Step |
Hyp |
Ref |
Expression |
1 |
|
elrgspn.b |
|
2 |
|
elrgspn.m |
|
3 |
|
elrgspn.x |
|
4 |
|
elrgspn.n |
|
5 |
|
elrgspn.f |
|
6 |
|
elrgspn.r |
|
7 |
|
elrgspn.a |
|
8 |
|
elrgspnlem1.1 |
|
9 |
6
|
ringgrpd |
|
10 |
|
simpr |
|
11 |
|
eqid |
|
12 |
6
|
ringcmnd |
|
13 |
12
|
adantr |
|
14 |
1
|
fvexi |
|
15 |
14
|
a1i |
|
16 |
15 7
|
ssexd |
|
17 |
|
wrdexg |
|
18 |
16 17
|
syl |
|
19 |
18
|
adantr |
|
20 |
9
|
ad2antrr |
|
21 |
5
|
ssrab3 |
|
22 |
21
|
a1i |
|
23 |
22
|
sselda |
|
24 |
|
zex |
|
25 |
24
|
a1i |
|
26 |
25 18
|
elmapd |
|
27 |
26
|
adantr |
|
28 |
23 27
|
mpbid |
|
29 |
28
|
ffvelcdmda |
|
30 |
2
|
ringmgp |
|
31 |
6 30
|
syl |
|
32 |
|
sswrd |
|
33 |
7 32
|
syl |
|
34 |
33
|
sselda |
|
35 |
2 1
|
mgpbas |
|
36 |
35
|
gsumwcl |
|
37 |
31 34 36
|
syl2an2r |
|
38 |
37
|
adantlr |
|
39 |
1 3 20 29 38
|
mulgcld |
|
40 |
39
|
fmpttd |
|
41 |
|
fvexd |
|
42 |
|
0zd |
|
43 |
|
ssidd |
|
44 |
|
breq1 |
|
45 |
44 5
|
elrab2 |
|
46 |
45
|
simprbi |
|
47 |
46
|
adantl |
|
48 |
1 11 3
|
mulg0 |
|
49 |
48
|
adantl |
|
50 |
41 42 19 43 38 28 47 49
|
fisuppov1 |
|
51 |
1 11 13 19 40 50
|
gsumcl |
|
52 |
51
|
ad4ant13 |
|
53 |
10 52
|
eqeltrd |
|
54 |
8
|
eleq2i |
|
55 |
|
eqid |
|
56 |
55
|
elrnmpt |
|
57 |
56
|
elv |
|
58 |
54 57
|
sylbb |
|
59 |
58
|
adantl |
|
60 |
53 59
|
r19.29a |
|
61 |
60 1
|
eleqtrdi |
|
62 |
61
|
ex |
|
63 |
62
|
ssrdv |
|
64 |
63 1
|
sseqtrrdi |
|
65 |
|
breq1 |
|
66 |
|
0z |
|
67 |
66
|
fconst6 |
|
68 |
67
|
a1i |
|
69 |
25 18 68
|
elmapdd |
|
70 |
|
c0ex |
|
71 |
70
|
a1i |
|
72 |
18 71
|
fczfsuppd |
|
73 |
65 69 72
|
elrabd |
|
74 |
73 5
|
eleqtrrdi |
|
75 |
|
simplr |
|
76 |
75
|
fveq1d |
|
77 |
70
|
fconst |
|
78 |
77
|
a1i |
|
79 |
|
simpr |
|
80 |
|
fvconst |
|
81 |
78 79 80
|
syl2anc |
|
82 |
76 81
|
eqtrd |
|
83 |
82
|
oveq1d |
|
84 |
37
|
adantlr |
|
85 |
1 11 3
|
mulg0 |
|
86 |
84 85
|
syl |
|
87 |
83 86
|
eqtrd |
|
88 |
87
|
mpteq2dva |
|
89 |
88
|
oveq2d |
|
90 |
12
|
cmnmndd |
|
91 |
11
|
gsumz |
|
92 |
90 18 91
|
syl2anc |
|
93 |
92
|
adantr |
|
94 |
89 93
|
eqtrd |
|
95 |
94
|
eqeq2d |
|
96 |
|
eqidd |
|
97 |
74 95 96
|
rspcedvd |
|
98 |
|
fvexd |
|
99 |
55 97 98
|
elrnmptd |
|
100 |
99 8
|
eleqtrrdi |
|
101 |
100
|
ne0d |
|
102 |
|
simpllr |
|
103 |
|
simpr |
|
104 |
102 103
|
oveq12d |
|
105 |
|
eqid |
|
106 |
13
|
adantr |
|
107 |
19
|
adantr |
|
108 |
39
|
adantlr |
|
109 |
9
|
ad2antrr |
|
110 |
|
breq1 |
|
111 |
110 5
|
elrab2 |
|
112 |
111
|
simplbi |
|
113 |
112
|
adantl |
|
114 |
