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 |
|
uzp1 |
|
22 |
|
fviss |
|
23 |
1 22
|
eqsstri |
|
24 |
1 2 3 4 5 6
|
efgsdm |
|
25 |
24
|
simp1bi |
|
26 |
8 25
|
syl |
|
27 |
26
|
eldifad |
|
28 |
|
wrdf |
|
29 |
27 28
|
syl |
|
30 |
|
fzossfz |
|
31 |
1 2 3 4 5 6 7 8 9 10 11
|
efgredlema |
|
32 |
31
|
simpld |
|
33 |
|
fzo0end |
|
34 |
32 33
|
syl |
|
35 |
12 34
|
eqeltrid |
|
36 |
30 35
|
sselid |
|
37 |
|
lencl |
|
38 |
27 37
|
syl |
|
39 |
38
|
nn0zd |
|
40 |
|
fzoval |
|
41 |
39 40
|
syl |
|
42 |
36 41
|
eleqtrrd |
|
43 |
29 42
|
ffvelrnd |
|
44 |
23 43
|
sselid |
|
45 |
|
lencl |
|
46 |
44 45
|
syl |
|
47 |
|
nn0uz |
|
48 |
46 47
|
eleqtrdi |
|
49 |
|
eluzfz2 |
|
50 |
48 49
|
syl |
|
51 |
|
ccatpfx |
|
52 |
44 14 50 51
|
syl3anc |
|
53 |
|
pfxid |
|
54 |
44 53
|
syl |
|
55 |
52 54
|
eqtrd |
|
56 |
1 2 3 4 5 6
|
efgsdm |
|
57 |
56
|
simp1bi |
|
58 |
9 57
|
syl |
|
59 |
58
|
eldifad |
|
60 |
|
wrdf |
|
61 |
59 60
|
syl |
|
62 |
|
fzossfz |
|
63 |
31
|
simprd |
|
64 |
|
fzo0end |
|
65 |
63 64
|
syl |
|
66 |
13 65
|
eqeltrid |
|
67 |
62 66
|
sselid |
|
68 |
|
lencl |
|
69 |
59 68
|
syl |
|
70 |
69
|
nn0zd |
|
71 |
|
fzoval |
|
72 |
70 71
|
syl |
|
73 |
67 72
|
eleqtrrd |
|
74 |
61 73
|
ffvelrnd |
|
75 |
23 74
|
sselid |
|
76 |
|
lencl |
|
77 |
75 76
|
syl |
|
78 |
77 47
|
eleqtrdi |
|
79 |
|
eluzfz2 |
|
80 |
78 79
|
syl |
|
81 |
|
ccatpfx |
|
82 |
75 15 80 81
|
syl3anc |
|
83 |
|
pfxid |
|
84 |
75 83
|
syl |
|
85 |
82 84
|
eqtrd |
|
86 |
55 85
|
eqeq12d |
|
87 |
20 86
|
mtbird |
|
88 |
1 2 3 4
|
efgtval |
|
89 |
43 14 16 88
|
syl3anc |
|
90 |
3
|
efgmf |
|
91 |
90
|
ffvelrni |
|
92 |
16 91
|
syl |
|
93 |
16 92
|
s2cld |
|
94 |
|
splval |
|
95 |
43 14 14 93 94
|
syl13anc |
|
96 |
18 89 95
|
3eqtrd |
|
97 |
1 2 3 4
|
efgtval |
|
98 |
74 15 17 97
|
syl3anc |
|
99 |
90
|
ffvelrni |
|
100 |
17 99
|
syl |
|
101 |
17 100
|
s2cld |
|
102 |
|
splval |
|
103 |
74 15 15 101 102
|
syl13anc |
|
104 |
19 98 103
|
3eqtrd |
|
105 |
10 96 104
|
3eqtr3d |
|
106 |
105
|
adantr |
|
107 |
|
pfxcl |
|
108 |
44 107
|
syl |
|
109 |
108
|
adantr |
|
110 |
93
|
adantr |
|
111 |
|
ccatcl |
|
112 |
109 110 111
|
syl2anc |
|
