Step |
Hyp |
Ref |
Expression |
1 |
|
dvfsum.s |
|
2 |
|
dvfsum.z |
|
3 |
|
dvfsum.m |
|
4 |
|
dvfsum.d |
|
5 |
|
dvfsum.md |
|
6 |
|
dvfsum.t |
|
7 |
|
dvfsum.a |
|
8 |
|
dvfsum.b1 |
|
9 |
|
dvfsum.b2 |
|
10 |
|
dvfsum.b3 |
|
11 |
|
dvfsum.c |
|
12 |
|
dvfsum.u |
|
13 |
|
dvfsum.l |
|
14 |
|
dvfsum.h |
|
15 |
|
dvfsumlem1.1 |
|
16 |
|
dvfsumlem1.2 |
|
17 |
|
dvfsumlem1.3 |
|
18 |
|
dvfsumlem1.4 |
|
19 |
|
dvfsumlem1.5 |
|
20 |
|
dvfsumlem1.6 |
|
21 |
|
ioossre |
|
22 |
1 21
|
eqsstri |
|
23 |
22 16
|
sseldi |
|
24 |
15 1
|
eleqtrdi |
|
25 |
6
|
rexrd |
|
26 |
|
elioopnf |
|
27 |
25 26
|
syl |
|
28 |
24 27
|
mpbid |
|
29 |
28
|
simpld |
|
30 |
|
reflcl |
|
31 |
29 30
|
syl |
|
32 |
23 31
|
resubcld |
|
33 |
|
csbeq1 |
|
34 |
33
|
eleq1d |
|
35 |
22
|
a1i |
|
36 |
35 7 8 10
|
dvmptrecl |
|
37 |
36
|
fmpttd |
|
38 |
|
nfcv |
|
39 |
|
nfcsb1v |
|
40 |
|
csbeq1a |
|
41 |
38 39 40
|
cbvmpt |
|
42 |
41
|
fmpt |
|
43 |
37 42
|
sylibr |
|
44 |
34 43 16
|
rspcdva |
|
45 |
32 44
|
remulcld |
|
46 |
|
csbeq1 |
|
47 |
46
|
eleq1d |
|
48 |
7
|
fmpttd |
|
49 |
|
nfcv |
|
50 |
|
nfcsb1v |
|
51 |
|
csbeq1a |
|
52 |
49 50 51
|
cbvmpt |
|
53 |
52
|
fmpt |
|
54 |
48 53
|
sylibr |
|
55 |
47 54 16
|
rspcdva |
|
56 |
45 55
|
resubcld |
|
57 |
29 31
|
resubcld |
|
58 |
|
csbeq1 |
|
59 |
58
|
eleq1d |
|
60 |
59 43 15
|
rspcdva |
|
61 |
57 60
|
remulcld |
|
62 |
|
csbeq1 |
|
63 |
62
|
eleq1d |
|
64 |
63 54 15
|
rspcdva |
|
65 |
61 64
|
resubcld |
|
66 |
|
fzfid |
|
67 |
9
|
ralrimiva |
|
68 |
|
elfzuz |
|
69 |
68 2
|
eleqtrrdi |
|
70 |
11
|
eleq1d |
|
71 |
70
|
rspccva |
|
72 |
67 69 71
|
syl2an |
|
73 |
66 72
|
fsumrecl |
|
74 |
57 44
|
remulcld |
|
75 |
74 64
|
resubcld |
|
76 |
23 29
|
resubcld |
|
77 |
44 76
|
remulcld |
|
78 |
44
|
recnd |
|
79 |
23
|
recnd |
|
80 |
29
|
recnd |
|
81 |
78 79 80
|
subdid |
|
82 |
|
eqid |
|
83 |
82
|
mulcn |
|
84 |
|
pnfxr |
|
85 |
84
|
a1i |
|
86 |
28
|
simprd |
|
87 |
23
|
ltpnfd |
|
88 |
|
iccssioo |
|
89 |
25 85 86 87 88
|
syl22anc |
|
90 |
89 21
|
sstrdi |
|
91 |
|
ax-resscn |
|
92 |
90 91
|
sstrdi |
|
93 |
91
|
a1i |
|
94 |
|
cncfmptc |
|
95 |
44 92 93 94
|
syl3anc |
|
96 |
|
cncfmptid |
|
97 |
90 91 96
|
sylancl |
|
98 |
|
remulcl |
|
99 |
82 83 95 97 91 98
|
cncfmpt2ss |
|
100 |
|
reelprrecn |
|
101 |
100
|
a1i |
|
102 |
|
ioossicc |
|
103 |
102 90
|
sstrid |
|
104 |
103
|
