anc |
|
208 |
205 207
|
eqtr3d |
|
209 |
208
|
oveq1d |
|
210 |
|
ccatpfx |
|
211 |
41 56 62 210
|
syl3anc |
|
212 |
|
pfxid |
|
213 |
41 212
|
syl |
|
214 |
209 211 213
|
3eqtrd |
|
215 |
98 176 214
|
3eqtrd |
|
216 |
1 2 3 4
|
efgtf |
|
217 |
29 216
|
syl |
|
218 |
217
|
simprd |
|
219 |
218
|
ffnd |
|
220 |
|
fnovrn |
|
221 |
219 96 17 220
|
syl3anc |
|
222 |
215 221
|
eqeltrrd |
|
223 |
|
uztrn |
|
224 |
92 31 223
|
syl2anc |
|
225 |
|
elfzuzb |
|
226 |
224 90 225
|
sylanbrc |
|
227 |
1 2 3 4
|
efgtval |
|
228 |
29 226 16 227
|
syl3anc |
|
229 |
|
pfxcl |
|
230 |
37 229
|
syl |
|
231 |
|
swrdcl |
|
232 |
37 231
|
syl |
|
233 |
|
ccatswrd |
|
234 |
41 180 14 62 233
|
syl13anc |
|
235 |
203
|
simprd |
|
236 |
|
elfzuzb |
|
237 |
31 92 236
|
sylanbrc |
|
238 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
|
efgredlemg |
|
239 |
238 52
|
eqeltrrd |
|
240 |
|
0le2 |
|
241 |
240
|
a1i |
|
242 |
79
|
zred |
|
243 |
|
2re |
|
244 |
|
subge02 |
|
245 |
242 243 244
|
sylancl |
|
246 |
241 245
|
mpbid |
|
247 |
|
eluz2 |
|
248 |
81 79 246 247
|
syl3anbrc |
|
249 |
|
uztrn |
|
250 |
239 248 249
|
syl2anc |
|
251 |
|
elfzuzb |
|
252 |
224 250 251
|
sylanbrc |
|
253 |
|
lencl |
|
254 |
37 253
|
syl |
|
255 |
254 59
|
eleqtrdi |
|
256 |
|
eluzfz2 |
|
257 |
255 256
|
syl |
|
258 |
|
ccatswrd |
|
259 |
37 237 252 257 258
|
syl13anc |
|
260 |
235 259
|
eqtr4d |
|
261 |
|
swrdcl |
|
262 |
37 261
|
syl |
|
263 |
|
swrdcl |
|
264 |
37 263
|
syl |
|
265 |
|
swrdlen |
|
266 |
41 180 14 265
|
syl3anc |
|
267 |
|
swrdlen |
|
268 |
37 237 252 267
|
syl3anc |
|
269 |
83 67 75
|
sub32d |
|
270 |
83 67 75
|
subsub4d |
|
271 |
268 269 270
|
3eqtr2d |
|
272 |
266 271
|
eqtr4d |
|
273 |
|
ccatopth |
|
274 |
187 143 262 264 272 273
|
syl221anc |
|
275 |
260 274
|
mpbid |
|
276 |
275
|
simpld |
|
277 |
275
|
simprd |
|
278 |
|
elfzuzb |
|
279 |
224 248 278
|
sylanbrc |
|
280 |
|
elfzuz |
|
281 |
14 280
|
syl |
|
282 |
|
elfzuzb |
|
283 |
281 239 282
|
sylanbrc |
|
284 |
|
ccatswrd |
|
285 |
37 279 283 257 284
|
syl13anc |
|
286 |
277 285
|
eqtr4d |
|
287 |
|
swrdcl |
|
288 |
37 287
|
syl |
|
289 |
|
s2len |
|
290 |
|
swrdlen |
|
291 |
37 279 283 290
|
syl3anc |
|
292 |
|
nncan |
|
293 |
83 74 292
|
sylancl |
|
294 |
291 293
|
eqtr2d |
|
295 |
289 294
|
syl5eq |
|
296 |
|
ccatopth |
|
297 |
123 125 288 232 295 296
|
syl221anc |
|
298 |
286 297
|
mpbid |
|
299 |
298
|
simprd |
|
300 |
276 299
|
oveq12d |
|
301 |
234 300
|
eqtr3d |
|
302 |
301
|
oveq2d |
|
303 |
|
ccatass |
|
304 |
39 262 232 303
|
syl3anc |
|
305 |
302 304
|
eqtr4d |
|
306 |
|
ccatpfx |
|
307 |
37 237 252 306
|
syl3anc |
|
308 |
307
|
oveq1d |
|
309 |
23 305 308
|
3eqtrd |
|
310 |
|
ccatrid |
|
311 |
230 310
|
syl |
|
312 |
311
|
oveq1d |
|
313 |
309 312
|
eqtr4d |
|
314 |
|
pfxlen |
|
315 |
37 252 314
|
syl2anc |
|
316 |
315
|
eqcomd |
|
317 |
172
|
oveq2i |
|
318 |
81
|
zcnd |
|
319 |
318
|
addid1d |
|
320 |
317 319
|
eqtr2id |
|
321 |
230 102 232 123 313 316 320
|
splval2 |
|
322 |
298
|
simpld |
|
323 |
322
|
oveq2d |
|
324 |
|
ccatpfx |
|
325 |
37 279 283 324
|
syl3anc |
|
326 |
323 325
|
eqtrd |
|
327 |
326
|
oveq1d |
|
328 |
|
ccatpfx |
|
329 |
37 283 257 328
|
syl3anc |
|
330 |
|
pfxid |
|
331 |
37 330
|
syl |
|
332 |
327 329 331
|
3eqtrd |
|
333 |
228 321 332
|
3eqtrd |
|
334 |
|
fnovrn |
|
335 |
219 226 16 334
|
syl3anc |
|
336 |
333 335
|
eqeltrrd |
|
337 |
222 336
|
jca |
|