113 |
|
swrdcl |
|
114 |
44 113
|
syl |
|
115 |
114
|
adantr |
|
116 |
|
pfxcl |
|
117 |
75 116
|
syl |
|
118 |
117
|
adantr |
|
119 |
101
|
adantr |
|
120 |
|
ccatcl |
|
121 |
118 119 120
|
syl2anc |
|
122 |
|
swrdcl |
|
123 |
75 122
|
syl |
|
124 |
123
|
adantr |
|
125 |
|
pfxlen |
|
126 |
44 14 125
|
syl2anc |
|
127 |
|
pfxlen |
|
128 |
75 15 127
|
syl2anc |
|
129 |
126 128
|
eqeq12d |
|
130 |
129
|
biimpar |
|
131 |
|
s2len |
|
132 |
|
s2len |
|
133 |
131 132
|
eqtr4i |
|
134 |
133
|
a1i |
|
135 |
130 134
|
oveq12d |
|
136 |
|
ccatlen |
|
137 |
109 110 136
|
syl2anc |
|
138 |
|
ccatlen |
|
139 |
118 119 138
|
syl2anc |
|
140 |
135 137 139
|
3eqtr4d |
|
141 |
|
ccatopth |
|
142 |
112 115 121 124 140 141
|
syl221anc |
|
143 |
106 142
|
mpbid |
|
144 |
143
|
simpld |
|
145 |
|
ccatopth |
|
146 |
109 110 118 119 130 145
|
syl221anc |
|
147 |
144 146
|
mpbid |
|
148 |
147
|
simpld |
|
149 |
143
|
simprd |
|
150 |
148 149
|
oveq12d |
|
151 |
87 150
|
mtand |
|
152 |
151
|
pm2.21d |
|
153 |
|
uzp1 |
|
154 |
16
|
s1cld |
|
155 |
|
ccatcl |
|
156 |
108 154 155
|
syl2anc |
|
157 |
92
|
s1cld |
|
158 |
|
ccatass |
|
159 |
156 157 114 158
|
syl3anc |
|
160 |
|
ccatass |
|
161 |
108 154 157 160
|
syl3anc |
|
162 |
|
df-s2 |
|
163 |
162
|
oveq2i |
|
164 |
161 163
|
eqtr4di |
|
165 |
164
|
oveq1d |
|
166 |
17
|
s1cld |
|
167 |
100
|
s1cld |
|
168 |
|
ccatass |
|
169 |
117 166 167 168
|
syl3anc |
|
170 |
|
df-s2 |
|
171 |
170
|
oveq2i |
|
172 |
169 171
|
eqtr4di |
|
173 |
172
|
oveq1d |
|
174 |
105 165 173
|
3eqtr4d |
|
175 |
159 174
|
eqtr3d |
|
176 |
175
|
adantr |
|
177 |
156
|
adantr |
|
178 |
157
|
adantr |
|
179 |
114
|
adantr |
|
180 |
|
ccatcl |
|
181 |
178 179 180
|
syl2anc |
|
182 |
|
ccatcl |
|
183 |
117 166 182
|
syl2anc |
|
184 |
183
|
adantr |
|
185 |
167
|
adantr |
|
186 |
|
ccatcl |
|
187 |
184 185 186
|
syl2anc |
|
188 |
123
|
adantr |
|
189 |
|
ccatlen |
|
190 |
117 166 189
|
syl2anc |
|
191 |
|
s1len |
|
192 |
191
|
a1i |
|
193 |
128 192
|
oveq12d |
|
194 |
190 193
|
eqtrd |
|
195 |
126 194
|
eqeq12d |
|
196 |
195
|
biimpar |
|
197 |
|
s1len |
|
198 |
|
s1len |
|
199 |
197 198
|
eqtr4i |
|
200 |
199
|
a1i |
