Step |
Hyp |
Ref |
Expression |
1 |
|
amgmwlem.0 |
|
2 |
|
amgmwlem.1 |
|
3 |
|
amgmwlem.2 |
|
4 |
|
amgmwlem.3 |
|
5 |
|
amgmwlem.4 |
|
6 |
|
amgmwlem.5 |
|
7 |
4
|
ffvelrnda |
|
8 |
5
|
ffvelrnda |
|
9 |
8
|
rpred |
|
10 |
7 9
|
rpcxpcld |
|
11 |
10
|
relogcld |
|
12 |
11
|
recnd |
|
13 |
2 12
|
gsumfsum |
|
14 |
12
|
negnegd |
|
15 |
14
|
sumeq2dv |
|
16 |
11
|
renegcld |
|
17 |
16
|
recnd |
|
18 |
2 17
|
fsumneg |
|
19 |
7 9
|
logcxpd |
|
20 |
19
|
negeqd |
|
21 |
20
|
sumeq2dv |
|
22 |
21
|
negeqd |
|
23 |
8
|
rpcnd |
|
24 |
7
|
relogcld |
|
25 |
24
|
recnd |
|
26 |
23 25
|
mulneg2d |
|
27 |
26
|
eqcomd |
|
28 |
27
|
sumeq2dv |
|
29 |
28
|
negeqd |
|
30 |
18 22 29
|
3eqtrd |
|
31 |
13 15 30
|
3eqtr2rd |
|
32 |
|
negex |
|
33 |
32
|
a1i |
|
34 |
5
|
feqmptd |
|
35 |
|
eqidd |
|
36 |
2 8 33 34 35
|
offval2 |
|
37 |
36
|
oveq2d |
|
38 |
25
|
negcld |
|
39 |
23 38
|
mulcld |
|
40 |
2 39
|
gsumfsum |
|
41 |
37 40
|
eqtrd |
|
42 |
41
|
negeqd |
|
43 |
|
relogf1o |
|
44 |
|
f1of |
|
45 |
43 44
|
ax-mp |
|
46 |
|
rpre |
|
47 |
46
|
anim2i |
|
48 |
47
|
adantl |
|
49 |
|
rpcxpcl |
|
50 |
48 49
|
syl |
|
51 |
|
inidm |
|
52 |
50 4 5 2 2 51
|
off |
|
53 |
|
fcompt |
|
54 |
45 52 53
|
sylancr |
|
55 |
52
|
ffvelrnda |
|
56 |
|
fvres |
|
57 |
55 56
|
syl |
|
58 |
4
|
ffnd |
|
59 |
5
|
ffnd |
|
60 |
|
eqidd |
|
61 |
|
eqidd |
|
62 |
58 59 2 2 51 60 61
|
ofval |
|
63 |
62
|
fveq2d |
|
64 |
57 63
|
eqtrd |
|
65 |
64
|
mpteq2dva |
|
66 |
54 65
|
eqtrd |
|
67 |
66
|
oveq2d |
|
68 |
31 42 67
|
3eqtr4d |
|
69 |
1
|
oveq1i |
|
70 |
69
|
rpmsubg |
|
71 |
|
subgsubm |
|
72 |
70 71
|
ax-mp |
|
73 |
|
cnring |
|
74 |
|
cnfldbas |
|
75 |
|
cnfld0 |
|
76 |
|
cndrng |
|
77 |
74 75 76
|
drngui |
|
78 |
77 1
|
unitsubm |
|
79 |
|
eqid |
|
80 |
79
|
subsubm |
|
81 |
73 78 80
|
mp2b |
|
82 |
72 81
|
mpbi |
|
83 |
82
|
simpli |
|
84 |
|
eqid |
|
85 |
84
|
submbas |
|
86 |
83 85
|
ax-mp |
|
87 |
|
cnfld1 |
|
88 |
1 87
|
ringidval |
|
89 |
|
eqid |
|
90 |
84 89
|
subm0 |
|
91 |
83 90
|
ax-mp |
|
92 |
88 91
|
eqtri |
|
93 |
|
cncrng |
|
94 |
1
|
crngmgp |
|
95 |
93 94
|
mp1i |
|
96 |
84
|
submmnd |
|
97 |
83 96
|
mp1i |
|
98 |
84
|
subcmn |
|
99 |
95 97 98
|
syl2anc |
|
100 |
|
resubdrg |
|
101 |
100
|
simpli |
|
102 |
|
df-refld |
|
103 |
102
|
subrgring |
|
104 |
101 103
|
ax-mp |
|
105 |
|
ringmnd |
|
106 |
104 105
|
mp1i |
|
107 |
1
|
oveq1i |
|
108 |
107
|
reloggim |
|
109 |
|
gimghm |
|
110 |
