Step |
Hyp |
Ref |
Expression |
1 |
|
rpvmasum.z |
|
2 |
|
rpvmasum.l |
|
3 |
|
rpvmasum.a |
|
4 |
|
rpvmasum2.g |
|
5 |
|
rpvmasum2.d |
|
6 |
|
rpvmasum2.1 |
|
7 |
|
rpvmasum2.w |
|
8 |
|
rpvmasum2.u |
|
9 |
|
rpvmasum2.b |
|
10 |
|
rpvmasum2.t |
|
11 |
|
rpvmasum2.z1 |
|
12 |
3
|
adantr |
|
13 |
4 5
|
dchrfi |
|
14 |
12 13
|
syl |
|
15 |
|
fzfid |
|
16 |
|
eqid |
|
17 |
|
simpr |
|
18 |
4 1 5 16 17
|
dchrf |
|
19 |
16 8
|
unitss |
|
20 |
19 9
|
sseldi |
|
21 |
20
|
adantr |
|
22 |
18 21
|
ffvelrnd |
|
23 |
22
|
cjcld |
|
24 |
23
|
adantlr |
|
25 |
24
|
adantrl |
|
26 |
18
|
ad4ant14 |
|
27 |
3
|
nnnn0d |
|
28 |
1 16 2
|
znzrhfo |
|
29 |
|
fof |
|
30 |
27 28 29
|
3syl |
|
31 |
30
|
adantr |
|
32 |
|
elfzelz |
|
33 |
|
ffvelrn |
|
34 |
31 32 33
|
syl2an |
|
35 |
34
|
adantr |
|
36 |
26 35
|
ffvelrnd |
|
37 |
36
|
anasss |
|
38 |
|
elfznn |
|
39 |
38
|
adantl |
|
40 |
|
vmacl |
|
41 |
39 40
|
syl |
|
42 |
41 39
|
nndivred |
|
43 |
42
|
recnd |
|
44 |
43
|
adantrr |
|
45 |
37 44
|
mulcld |
|
46 |
25 45
|
mulcld |
|
47 |
46
|
anass1rs |
|
48 |
15 47
|
fsumcl |
|
49 |
|
relogcl |
|
50 |
49
|
adantl |
|
51 |
50
|
recnd |
|
52 |
51
|
adantr |
|
53 |
|
ax-1cn |
|
54 |
|
neg1cn |
|
55 |
|
0cn |
|
56 |
54 55
|
ifcli |
|
57 |
53 56
|
ifcli |
|
58 |
|
mulcl |
|
59 |
52 57 58
|
sylancl |
|
60 |
14 48 59
|
fsumsub |
|
61 |
45
|
anass1rs |
|
62 |
15 61
|
fsumcl |
|
63 |
24 62 59
|
subdid |
|
64 |
15 24 61
|
fsummulc2 |
|
65 |
57
|
a1i |
|
66 |
24 52 65
|
mul12d |
|
67 |
|
ovif2 |
|
68 |
|
fveq1 |
|
69 |
3
|
ad2antrr |
|
70 |
9
|
ad2antrr |
|
71 |
4 1 6 8 69 70
|
dchr1 |
|
72 |
68 71
|
sylan9eqr |
|
73 |
72
|
fveq2d |
|
74 |
|
1re |
|
75 |
|
cjre |
|
76 |
74 75
|
ax-mp |
|
77 |
73 76
|
eqtrdi |
|
78 |
77
|
oveq1d |
|
79 |
|
1t1e1 |
|
80 |
78 79
|
eqtrdi |
|
81 |
|
df-ne |
|
82 |
|
ovif2 |
|
83 |
11
|
fveq2d |
|
84 |
83
|
ad5ant15 |
|
85 |
4 1 5
|
dchrmhm |
|
86 |
|
simpr |
|
87 |
85 86
|
sseldi |
|
88 |
|
eqid |
|
89 |
|
eqid |
|
90 |
88 89
|
ringidval |
|
91 |
|
eqid |
|
92 |
|
cnfld1 |
|
93 |
91 92
|
ringidval |
|
94 |
90 93
|
mhm0 |
|
95 |
87 94
|
syl |
|
96 |
95
|
ad2antrr |
|
97 |
84 96
|
eqtrd |
|
98 |
97
|
fveq2d |
|
99 |
98 76
|
eqtrdi |
|
100 |
99
|
oveq1d |
|
101 |
54
|
mulid2i |
|
102 |
100 101
|
eqtrdi |
|
103 |
102
|
ifeq1da |
|
104 |
24
|
adantr |
|
105 |
104
|
mul01d |
|
106 |
105
|
ifeq2d |
|
107 |
103 106
|
eqtrd |
|
108 |
82 107
|
syl5eq |
|
109 |
81 108
|
sylan2br |
|
110 |
80 109
|
ifeq12da |
|
111 |
67 110
|
syl5eq |
|
112 |
111
|
oveq2d |
|
113 |
66 112
|
eqtrd |
|
114 |
64 113
|
oveq12d |