|
201 |
196 200
|
oveq12d |
|
202 |
108
|
adantr |
|
203 |
154
|
adantr |
|
204 |
|
ccatlen |
|
205 |
202 203 204
|
syl2anc |
|
206 |
|
ccatlen |
|
207 |
184 185 206
|
syl2anc |
|
208 |
201 205 207
|
3eqtr4d |
|
209 |
|
ccatopth |
|
210 |
177 181 187 188 208 209
|
syl221anc |
|
211 |
176 210
|
mpbid |
|
212 |
211
|
simpld |
|
213 |
|
ccatopth |
|
214 |
202 203 184 185 196 213
|
syl221anc |
|
215 |
212 214
|
mpbid |
|
216 |
215
|
simpld |
|
217 |
216
|
oveq1d |
|
218 |
117
|
adantr |
|
219 |
166
|
adantr |
|
220 |
|
ccatass |
|
221 |
218 219 179 220
|
syl3anc |
|
222 |
215
|
simprd |
|
223 |
|
s111 |
|
224 |
16 100 223
|
syl2anc |
|
225 |
224
|
adantr |
|
226 |
222 225
|
mpbid |
|
227 |
226
|
fveq2d |
|
228 |
3
|
efgmnvl |
|
229 |
17 228
|
syl |
|
230 |
229
|
adantr |
|
231 |
227 230
|
eqtrd |
|
232 |
231
|
s1eqd |
|
233 |
232
|
oveq1d |
|
234 |
211
|
simprd |
|
235 |
233 234
|
eqtr3d |
|
236 |
235
|
oveq2d |
|
237 |
217 221 236
|
3eqtrd |
|
238 |
87 237
|
mtand |
|
239 |
238
|
pm2.21d |
|
240 |
15
|
elfzelzd |
|
241 |
240
|
zcnd |
|
242 |
|
1cnd |
|
243 |
241 242 242
|
addassd |
|
244 |
|
df-2 |
|
245 |
244
|
oveq2i |
|
246 |
243 245
|
eqtr4di |
|
247 |
246
|
fveq2d |
|
248 |
247
|
eleq2d |
|
249 |
1 2 3 4 5 6
|
efgsfo |
|
250 |
|
swrdcl |
|
251 |
44 250
|
syl |
|
252 |
|
ccatcl |
|
253 |
117 251 252
|
syl2anc |
|
254 |
1
|
efgrcl |
|
255 |
43 254
|
syl |
|
256 |
255
|
simprd |
|
257 |
253 256
|
eleqtrrd |
|
258 |
|
foelrn |
|
259 |
249 257 258
|
sylancr |
|
260 |
259
|
adantr |
|
261 |
7
|
ad2antrr |
|
262 |
8
|
ad2antrr |
|
263 |
9
|
ad2antrr |
|
264 |
10
|
ad2antrr |
|
265 |
11
|
ad2antrr |
|
266 |
14
|
ad2antrr |
|
267 |
15
|
ad2antrr |
|
268 |
16
|
ad2antrr |
|
269 |
17
|
ad2antrr |
|
270 |
18
|
ad2antrr |
|
271 |
19
|
ad2antrr |
|
272 |
20
|
ad2antrr |
|
273 |
|
simplr |
|
274 |
|
simprl |
|
275 |
|
simprr |
|
276 |
275
|
eqcomd |
|
277 |
1 2 3 4 5 6 261 262 263 264 265 12 13 266 267 268 269 270 271 272 273 274 276
|
efgredlemd |
|
278 |
260 277
|
rexlimddv |
|
279 |
278
|
ex |
|
280 |
248 279
|
sylbid |
|
281 |
239 280
|
jaod |
|
282 |
153 281
|
syl5 |
|
283 |
152 282
|
jaod |
|
284 |
21 283
|
syl5 |
|