25 18
|
elmapd |
|
115 |
114
|
adantr |
|
116 |
113 115
|
mpbid |
|
117 |
116
|
ffvelcdmda |
|
118 |
37
|
adantlr |
|
119 |
1 3 109 117 118
|
mulgcld |
|
120 |
119
|
adantllr |
|
121 |
|
eqidd |
|
122 |
|
eqidd |
|
123 |
50
|
adantr |
|
124 |
50
|
ralrimiva |
|
125 |
|
fveq1 |
|
126 |
125
|
oveq1d |
|
127 |
126
|
mpteq2dv |
|
128 |
127
|
breq1d |
|
129 |
128
|
cbvralvw |
|
130 |
124 129
|
sylib |
|
131 |
130
|
r19.21bi |
|
132 |
131
|
adantlr |
|
133 |
1 11 105 106 107 108 120 121 122 123 132
|
gsummptfsadd |
|
134 |
28
|
ffnd |
|
135 |
134
|
adantr |
|
136 |
116
|
ffnd |
|
137 |
136
|
adantlr |
|
138 |
|
inidm |
|
139 |
|
eqidd |
|
140 |
|
eqidd |
|
141 |
135 137 107 107 138 139 140
|
ofval |
|
142 |
141
|
oveq1d |
|
143 |
20
|
adantlr |
|
144 |
29
|
adantlr |
|
145 |
117
|
adantllr |
|
146 |
38
|
adantlr |
|
147 |
1 3 105
|
mulgdir |
|
148 |
143 144 145 146 147
|
syl13anc |
|
149 |
142 148
|
eqtr2d |
|
150 |
149
|
mpteq2dva |
|
151 |
150
|
oveq2d |
|
152 |
133 151
|
eqtr3d |
|
153 |
|
fveq1 |
|
154 |
153
|
oveq1d |
|
155 |
154
|
mpteq2dv |
|
156 |
155
|
oveq2d |
|
157 |
156
|
cbvmptv |
|
158 |
|
fveq1 |
|
159 |
158
|
oveq1d |
|
160 |
159
|
mpteq2dv |
|
161 |
160
|
oveq2d |
|
162 |
161
|
eqeq2d |
|
163 |
|
breq1 |
|
164 |
24
|
a1i |
|
165 |
|
zaddcl |
|
166 |
165
|
adantl |
|
167 |
28
|
adantr |
|
168 |
116
|
adantlr |
|
169 |
166 167 168 107 107 138
|
off |
|
170 |
164 107 169
|
elmapdd |
|
171 |
|
zringring |
|
172 |
|
ringmnd |
|
173 |
171 172
|
ax-mp |
|
174 |
173
|
a1i |
|
175 |
23
|
adantr |
|
176 |
112
|
adantl |
|
177 |
47
|
adantr |
|
178 |
|
zring0 |
|
179 |
177 178
|
breqtrdi |
|
180 |
111
|
simprbi |
|
181 |
180
|
adantl |
|
182 |
181 178
|
breqtrdi |
|
183 |
|
zringbas |
|
184 |
183
|
mndpfsupp |
|
185 |
174 107 175 176 179 182 184
|
syl222anc |
|
186 |
|
zringplusg |
|
187 |
186
|
a1i |
|
188 |
187
|
ofeqd |
|
189 |
188
|
oveqd |
|
190 |
178
|
a1i |
|
191 |
185 189 190
|
3brtr4d |
|
192 |
163 170 191
|
elrabd |
|
193 |
192 5
|
eleqtrrdi |
|
194 |
|
eqidd |
|
195 |
162 193 194
|
rspcedvdw |
|
196 |
|
ovexd |
|
197 |
157 195 196
|
elrnmptd |
|
198 |
197 8
|
eleqtrrdi |
|
199 |
152 198
|
eqeltrd |
|
200 |
199
|
adantllr |
|
201 |
200
|
adantllr |
|
202 |
201
|
ad4ant13 |
|
203 |
104 202
|
eqeltrd |
|
204 |
8
|
eleq2i |
|
205 |
127
|
oveq2d |
|
206 |
205
|
cbvmptv |
|
207 |
206
|
elrnmpt |
|
208 |
207
|
elv |
|
209 |
204 208
|
sylbb |
|
210 |
209
|
adantl |
|
211 |
210
|
ad2antrr |
|
212 |
203 211
|
r19.29a |
|
213 |
59
|
adantr |
