Step |
Hyp |
Ref |
Expression |
1 |
|
chpdifbnd.a |
|
2 |
|
chpdifbnd.1 |
|
3 |
|
chpdifbnd.b |
|
4 |
|
chpdifbnd.2 |
|
5 |
|
chpdifbnd.c |
|
6 |
|
chpdifbnd.x |
|
7 |
|
chpdifbnd.y |
|
8 |
|
ioossre |
|
9 |
8 6
|
sseldi |
|
10 |
1
|
rpred |
|
11 |
10 9
|
remulcld |
|
12 |
|
elicc2 |
|
13 |
9 11 12
|
syl2anc |
|
14 |
7 13
|
mpbid |
|
15 |
14
|
simp1d |
|
16 |
|
chpcl |
|
17 |
15 16
|
syl |
|
18 |
|
chpcl |
|
19 |
9 18
|
syl |
|
20 |
17 19
|
resubcld |
|
21 |
|
0red |
|
22 |
|
1re |
|
23 |
22
|
a1i |
|
24 |
|
0lt1 |
|
25 |
24
|
a1i |
|
26 |
|
eliooord |
|
27 |
6 26
|
syl |
|
28 |
27
|
simpld |
|
29 |
21 23 9 25 28
|
lttrd |
|
30 |
9 29
|
elrpd |
|
31 |
30
|
relogcld |
|
32 |
20 31
|
remulcld |
|
33 |
|
2re |
|
34 |
15 9
|
resubcld |
|
35 |
|
remulcl |
|
36 |
33 34 35
|
sylancr |
|
37 |
36 31
|
remulcld |
|
38 |
3
|
rpred |
|
39 |
15 9
|
readdcld |
|
40 |
38 39
|
remulcld |
|
41 |
1
|
relogcld |
|
42 |
|
remulcl |
|
43 |
33 41 42
|
sylancr |
|
44 |
43 15
|
remulcld |
|
45 |
40 44
|
readdcld |
|
46 |
37 45
|
readdcld |
|
47 |
|
peano2re |
|
48 |
10 47
|
syl |
|
49 |
38 48
|
remulcld |
|
50 |
|
remulcl |
|
51 |
33 10 50
|
sylancr |
|
52 |
51 41
|
remulcld |
|
53 |
49 52
|
readdcld |
|
54 |
5 53
|
eqeltrid |
|
55 |
54 9
|
remulcld |
|
56 |
37 55
|
readdcld |
|
57 |
17 31
|
remulcld |
|
58 |
|
fzfid |
|
59 |
14
|
simp2d |
|
60 |
|
flword2 |
|
61 |
9 15 59 60
|
syl3anc |
|
62 |
|
fzss2 |
|
63 |
61 62
|
syl |
|
64 |
63
|
sselda |
|
65 |
|
elfznn |
|
66 |
65
|
adantl |
|
67 |
|
vmacl |
|
68 |
66 67
|
syl |
|
69 |
|
nndivre |
|
70 |
9 65 69
|
syl2an |
|
71 |
|
chpcl |
|
72 |
70 71
|
syl |
|
73 |
68 72
|
remulcld |
|
74 |
64 73
|
syldan |
|
75 |
58 74
|
fsumrecl |
|
76 |
57 75
|
readdcld |
|
77 |
|
remulcl |
|
78 |
33 31 77
|
sylancr |
|
79 |
78 38
|
resubcld |
|
80 |
79 9
|
remulcld |
|
81 |
1 30
|
rpmulcld |
|
82 |
81
|
relogcld |
|
83 |
|
remulcl |
|
84 |
33 82 83
|
sylancr |
|
85 |
38 84
|
readdcld |
|
86 |
85 15
|
remulcld |
|
87 |
19 31
|
remulcld |
|
88 |
87 75
|
readdcld |
|
89 |
21 9 15 29 59
|
ltletrd |
|
90 |
15 89
|
elrpd |
|
91 |
90
|
relogcld |
|
92 |
17 91
|
remulcld |
|
93 |
|
fzfid |
|
94 |
|
nndivre |
|
95 |
15 65 94
|
syl2an |
|
96 |
|
chpcl |
|
97 |
95 96
|
syl |
|
98 |
68 97
|
remulcld |
|
99 |
93 98
|
fsumrecl |
|
100 |
92 99
|
readdcld |
|
101 |
|
chpge0 |
|
102 |
15 101
|
syl |
|
103 |
30 90
|
logled |
|
104 |
59 103
|
mpbid |
|
105 |
31 91 17 102 104
|
lemul2ad |
|
106 |
93 73
|
fsumrecl |
|
107 |
|
vmage0 |
|
108 |
66 107
|
syl |
|
109 |
|
chpge0 |
|
110 |
70 109
|
syl |
|
111 |
68 72 108 110
|
mulge0d |
|
112 |
93 73 111 63
|
fsumless |
|
113 |
9
|
adantr |
|
114 |
15
|
adantr |
|
115 |
66
|
nnrpd |
|
116 |
59
|
adantr |
|
117 |