108 109
|
ax-mp |
|
111 |
|
ghmmhm |
|
112 |
110 111
|
mp1i |
|
113 |
|
1red |
|
114 |
52 2 113
|
fdmfifsupp |
|
115 |
86 92 99 106 2 112 52 114
|
gsummhm |
|
116 |
|
subrgsubg |
|
117 |
101 116
|
ax-mp |
|
118 |
|
subgsubm |
|
119 |
117 118
|
ax-mp |
|
120 |
119
|
a1i |
|
121 |
43 44
|
mp1i |
|
122 |
|
fco |
|
123 |
121 52 122
|
syl2anc |
|
124 |
2 120 123 102
|
gsumsubm |
|
125 |
83
|
a1i |
|
126 |
2 125 52 84
|
gsumsubm |
|
127 |
126
|
fveq2d |
|
128 |
115 124 127
|
3eqtr4d |
|
129 |
88 95 2 125 52 114
|
gsumsubmcl |
|
130 |
|
fvres |
|
131 |
129 130
|
syl |
|
132 |
68 128 131
|
3eqtrd |
|
133 |
|
simprl |
|
134 |
133
|
rpcnd |
|
135 |
|
simprr |
|
136 |
135
|
rpcnd |
|
137 |
134 136
|
mulcomd |
|
138 |
2 5 4 137
|
caofcom |
|
139 |
138
|
oveq2d |
|
140 |
4
|
feqmptd |
|
141 |
2 8 7 34 140
|
offval2 |
|
142 |
141
|
oveq2d |
|
143 |
8 7
|
rpmulcld |
|
144 |
143
|
rpcnd |
|
145 |
2 144
|
gsumfsum |
|
146 |
142 145
|
eqtrd |
|
147 |
2 3 143
|
fsumrpcl |
|
148 |
146 147
|
eqeltrd |
|
149 |
139 148
|
eqeltrrd |
|
150 |
149
|
relogcld |
|
151 |
|
ringcmn |
|
152 |
73 151
|
mp1i |
|
153 |
|
remulcl |
|
154 |
153
|
adantl |
|
155 |
|
rpssre |
|
156 |
|
fss |
|
157 |
5 155 156
|
sylancl |
|
158 |
24
|
renegcld |
|
159 |
158
|
fmpttd |
|
160 |
154 157 159 2 2 51
|
off |
|
161 |
|
0red |
|
162 |
160 2 161
|
fdmfifsupp |
|
163 |
75 152 2 120 160 162
|
gsumsubmcl |
|
164 |
155
|
a1i |
|
165 |
|
simpr |
|
166 |
165
|
relogcld |
|
167 |
166
|
renegcld |
|
168 |
167
|
fmpttd |
|
169 |
|
simpl |
|
170 |
|
ioorp |
|
171 |
169 170
|
eleqtrrdi |
|
172 |
|
simpr |
|
173 |
172 170
|
eleqtrrdi |
|
174 |
|
iccssioo2 |
|
175 |
171 173 174
|
syl2anc |
|
176 |
175 170
|
sseqtrdi |
|
177 |
176
|
adantl |
|
178 |
|
ioossico |
|
179 |
170 178
|
eqsstrri |
|
180 |
|
fss |
|
181 |
5 179 180
|
sylancl |
|
182 |
|
0lt1 |
|
183 |
182 6
|
breqtrrid |
|
184 |
|
logccv |
|
185 |
184
|
3adant1 |
|
186 |
|
elioore |
|
187 |
186
|
3ad2ant3 |
|
188 |
|
simp21 |
|
189 |
188
|
relogcld |
|
190 |
187 189
|
remulcld |
|
191 |
|
1red |
|
192 |
191 186
|
resubcld |
|
193 |
192
|
3ad2ant3 |
|
194 |
|
simp22 |
|
195 |
194
|
relogcld |
|
196 |
193 195
|
remulcld |
|
197 |
190 196
|
readdcld |
|
198 |
|
eliooord |
|
199 |
198
|
simpld |
|
200 |
186 199
|
elrpd |
|
201 |
200
|
3ad2ant3 |
|
202 |
201 188
|
rpmulcld |
|
203 |
|
0red |
|
204 |
198
|
simprd |
|
205 |
|
1m0e1 |
|
206 |
204 205
|
breqtrrdi |
|
207 |
186 191 203 206