sselda |
|
105 |
104
|
recnd |
|
106 |
|
1cnd |
|
107 |
|
simpr |
|
108 |
107
|
recnd |
|
109 |
|
1cnd |
|
110 |
101
|
dvmptid |
|
111 |
82
|
tgioo2 |
|
112 |
|
iooretop |
|
113 |
112
|
a1i |
|
114 |
101 108 109 110 103 111 82 113
|
dvmptres |
|
115 |
101 105 106 114 78
|
dvmptcmul |
|
116 |
78
|
mulid1d |
|
117 |
116
|
mpteq2dv |
|
118 |
115 117
|
eqtrd |
|
119 |
89 1
|
sseqtrrdi |
|
120 |
119
|
resmptd |
|
121 |
7
|
recnd |
|
122 |
121
|
fmpttd |
|
123 |
10
|
dmeqd |
|
124 |
8
|
ralrimiva |
|
125 |
|
dmmptg |
|
126 |
124 125
|
syl |
|
127 |
123 126
|
eqtrd |
|
128 |
|
dvcn |
|
129 |
93 122 35 127 128
|
syl31anc |
|
130 |
|
cncffvrn |
|
131 |
91 129 130
|
sylancr |
|
132 |
48 131
|
mpbird |
|
133 |
52 132
|
eqeltrrid |
|
134 |
|
rescncf |
|
135 |
119 133 134
|
sylc |
|
136 |
120 135
|
eqeltrrd |
|
137 |
54
|
r19.21bi |
|
138 |
137
|
recnd |
|
139 |
43
|
r19.21bi |
|
140 |
52
|
oveq2i |
|
141 |
10 140 41
|
3eqtr3g |
|
142 |
102 119
|
sstrid |
|
143 |
101 138 139 141 142 111 82 113
|
dvmptres |
|
144 |
102
|
sseli |
|
145 |
|
simpl |
|
146 |
119
|
sselda |
|
147 |
16
|
adantr |
|
148 |
4
|
adantr |
|
149 |
29
|
adantr |
|
150 |
|
elicc2 |
|
151 |
29 23 150
|
syl2anc |
|
152 |
151
|
biimpa |
|
153 |
152
|
simp1d |
|
154 |
17
|
adantr |
|
155 |
152
|
simp2d |
|
156 |
148 149 153 154 155
|
letrd |
|
157 |
152
|
simp3d |
|
158 |
19
|
adantr |
|
159 |
|
simp2r |
|
160 |
|
eleq1 |
|
161 |
160
|
anbi2d |
|
162 |
|
breq2 |
|
163 |
|
breq1 |
|
164 |
162 163
|
3anbi23d |
|
165 |
161 164
|
3anbi23d |
|
166 |
|
vex |
|
167 |
166 11
|
csbie |
|
168 |
|
csbeq1 |
|
169 |
167 168
|
syl5eqr |
|
170 |
169
|
breq1d |
|
171 |
165 170
|
imbi12d |
|
172 |
|
nfv |
|
173 |
|
nfcv |
|
174 |
|
nfcv |
|
175 |
173 174 39
|
nfbr |
|
176 |
172 175
|
nfim |
|
177 |
|
eleq1 |
|
178 |
177
|
anbi1d |
|
179 |
|
breq2 |
|
180 |
|
breq1 |
|
181 |
179 180
|
3anbi12d |
|
182 |
178 181
|
3anbi23d |
|
183 |
40
|
breq2d |
|
184 |
182 183
|
imbi12d |
|
185 |
176 184 13
|
chvarfv |
|
186 |
171 185
|
vtoclg |
|
187 |
159 186
|
mpcom |
|
188 |
145 146 147 156 157 158 187
|
syl123anc |
|
189 |
144 188
|
sylan2 |
|
190 |
29
|
rexrd |
|
191 |
23
|
rexrd |
|
192 |
|
lbicc2 |
|
193 |
190 191 18 192
|
syl3anc |
|
194 |
|
ubicc2 |
|
195 |
190 191 18 194
|
syl3anc |
|
196 |
|
oveq2 |
|
197 |
|
oveq2 |
|
198 |
29 23 99 118 136 143 189 193 195 18 196 62 197 46
