Step |
Hyp |
Ref |
Expression |
1 |
|
pntpbnd.r |
|
2 |
|
pntpbnd1.e |
|
3 |
|
pntpbnd1.x |
|
4 |
|
pntpbnd1.y |
|
5 |
|
pntpbnd1.1 |
|
6 |
|
pntpbnd1.2 |
|
7 |
|
pntpbnd1.c |
|
8 |
|
pntpbnd1.k |
|
9 |
|
pntpbnd1.3 |
|
10 |
|
2div2e1 |
|
11 |
|
2re |
|
12 |
11
|
a1i |
|
13 |
|
ioossre |
|
14 |
13 2
|
sseldi |
|
15 |
|
eliooord |
|
16 |
2 15
|
syl |
|
17 |
16
|
simpld |
|
18 |
14 17
|
elrpd |
|
19 |
|
2rp |
|
20 |
19
|
a1i |
|
21 |
7
|
oveq1i |
|
22 |
5
|
rpcnd |
|
23 |
|
2cn |
|
24 |
|
pncan2 |
|
25 |
22 23 24
|
sylancl |
|
26 |
21 25
|
syl5eq |
|
27 |
26
|
oveq1d |
|
28 |
|
rpaddcl |
|
29 |
5 19 28
|
sylancl |
|
30 |
7 29
|
eqeltrid |
|
31 |
30
|
rpcnd |
|
32 |
14
|
recnd |
|
33 |
18
|
rpne0d |
|
34 |
31 22 32 33
|
divsubdird |
|
35 |
27 34
|
eqtr3d |
|
36 |
30 18
|
rpdivcld |
|
37 |
36
|
rpred |
|
38 |
5
|
rpred |
|
39 |
38 18
|
rerpdivcld |
|
40 |
|
resubcl |
|
41 |
37 11 40
|
sylancl |
|
42 |
37
|
reefcld |
|
43 |
|
elicopnf |
|
44 |
42 43
|
syl |
|
45 |
8 44
|
mpbid |
|
46 |
45
|
simpld |
|
47 |
|
0red |
|
48 |
|
1re |
|
49 |
48
|
a1i |
|
50 |
|
0lt1 |
|
51 |
50
|
a1i |
|
52 |
|
efgt1 |
|
53 |
36 52
|
syl |
|
54 |
45
|
simprd |
|
55 |
49 42 46 53 54
|
ltletrd |
|
56 |
47 49 46 51 55
|
lttrd |
|
57 |
46 56
|
elrpd |
|
58 |
57
|
relogcld |
|
59 |
|
resubcl |
|
60 |
58 11 59
|
sylancl |
|
61 |
57
|
reeflogd |
|
62 |
54 61
|
breqtrrd |
|
63 |
|
efle |
|
64 |
37 58 63
|
syl2anc |
|
65 |
62 64
|
mpbird |
|
66 |
37 58 12 65
|
lesub1dd |
|
67 |
|
fzfid |
|
68 |
|
ioossre |
|
69 |
68 4
|
sseldi |
|
70 |
|
rerpdivcl |
|
71 |
11 18 70
|
sylancr |
|
72 |
71
|
reefcld |
|
73 |
3 72
|
eqeltrid |
|
74 |
|
efgt0 |
|
75 |
71 74
|
syl |
|
76 |
75 3
|
breqtrrdi |
|
77 |
73
|
rexrd |
|
78 |
|
elioopnf |
|
79 |
77 78
|
syl |
|
80 |
4 79
|
mpbid |
|
81 |
80
|
simprd |
|
82 |
47 73 69 76 81
|
lttrd |
|
83 |
47 69 82
|
ltled |
|
84 |
|
flge0nn0 |
|
85 |
69 83 84
|
syl2anc |
|
86 |
|
nn0p1nn |
|
87 |
85 86
|
syl |
|
88 |
|
elfzuz |
|
89 |
|
eluznn |
|
90 |
87 88 89
|
syl2an |
|
91 |
90
|
peano2nnd |
|
92 |
91
|
nnrecred |
|
93 |
67 92
|
fsumrecl |
|
94 |
58
|
recnd |
|
95 |
|
2cnd |
|
96 |
69 82
|
elrpd |
|
97 |
96
|
relogcld |
|
98 |
97
|
recnd |
|
99 |
94 95 98
|
pnpcan2d |
|
100 |
57 96
|
relogmuld |
|
101 |
58 97
|
readdcld |
|
102 |
100 101
|
eqeltrd |
|
103 |
|
fzfid |
|
104 |
|
elfznn0 |
|
105 |
104
|
adantl |
|
106 |
|
nn0p1nn |
|
107 |
105 106
|
syl |
|
108 |
107
|
nnrecred |
|
109 |
103 108
|
fsumrecl |
|
110 |
109 93
|
readdcld |
|
111 |
|
readdcl |
|
112 |
11 97 111
|
sylancr |
|
113 |
112 93
|
readdcld |
|
114 |
46 69
|
remulcld |
|
115 |
69
|
recnd |
|
116 |
115
|
mulid2d |
|
117 |
49 46 55
|
ltled |
|
118 |
|
lemul1 |
|
119 |
49 46 69 82 118
|
syl112anc |
|
120 |
117 119
|
mpbid |
|
121 |
116 120