|
115 |
63 114
|
eqtrd |
|
116 |
115
|
sumeq2dv |
|
117 |
|
fzfid |
|
118 |
|
inss1 |
|
119 |
|
ssfi |
|
120 |
117 118 119
|
sylancl |
|
121 |
12
|
phicld |
|
122 |
121
|
nncnd |
|
123 |
118
|
a1i |
|
124 |
123
|
sselda |
|
125 |
124 43
|
syldan |
|
126 |
120 122 125
|
fsummulc2 |
|
127 |
122
|
adantr |
|
128 |
127 43
|
mulcld |
|
129 |
124 128
|
syldan |
|
130 |
129
|
ralrimiva |
|
131 |
117
|
olcd |
|
132 |
|
sumss2 |
|
133 |
123 130 131 132
|
syl21anc |
|
134 |
|
elin |
|
135 |
134
|
baib |
|
136 |
135
|
adantl |
|
137 |
10
|
eleq2i |
|
138 |
31
|
ffnd |
|
139 |
|
fniniseg |
|
140 |
139
|
baibd |
|
141 |
138 32 140
|
syl2an |
|
142 |
137 141
|
syl5bb |
|
143 |
136 142
|
bitr2d |
|
144 |
43
|
mul02d |
|
145 |
143 144
|
ifbieq2d |
|
146 |
|
ovif |
|
147 |
3
|
ad2antrr |
|
148 |
147 13
|
syl |
|
149 |
23
|
ad4ant14 |
|
150 |
36 149
|
mulcld |
|
151 |
148 43 150
|
fsummulc1 |
|
152 |
9
|
ad2antrr |
|
153 |
4 5 1 16 8 147 34 152
|
sum2dchr |
|
154 |
153
|
oveq1d |
|
155 |
43
|
adantr |
|
156 |
|
mulass |
|
157 |
|
mul12 |
|
158 |
156 157
|
eqtrd |
|
159 |
36 149 155 158
|
syl3anc |
|
160 |
159
|
sumeq2dv |
|
161 |
151 154 160
|
3eqtr3d |
|
162 |
146 161
|
syl5eqr |
|
163 |
145 162
|
eqtr3d |
|
164 |
163
|
sumeq2dv |
|
165 |
126 133 164
|
3eqtrd |
|
166 |
117 14 46
|
fsumcom |
|
167 |
165 166
|
eqtrd |
|
168 |
4
|
dchrabl |
|
169 |
|
ablgrp |
|
170 |
5 6
|
grpidcl |
|
171 |
12 168 169 170
|
4syl |
|
172 |
51
|
mulid1d |
|
173 |
172 51
|
eqeltrd |
|
174 |
|
iftrue |
|
175 |
174
|
oveq2d |
|
176 |
175
|
sumsn |
|
177 |
171 173 176
|
syl2anc |
|
178 |
|
eldifsn |
|
179 |
|
ifnefalse |
|
180 |
179
|
ad2antll |
|
181 |
|
negeq |
|
182 |
|
negeq |
|
183 |
|
neg0 |
|
184 |
182 183
|
eqtrdi |
|
185 |
181 184
|
ifsb |
|
186 |
180 185
|
eqtr4di |
|
187 |
186
|
oveq2d |
|
188 |
51
|
adantr |
|
189 |
53 55
|
ifcli |
|
190 |
|
mulneg2 |
|
191 |
188 189 190
|
sylancl |
|
192 |
187 191
|
eqtrd |
|
193 |
178 192
|
sylan2b |
|
194 |
193
|
sumeq2dv |
|
195 |
|
diffi |
|
196 |
14 195
|
syl |
|
197 |
51
|
adantr |
|
198 |
|
mulcl |
|
199 |
197 189 198
|
sylancl |
|
200 |
196 199
|
fsumneg |
|
201 |
189
|
a1i |
|
202 |
196 51 201
|
fsummulc2 |
|
203 |
7
|
ssrab3 |
|
204 |
|
difss |
|
205 |
203 204
|
sstri |
|
206 |
|
ssfi |
|
207 |
14 205 206
|
sylancl |
|
208 |
|
fsumconst |
|
209 |
207 53 208
|
sylancl |
|
210 |
203
|
a1i |
|
211 |
53
|
a1i |
|
212 |
211
|
ralrimivw |
|
213 |
196
|
olcd |
|
214 |
|
sumss2 |
|
215 |
210 212 213 214
|
syl21anc |
|
216 |
|
hashcl |
|
217 |
207 216
|
syl |
|
218 |
217
|
nn0cnd |
|
219 |