|
dvle |
|
199 |
81 198
|
eqbrtrd |
|
200 |
77 55 64 199
|
lesubd |
|
201 |
74
|
recnd |
|
202 |
45
|
recnd |
|
203 |
55
|
recnd |
|
204 |
201 202 203
|
subsubd |
|
205 |
202 201
|
negsubdi2d |
|
206 |
31
|
recnd |
|
207 |
79 80 206
|
nnncan2d |
|
208 |
207
|
oveq1d |
|
209 |
32
|
recnd |
|
210 |
57
|
recnd |
|
211 |
209 210 78
|
subdird |
|
212 |
76
|
recnd |
|
213 |
212 78
|
mulcomd |
|
214 |
208 211 213
|
3eqtr3d |
|
215 |
214
|
negeqd |
|
216 |
205 215
|
eqtr3d |
|
217 |
216
|
oveq1d |
|
218 |
77
|
recnd |
|
219 |
218 203
|
negsubdid |
|
220 |
217 219
|
eqtr4d |
|
221 |
218 203
|
negsubdi2d |
|
222 |
204 220 221
|
3eqtrd |
|
223 |
200 222
|
breqtrrd |
|
224 |
64 74 56 223
|
lesubd |
|
225 |
|
flle |
|
226 |
29 225
|
syl |
|
227 |
29 31
|
subge0d |
|
228 |
226 227
|
mpbird |
|
229 |
58
|
breq2d |
|
230 |
188
|
ralrimiva |
|
231 |
229 230 193
|
rspcdva |
|
232 |
44 60 57 228 231
|
lemul2ad |
|
233 |
74 61 64 232
|
lesub1dd |
|
234 |
56 75 65 224 233
|
letrd |
|
235 |
56 65 73 234
|
leadd1dd |
|
236 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
|
dvfsumlem1 |
|
237 |
29
|
leidd |
|
238 |
190 191 12 18 19
|
xrletrd |
|
239 |
|
fllep1 |
|
240 |
29 239
|
syl |
|
241 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 17 237 238 240
|
dvfsumlem1 |
|
242 |
235 236 241
|
3brtr4d |
|
243 |
65 60
|
resubcld |
|
244 |
56 44
|
resubcld |
|
245 |
|
peano2rem |
|
246 |
57 245
|
syl |
|
247 |
246 60
|
remulcld |
|
248 |
247 64
|
resubcld |
|
249 |
|
peano2rem |
|
250 |
32 249
|
syl |
|
251 |
250 60
|
remulcld |
|
252 |
251 55
|
resubcld |
|
253 |
250 44
|
remulcld |
|
254 |
253 55
|
resubcld |
|
255 |
247
|
recnd |
|
256 |
251
|
recnd |
|
257 |
255 256
|
subcld |
|
258 |
257 203
|
addcomd |
|
259 |
255 256 203
|
subsubd |
|
260 |
203 256 255
|
subsub2d |
|
261 |
258 259 260
|
3eqtr4d |
|
262 |
|
1cnd |
|
263 |
209 210 262
|
nnncan2d |
|
264 |
263 207
|
eqtrd |
|
265 |
264
|
oveq1d |
|
266 |
250
|
recnd |
|
267 |
246
|
recnd |
|
268 |
60
|
recnd |
|
269 |
266 267 268
|
subdird |
|
270 |
212 268
|
mulcomd |
|
271 |
265 269 270
|
3eqtr3d |
|
272 |
271
|
oveq2d |
|
273 |
261 272
|
eqtrd |
|
274 |
60 76
|
remulcld |
|
275 |
|
cncfmptc |
|
276 |
60 92 93 275
|
syl3anc |
|
277 |
|
remulcl |
|
278 |
82 83 276 97 91 277
|
cncfmpt2ss |
|
279 |
101 105 106 114 268
|
dvmptcmul |
|
280 |
268
|
mulid1d |
|
281 |