|
eqbrtrrd |
|
122 |
47 69 114 83 121
|
letrd |
|
123 |
|
flge0nn0 |
|
124 |
114 122 123
|
syl2anc |
|
125 |
|
nn0p1nn |
|
126 |
124 125
|
syl |
|
127 |
126
|
nnrpd |
|
128 |
127
|
relogcld |
|
129 |
|
1zzd |
|
130 |
114
|
flcld |
|
131 |
130
|
peano2zd |
|
132 |
|
elfznn |
|
133 |
132
|
adantl |
|
134 |
|
nnrecre |
|
135 |
134
|
recnd |
|
136 |
133 135
|
syl |
|
137 |
|
oveq2 |
|
138 |
129 129 131 136 137
|
fsumshftm |
|
139 |
|
1m1e0 |
|
140 |
139
|
a1i |
|
141 |
130
|
zcnd |
|
142 |
|
ax-1cn |
|
143 |
|
pncan |
|
144 |
141 142 143
|
sylancl |
|
145 |
140 144
|
oveq12d |
|
146 |
145
|
sumeq1d |
|
147 |
|
reflcl |
|
148 |
69 147
|
syl |
|
149 |
148
|
ltp1d |
|
150 |
|
fzdisj |
|
151 |
149 150
|
syl |
|
152 |
|
flwordi |
|
153 |
69 114 121 152
|
syl3anc |
|
154 |
|
elfz2nn0 |
|
155 |
85 124 153 154
|
syl3anbrc |
|
156 |
|
fzsplit |
|
157 |
155 156
|
syl |
|
158 |
|
fzfid |
|
159 |
|
elfznn0 |
|
160 |
159
|
adantl |
|
161 |
160 106
|
syl |
|
162 |
161
|
nnrecred |
|
163 |
162
|
recnd |
|
164 |
151 157 158 163
|
fsumsplit |
|
165 |
138 146 164
|
3eqtrd |
|
166 |
165 110
|
eqeltrd |
|
167 |
|
fllep1 |
|
168 |
114 167
|
syl |
|
169 |
57 96
|
rpmulcld |
|
170 |
169 127
|
logled |
|
171 |
168 170
|
mpbid |
|
172 |
|
emre |
|
173 |
172
|
a1i |
|
174 |
166 128
|
resubcld |
|
175 |
|
0re |
|
176 |
|
emgt0 |
|
177 |
175 172 176
|
ltleii |
|
178 |
177
|
a1i |
|
179 |
|
harmonicbnd |
|
180 |
126 179
|
syl |
|
181 |
172 48
|
elicc2i |
|
182 |
181
|
simp2bi |
|
183 |
180 182
|
syl |
|
184 |
47 173 174 178 183
|
letrd |
|
185 |
166 128
|
subge0d |
|
186 |
184 185
|
mpbid |
|
187 |
102 128 166 171 186
|
letrd |
|
188 |
187 165
|
breqtrd |
|
189 |
69
|
flcld |
|
190 |
189
|
peano2zd |
|
191 |
|
elfznn |
|
192 |
191
|
adantl |
|
193 |
192 135
|
syl |
|
194 |
129 129 190 193 137
|
fsumshftm |
|
195 |
148
|
recnd |
|
196 |
|
pncan |
|
197 |
195 142 196
|
sylancl |
|
198 |
140 197
|
oveq12d |
|
199 |
198
|
sumeq1d |
|
200 |
194 199
|
eqtrd |
|
201 |
200 109
|
eqeltrd |
|
202 |
87
|
nnrpd |
|
203 |
202
|
relogcld |
|
204 |
|
readdcl |
|
205 |
48 203 204
|
sylancr |
|
206 |
|
harmonicbnd |
|
207 |
87 206
|
syl |
|
208 |
172 48
|
elicc2i |
|
209 |
208
|
simp3bi |
|
210 |
207 209
|
syl |
|
211 |
201 203 49
|
lesubaddd |
|
212 |
210 211
|
mpbid |
|
213 |
|
readdcl |
|
214 |
48 97 213
|
sylancr |
|
215 |
|
peano2re |
|
216 |
148 215
|
syl |
|
217 |
12 69
|
remulcld |
|
218 |
|
epr |
|
219 |
|
rpmulcl |
|
220 |
218 96 219
|
sylancr |
|
221 |
220
|
rpred |
|
222 |
|
flle |
|
223 |
69 222
|
syl |
|
224 |
20 18
|
rpdivcld |
|
225 |
|
efgt1 |
|
226 |
224 225
|
syl |
|
227 |
226 3
|
breqtrrdi |
|
228 |
49 73 69 227 81
|
lttrd |
|
229 |
49 69 228
|
ltled |
|
230 |
148 49 69 69 223 229
|
le2addd |
|
231 |
115
|
2timesd |
|