|
ltsub13d |
|
208 |
192 207
|
elrpd |
|
209 |
208
|
3ad2ant3 |
|
210 |
209 194
|
rpmulcld |
|
211 |
|
rpaddcl |
|
212 |
202 210 211
|
syl2anc |
|
213 |
212
|
relogcld |
|
214 |
197 213
|
ltnegd |
|
215 |
185 214
|
mpbid |
|
216 |
|
eqidd |
|
217 |
|
fveq2 |
|
218 |
217
|
adantl |
|
219 |
218
|
negeqd |
|
220 |
|
negex |
|
221 |
220
|
a1i |
|
222 |
216 219 212 221
|
fvmptd |
|
223 |
|
fveq2 |
|
224 |
223
|
negeqd |
|
225 |
|
eqid |
|
226 |
|
negex |
|
227 |
224 225 226
|
fvmpt3i |
|
228 |
188 227
|
syl |
|
229 |
228
|
oveq2d |
|
230 |
187
|
recnd |
|
231 |
189
|
recnd |
|
232 |
230 231
|
mulneg2d |
|
233 |
229 232
|
eqtrd |
|
234 |
|
fveq2 |
|
235 |
234
|
negeqd |
|
236 |
235 225 226
|
fvmpt3i |
|
237 |
194 236
|
syl |
|
238 |
237
|
oveq2d |
|
239 |
209
|
rpcnd |
|
240 |
195
|
recnd |
|
241 |
239 240
|
mulneg2d |
|
242 |
238 241
|
eqtrd |
|
243 |
233 242
|
oveq12d |
|
244 |
190
|
recnd |
|
245 |
196
|
recnd |
|
246 |
244 245
|
negdid |
|
247 |
243 246
|
eqtr4d |
|
248 |
215 222 247
|
3brtr4d |
|
249 |
164 168 177 248
|
scvxcvx |
|
250 |
164 168 177 2 181 4 183 249
|
jensen |
|
251 |
250
|
simprd |
|
252 |
6
|
oveq2d |
|
253 |
252
|
fveq2d |
|
254 |
148
|
rpcnd |
|
255 |
254
|
div1d |
|
256 |
255
|
fveq2d |
|
257 |
|
fveq2 |
|
258 |
257
|
negeqd |
|
259 |
258 225 226
|
fvmpt3i |
|
260 |
148 259
|
syl |
|
261 |
139
|
fveq2d |
|
262 |
261
|
negeqd |
|
263 |
260 262
|
eqtrd |
|
264 |
253 256 263
|
3eqtrd |
|
265 |
6
|
oveq2d |
|
266 |
|
ringmnd |
|
267 |
73 266
|
ax-mp |
|
268 |
74
|
submid |
|
269 |
267 268
|
mp1i |
|
270 |
|
mulcl |
|
271 |
270
|
adantl |
|
272 |
|
rpcn |
|
273 |
272
|
ssriv |
|
274 |
273
|
a1i |
|
275 |
5 274
|
fssd |
|
276 |
166
|
recnd |
|
277 |
276
|
negcld |
|
278 |
277
|
fmpttd |
|
279 |
|
fco |
|
280 |
278 4 279
|
syl2anc |
|
281 |
271 275 280 2 2 51
|
off |
|
282 |
281 2 161
|
fdmfifsupp |
|
283 |
75 152 2 269 281 282
|
gsumsubmcl |
|
284 |
283
|
div1d |
|
285 |
|
eqidd |
|
286 |
|
fveq2 |
|
287 |
286
|
negeqd |
|
288 |
7 140 285 287
|
fmptco |
|
289 |
288
|
oveq2d |
|
290 |
289
|
oveq2d |
|
291 |
265 284 290
|
3eqtrd |
|
292 |
251 264 291
|
3brtr3d |
|
293 |
150 163 292
|
lenegcon1d |
|
294 |
132 293
|
eqbrtrrd |
|
295 |
129
|
relogcld |
|
296 |
|
efle |
|
297 |
295 150 296
|
syl2anc |
|
298 |
294 297
|
mpbid |
|
299 |
129
|
reeflogd |
|
300 |
299
|
eqcomd |
|
301 |
149
|
reeflogd |
|
302 |
301
|
eqcomd |
|
303 |
298 300 302
|
3brtr4d |
|