280
|
mpteq2dv |
|
282 |
279 281
|
eqtrd |
|
283 |
15
|
adantr |
|
284 |
153
|
rexrd |
|
285 |
191
|
adantr |
|
286 |
12
|
adantr |
|
287 |
284 285 286 157 158
|
xrletrd |
|
288 |
|
vex |
|
289 |
|
eleq1 |
|
290 |
289
|
anbi2d |
|
291 |
|
breq2 |
|
292 |
|
breq1 |
|
293 |
291 292
|
3anbi23d |
|
294 |
290 293
|
3anbi23d |
|
295 |
|
csbeq1 |
|
296 |
167 295
|
syl5eqr |
|
297 |
296
|
breq1d |
|
298 |
294 297
|
imbi12d |
|
299 |
|
simp2l |
|
300 |
|
nfv |
|
301 |
|
nfcsb1v |
|
302 |
173 174 301
|
nfbr |
|
303 |
300 302
|
nfim |
|
304 |
|
eleq1 |
|
305 |
304
|
anbi1d |
|
306 |
|
breq2 |
|
307 |
|
breq1 |
|
308 |
306 307
|
3anbi12d |
|
309 |
305 308
|
3anbi23d |
|
310 |
|
csbeq1a |
|
311 |
310
|
breq2d |
|
312 |
309 311
|
imbi12d |
|
313 |
303 312 13
|
vtoclg1f |
|
314 |
299 313
|
mpcom |
|
315 |
288 298 314
|
vtocl |
|
316 |
145 283 146 154 155 287 315
|
syl123anc |
|
317 |
144 316
|
sylan2 |
|
318 |
|
oveq2 |
|
319 |
|
oveq2 |
|
320 |
29 23 136 143 278 282 317 193 195 18 62 318 46 319
|
dvle |
|
321 |
268 79 80
|
subdid |
|
322 |
320 321
|
breqtrrd |
|
323 |
55 64 274 322
|
subled |
|
324 |
273 323
|
eqbrtrd |
|
325 |
247 252 64 324
|
subled |
|
326 |
250
|
renegcld |
|
327 |
|
1red |
|
328 |
23 31 327
|
lesubadd2d |
|
329 |
20 328
|
mpbird |
|
330 |
32 327
|
suble0d |
|
331 |
329 330
|
mpbird |
|
332 |
250
|
le0neg1d |
|
333 |
331 332
|
mpbid |
|
334 |
44 60 326 333 231
|
lemul2ad |
|
335 |
266 78
|
mulneg1d |
|
336 |
266 268
|
mulneg1d |
|
337 |
334 335 336
|
3brtr3d |
|
338 |
251 253
|
lenegd |
|
339 |
337 338
|
mpbird |
|
340 |
251 253 55 339
|
lesub1dd |
|
341 |
248 252 254 325 340
|
letrd |
|
342 |
210 262 268
|
subdird |
|
343 |
268
|
mulid2d |
|
344 |
343
|
oveq2d |
|
345 |
342 344
|
eqtrd |
|
346 |
345
|
oveq1d |
|
347 |
209 262 78
|
subdird |
|
348 |
78
|
mulid2d |
|
349 |
348
|
oveq2d |
|
350 |
347 349
|
eqtrd |
|
351 |
350
|
oveq1d |
|
352 |
341 346 351
|
3brtr3d |
|
353 |
61
|
recnd |
|
354 |
64
|
recnd |
|
355 |
353 354 268
|
sub32d |
|
356 |
202 203 78
|
sub32d |
|
357 |
352 355 356
|
3brtr4d |
|
358 |
243 244 73 357
|
leadd1dd |
|
359 |
65
|
recnd |
|
360 |
73
|
recnd |
|
361 |
359 360 268
|
addsubd |
|
362 |
56
|
recnd |
|
363 |
362 360 78
|
addsubd |
|
364 |
358 361 363
|
3brtr4d |
|
365 |
241
|
oveq1d |
|
366 |
236
|
oveq1d |
|
367 |
364 365 366
|
3brtr4d |
|
368 |
242 367
|
jca |
|