113 114 115 116
|
lediv1dd |
|
118 |
|
chpwordi |
|
119 |
70 95 117 118
|
syl3anc |
|
120 |
72 97 68 108 119
|
lemul2ad |
|
121 |
93 73 98 120
|
fsumle |
|
122 |
75 106 99 112 121
|
letrd |
|
123 |
57 75 92 99 105 122
|
le2addd |
|
124 |
100 90
|
rerpdivcld |
|
125 |
|
remulcl |
|
126 |
33 91 125
|
sylancr |
|
127 |
38 126
|
readdcld |
|
128 |
124 126
|
resubcld |
|
129 |
128
|
recnd |
|
130 |
129
|
abscld |
|
131 |
128
|
leabsd |
|
132 |
|
fveq2 |
|
133 |
|
fveq2 |
|
134 |
132 133
|
oveq12d |
|
135 |
|
fveq2 |
|
136 |
|
oveq2 |
|
137 |
136
|
fveq2d |
|
138 |
135 137
|
oveq12d |
|
139 |
138
|
cbvsumv |
|
140 |
|
fveq2 |
|
141 |
140
|
oveq2d |
|
142 |
|
simpl |
|
143 |
142
|
fvoveq1d |
|
144 |
143
|
oveq2d |
|
145 |
141 144
|
sumeq12rdv |
|
146 |
139 145
|
syl5eq |
|
147 |
134 146
|
oveq12d |
|
148 |
|
id |
|
149 |
147 148
|
oveq12d |
|
150 |
133
|
oveq2d |
|
151 |
149 150
|
oveq12d |
|
152 |
151
|
fveq2d |
|
153 |
152
|
breq1d |
|
154 |
23 9 28
|
ltled |
|
155 |
23 9 15 154 59
|
letrd |
|
156 |
|
elicopnf |
|
157 |
22 156
|
ax-mp |
|
158 |
15 155 157
|
sylanbrc |
|
159 |
153 4 158
|
rspcdva |
|
160 |
128 130 38 131 159
|
letrd |
|
161 |
124 126 38
|
lesubaddd |
|
162 |
160 161
|
mpbid |
|
163 |
14
|
simp3d |
|
164 |
90 81
|
logled |
|
165 |
163 164
|
mpbid |
|
166 |
|
2pos |
|
167 |
33 166
|
pm3.2i |
|
168 |
167
|
a1i |
|
169 |
|
lemul2 |
|
170 |
91 82 168 169
|
syl3anc |
|
171 |
165 170
|
mpbid |
|
172 |
126 84 38 171
|
leadd2dd |
|
173 |
124 127 85 162 172
|
letrd |
|
174 |
100 85 90
|
ledivmul2d |
|
175 |
173 174
|
mpbid |
|
176 |
76 100 86 123 175
|
letrd |
|
177 |
|
fveq2 |
|
178 |
|
fveq2 |
|
179 |
177 178
|
oveq12d |
|
180 |
|
fveq2 |
|
181 |
180
|
oveq2d |
|
182 |
|
simpl |
|
183 |
182
|
fvoveq1d |
|
184 |
183
|
oveq2d |
|
185 |
181 184
|
sumeq12rdv |
|
186 |
139 185
|
syl5eq |
|
187 |
179 186
|
oveq12d |
|
188 |
|
id |
|
189 |
187 188
|
oveq12d |
|
190 |
178
|
oveq2d |
|
191 |
189 190
|
oveq12d |
|
192 |
191
|
fveq2d |
|
193 |
192
|
breq1d |
|
194 |
|
elicopnf |
|
195 |
22 194
|
ax-mp |
|
196 |
9 154 195
|
sylanbrc |
|
197 |
193 4 196
|
rspcdva |
|
198 |
88 30
|
rerpdivcld |
|
199 |
198 78 38
|
absdifled |
|
200 |
197 199
|
mpbid |
|
201 |
200
|
simpld |
|
202 |
79 88 30
|
lemuldivd |
|
203 |
201 202
|
mpbird |
|
204 |
76 80 86 88 176 203
|
le2subd |
|
205 |
57
|
recnd |
|
206 |
87
|
recnd |
|
207 |
75
|
recnd |
|
208 |
205 206 207
|
pnpcan2d |
|
209 |
17
|
recnd |
|
210 |
19
|
recnd |
|
211 |
31
|
recnd |
|
212 |
209 210 211
|
subdird |
|
213 |
208 212
|
eqtr4d |
|
214 |
78 15
|
remulcld |
|
215 |
214
|
recnd |
|
216 |
38 43
|
readdcld |
|
217 |
216 15
|
remulcld |
|
218 |
217
|
recnd |
|
219 |
78 9
|
remulcld |
|
220 |
219
|