|
214 |
212 213
|
r19.29a |
|
215 |
214
|
ralrimiva |
|
216 |
9
|
ad3antrrr |
|
217 |
29
|
znegcld |
|
218 |
1 3 20 217 38
|
mulgcld |
|
219 |
218
|
fmpttd |
|
220 |
28
|
adantr |
|
221 |
|
simpr |
|
222 |
220 221
|
fvco3d |
|
223 |
|
eqid |
|
224 |
|
negeq |
|
225 |
223 224 29 217
|
fvmptd3 |
|
226 |
222 225
|
eqtrd |
|
227 |
226
|
oveq1d |
|
228 |
227
|
mpteq2dva |
|
229 |
|
simpr |
|
230 |
229
|
znegcld |
|
231 |
230
|
fmpttd |
|
232 |
231
|
adantr |
|
233 |
232 28
|
fcod |
|
234 |
24
|
a1i |
|
235 |
|
negeq |
|
236 |
|
neg0 |
|
237 |
235 236
|
eqtrdi |
|
238 |
|
0zd |
|
239 |
223 237 238 238
|
fvmptd3 |
|
240 |
239
|
adantr |
|
241 |
42 28 232 19 234 47 240
|
fsuppco2 |
|
242 |
41 42 19 43 38 233 241 49
|
fisuppov1 |
|
243 |
228 242
|
eqbrtrrd |
|
244 |
1 11 13 19 219 243
|
gsumcl |
|
245 |
244
|
ad4ant13 |
|
246 |
10
|
oveq1d |
|
247 |
|
eqidd |
|
248 |
|
eqidd |
|
249 |
1 11 105 13 19 39 218 247 248 50 243
|
gsummptfsadd |
|
250 |
249
|
ad4ant13 |
|
251 |
29
|
zcnd |
|
252 |
251
|
negidd |
|
253 |
252
|
oveq1d |
|
254 |
1 3 105
|
mulgdir |
|
255 |
20 29 217 38 254
|
syl13anc |
|
256 |
38 85
|
syl |
|
257 |
253 255 256
|
3eqtr3d |
|
258 |
257
|
mpteq2dva |
|
259 |
258
|
oveq2d |
|
260 |
92
|
adantr |
|
261 |
259 260
|
eqtrd |
|
262 |
261
|
ad4ant13 |
|
263 |
246 250 262
|
3eqtr2d |
|
264 |
|
eqid |
|
265 |
1 105 11 264
|
grpinvid1 |
|
266 |
265
|
biimpar |
|
267 |
216 53 245 263 266
|
syl31anc |
|
268 |
|
fveq1 |
|
269 |
268
|
oveq1d |
|
270 |
269
|
mpteq2dv |
|
271 |
270
|
oveq2d |
|
272 |
271
|
eqeq2d |
|
273 |
|
breq1 |
|
274 |
28
|
ffvelcdmda |
|
275 |
274
|
znegcld |
|
276 |
275
|
fmpttd |
|
277 |
234 19 276
|
elmapdd |
|
278 |
276
|
ffund |
|
279 |
134
|
adantr |
|
280 |
19
|
adantr |
|
281 |
|
0zd |
|
282 |
|
simpr |
|
283 |
279 280 281 282
|
fvdifsupp |
|
284 |
283
|
negeqd |
|
285 |
284 236
|
eqtrdi |
|
286 |
285 19
|
suppss2 |
|
287 |
277 42 278 47 286
|
fsuppsssuppgd |
|
288 |
273 277 287
|
elrabd |
|
289 |
288 5
|
eleqtrrdi |
|
290 |
|
eqid |
|
291 |
|
fveq2 |
|
292 |
291
|
negeqd |
|
293 |
290 292 221 217
|
fvmptd3 |
|
294 |
293
|
eqcomd |
|
295 |
294
|
oveq1d |
|
296 |
295
|
mpteq2dva |
|
297 |
296
|
oveq2d |
|
298 |
272 289 297
|
rspcedvdw |
|
299 |
157 298 244
|
elrnmptd |
|
300 |
299 8
|
eleqtrrdi |
|
301 |
300
|
ad4ant13 |
|
302 |
267 301
|
eqeltrd |
|
303 |
302 59
|
r19.29a |
|
304 |
215 303
|
jca |
|
305 |
304
|
ralrimiva |
|
306 |
1 105 264
|
issubg2 |
|
307 |
306
|
biimpar |
|
308 |
9 64 101 305 307
|
syl13anc |
|