218
|
mulid1d |
|
220 |
209 215 219
|
3eqtr3d |
|
221 |
220
|
oveq2d |
|
222 |
202 221
|
eqtr3d |
|
223 |
222
|
negeqd |
|
224 |
194 200 223
|
3eqtrd |
|
225 |
177 224
|
oveq12d |
|
226 |
51 218
|
mulcld |
|
227 |
173 226
|
negsubd |
|
228 |
225 227
|
eqtrd |
|
229 |
|
disjdif |
|
230 |
229
|
a1i |
|
231 |
|
undif2 |
|
232 |
171
|
snssd |
|
233 |
|
ssequn1 |
|
234 |
232 233
|
sylib |
|
235 |
231 234
|
syl5req |
|
236 |
230 235 14 59
|
fsumsplit |
|
237 |
51 211 218
|
subdid |
|
238 |
228 236 237
|
3eqtr4rd |
|
239 |
167 238
|
oveq12d |
|
240 |
60 116 239
|
3eqtr4d |
|
241 |
240
|
mpteq2dva |
|
242 |
|
rpssre |
|
243 |
242
|
a1i |
|
244 |
3 13
|
syl |
|
245 |
22
|
adantlr |
|
246 |
245
|
cjcld |
|
247 |
62 59
|
subcld |
|
248 |
246 247
|
mulcld |
|
249 |
248
|
anasss |
|
250 |
23
|
adantr |
|
251 |
247
|
an32s |
|
252 |
|
o1const |
|
253 |
242 23 252
|
sylancr |
|
254 |
|
fveq1 |
|
255 |
254
|
oveq1d |
|
256 |
255
|
sumeq2sdv |
|
257 |
256 175
|
oveq12d |
|
258 |
257
|
adantl |
|
259 |
49
|
recnd |
|
260 |
259
|
mulid1d |
|
261 |
260
|
oveq2d |
|
262 |
258 261
|
sylan9eq |
|
263 |
262
|
mpteq2dva |
|
264 |
1 2 3 4 5 6
|
rpvmasumlem |
|
265 |
264
|
ad2antrr |
|
266 |
263 265
|
eqeltrd |
|
267 |
179
|
oveq2d |
|
268 |
267
|
oveq2d |
|
269 |
51
|
adantlr |
|
270 |
|
mulcom |
|
271 |
269 54 270
|
sylancl |
|
272 |
269
|
mulm1d |
|
273 |
271 272
|
eqtrd |
|
274 |
269
|
mul01d |
|
275 |
273 274
|
ifeq12d |
|
276 |
|
ovif2 |
|
277 |
|
negeq |
|
278 |
|
negeq |
|
279 |
278 183
|
eqtrdi |
|
280 |
277 279
|
ifsb |
|
281 |
275 276 280
|
3eqtr4g |
|
282 |
281
|
oveq2d |
|
283 |
62
|
an32s |
|
284 |
|
ifcl |
|
285 |
269 55 284
|
sylancl |
|
286 |
283 285
|
subnegd |
|
287 |
282 286
|
eqtrd |
|
288 |
268 287
|
sylan9eqr |
|
289 |
288
|
an32s |
|
290 |
289
|
mpteq2dva |
|
291 |
3
|
ad2antrr |
|
292 |
|
simplr |
|
293 |
|
simpr |
|
294 |
|
eqid |
|
295 |
1 2 291 4 5 6 292 293 294
|
dchrmusumlema |
|
296 |
3
|
adantr |
|
297 |
296
|
ad2antrr |
|
298 |
292
|
adantr |
|
299 |
|
simplr |
|
300 |
|
simprl |
|
301 |
|
simprrl |
|
302 |
|
simprrr |
|
303 |
1 2 297 4 5 6 298 299 294 300 301 302 7
|
dchrvmaeq0 |
|
304 |
|
ifbi |
|
305 |
304
|
oveq2d |
|
306 |
305
|
mpteq2dv |
|
307 |
303 306
|
syl |
|
308 |
1 2 297 4 5 6 298 299 294 300 301 302
|
dchrvmasumif |
|
309 |
307 308
|
eqeltrd |
|
310 |
309
|
rexlimdvaa |
|
311 |
310
|
exlimdv |
|
312 |
295 311
|
mpd |
|
313 |
290 312
|
eqeltrd |
|
314 |
266 313
|
pm2.61dane |
|
315 |
250 251 253 314
|
o1mul2 |
|
316 |
243 244 249 315
|
fsumo1 |
|
317 |
241 316
|
eqeltrrd |
|