recnd |
|
221 |
38 9
|
remulcld |
|
222 |
221
|
recnd |
|
223 |
222
|
negcld |
|
224 |
215 218 220 223
|
addsub4d |
|
225 |
41
|
recnd |
|
226 |
1 30
|
relogmuld |
|
227 |
225 211 226
|
comraddd |
|
228 |
227
|
oveq2d |
|
229 |
|
2cnd |
|
230 |
229 211 225
|
adddid |
|
231 |
228 230
|
eqtrd |
|
232 |
231
|
oveq2d |
|
233 |
38
|
recnd |
|
234 |
78
|
recnd |
|
235 |
43
|
recnd |
|
236 |
233 234 235
|
add12d |
|
237 |
232 236
|
eqtrd |
|
238 |
237
|
oveq1d |
|
239 |
216
|
recnd |
|
240 |
15
|
recnd |
|
241 |
234 239 240
|
adddird |
|
242 |
238 241
|
eqtrd |
|
243 |
9
|
recnd |
|
244 |
234 233 243
|
subdird |
|
245 |
220 222
|
negsubd |
|
246 |
244 245
|
eqtr4d |
|
247 |
242 246
|
oveq12d |
|
248 |
34
|
recnd |
|
249 |
229 248 211
|
mul32d |
|
250 |
234 240 243
|
subdid |
|
251 |
249 250
|
eqtrd |
|
252 |
38 15
|
remulcld |
|
253 |
252
|
recnd |
|
254 |
44
|
recnd |
|
255 |
253 222 254
|
add32d |
|
256 |
233 240 243
|
adddid |
|
257 |
256
|
oveq1d |
|
258 |
233 235 240
|
adddird |
|
259 |
258
|
oveq1d |
|
260 |
255 257 259
|
3eqtr4d |
|
261 |
218 222
|
subnegd |
|
262 |
260 261
|
eqtr4d |
|
263 |
251 262
|
oveq12d |
|
264 |
224 247 263
|
3eqtr4d |
|
265 |
204 213 264
|
3brtr3d |
|
266 |
49 9
|
remulcld |
|
267 |
52 9
|
remulcld |
|
268 |
15 11 9 163
|
leadd1dd |
|
269 |
10
|
recnd |
|
270 |
269 243
|
adddirp1d |
|
271 |
268 270
|
breqtrrd |
|
272 |
48 9
|
remulcld |
|
273 |
39 272 3
|
lemul2d |
|
274 |
271 273
|
mpbid |
|
275 |
48
|
recnd |
|
276 |
233 275 243
|
mulassd |
|
277 |
274 276
|
breqtrrd |
|
278 |
33
|
a1i |
|
279 |
|
0le2 |
|
280 |
279
|
a1i |
|
281 |
|
log1 |
|
282 |
|
1rp |
|
283 |
|
logleb |
|
284 |
282 1 283
|
sylancr |
|
285 |
2 284
|
mpbid |
|
286 |
281 285
|
eqbrtrrid |
|
287 |
278 41 280 286
|
mulge0d |
|
288 |
15 11 43 287 163
|
lemul2ad |
|
289 |
51
|
recnd |
|
290 |
289 225 243
|
mulassd |
|
291 |
229 269 225 243
|
mul4d |
|
292 |
290 291
|
eqtrd |
|
293 |
288 292
|
breqtrrd |
|
294 |
40 44 266 267 277 293
|
le2addd |
|
295 |
5
|
oveq1i |
|
296 |
49
|
recnd |
|
297 |
52
|
recnd |
|
298 |
296 297 243
|
adddird |
|
299 |
295 298
|
syl5eq |
|
300 |
294 299
|
breqtrrd |
|
301 |
45 55 37 300
|
leadd2dd |
|
302 |
32 46 56 265 301
|
letrd |
|
303 |
36
|
recnd |
|
304 |
9 28
|
rplogcld |
|
305 |
9 304
|
rerpdivcld |
|
306 |
54 305
|
remulcld |
|
307 |
306
|
recnd |
|
308 |
303 307 211
|
adddird |
|
309 |
54
|
recnd |
|
310 |
305
|
recnd |
|
311 |
309 310 211
|
mulassd |
|
312 |
304
|
rpne0d |
|
313 |
243 211 312
|
divcan1d |
|
314 |
313
|
oveq2d |
|
315 |
311 314
|
eqtrd |
|
316 |
315
|
oveq2d |
|
317 |
308 316
|
eqtrd |
|
318 |
302 317
|
breqtrrd |
|
319 |
36 306
|
readdcld |
|
320 |
20 319 304
|
lemul1d |
|
321 |
318 320
|
mpbird |
|