232 |
230 231
|
breqtrrd |
|
233 |
|
ere |
|
234 |
|
egt2lt3 |
|
235 |
234
|
simpli |
|
236 |
11 233 235
|
ltleii |
|
237 |
236
|
a1i |
|
238 |
233
|
a1i |
|
239 |
|
lemul1 |
|
240 |
12 238 69 82 239
|
syl112anc |
|
241 |
237 240
|
mpbid |
|
242 |
216 217 221 232 241
|
letrd |
|
243 |
202 220
|
logled |
|
244 |
242 243
|
mpbid |
|
245 |
|
relogmul |
|
246 |
218 96 245
|
sylancr |
|
247 |
|
loge |
|
248 |
247
|
oveq1i |
|
249 |
246 248
|
eqtrdi |
|
250 |
244 249
|
breqtrd |
|
251 |
203 214 49 250
|
leadd2dd |
|
252 |
|
df-2 |
|
253 |
252
|
oveq1i |
|
254 |
142
|
a1i |
|
255 |
254 254 98
|
addassd |
|
256 |
253 255
|
syl5eq |
|
257 |
251 256
|
breqtrrd |
|
258 |
201 205 112 212 257
|
letrd |
|
259 |
200 258
|
eqbrtrrd |
|
260 |
109 112 93 259
|
leadd1dd |
|
261 |
102 110 113 188 260
|
letrd |
|
262 |
100 261
|
eqbrtrrd |
|
263 |
101 112 93
|
lesubadd2d |
|
264 |
262 263
|
mpbird |
|
265 |
99 264
|
eqbrtrrd |
|
266 |
92
|
recnd |
|
267 |
67 32 266
|
fsummulc2 |
|
268 |
14
|
adantr |
|
269 |
268
|
recnd |
|
270 |
91
|
nncnd |
|
271 |
91
|
nnne0d |
|
272 |
269 270 271
|
divrecd |
|
273 |
268 91
|
nndivred |
|
274 |
272 273
|
eqeltrrd |
|
275 |
67 274
|
fsumrecl |
|
276 |
90
|
nnrpd |
|
277 |
1
|
pntrf |
|
278 |
277
|
ffvelrni |
|
279 |
276 278
|
syl |
|
280 |
90 91
|
nnmulcld |
|
281 |
279 280
|
nndivred |
|
282 |
281
|
recnd |
|
283 |
282
|
abscld |
|
284 |
67 283
|
fsumrecl |
|
285 |
279 90
|
nndivred |
|
286 |
285
|
recnd |
|
287 |
286
|
abscld |
|
288 |
91
|
nnrpd |
|
289 |
9
|
adantr |
|
290 |
|
elfzle1 |
|
291 |
290
|
adantl |
|
292 |
69
|
adantr |
|
293 |
292
|
flcld |
|
294 |
90
|
nnzd |
|
295 |
|
zltp1le |
|
296 |
293 294 295
|
syl2anc |
|
297 |
291 296
|
mpbird |
|
298 |
|
fllt |
|
299 |
292 294 298
|
syl2anc |
|
300 |
297 299
|
mpbird |
|
301 |
|
elfzle2 |
|
302 |
301
|
adantl |
|
303 |
114
|
adantr |
|
304 |
|
flge |
|
305 |
303 294 304
|
syl2anc |
|
306 |
302 305
|
mpbird |
|
307 |
|
breq2 |
|
308 |
|
breq1 |
|
309 |
307 308
|
anbi12d |
|
310 |
|
fveq2 |
|
311 |
|
id |
|
312 |
310 311
|
oveq12d |
|
313 |
312
|
fveq2d |
|
314 |
313
|
breq1d |
|
315 |
309 314
|
anbi12d |
|
316 |
315
|
rspcev |
|
317 |
316
|
expr |
|
318 |
90 300 306 317
|
syl12anc |
|
319 |
289 318
|
mtod |
|
320 |
287 268
|
letrid |
|
321 |
320
|
ord |
|
322 |
319 321
|
mpd |
|
323 |
268 287 288 322
|
lediv1dd |
|
324 |
286 270 271
|
absdivd |
|
325 |
279
|
recnd |
|
326 |
90
|
nncnd |
|
327 |
90
|
nnne0d |
|
328 |
325 326 270 327 271
|
divdiv1d |
|
329 |
328
|
fveq2d |
|
330 |
288
|
rprege0d |
|
331 |
|
absid |
|
332 |
330 331
|
syl |
|
333 |
332
|
oveq2d |
|
334 |
324 329 333
|
3eqtr3rd |
|
335 |
323 272 334
|
3brtr3d |
|
336 |
67 274 283 335
|
fsumle |
|
337 |
1 2 3 4 5 6 7 8 9
|
pntpbnd1 |
|
338 |
275 284 38 336 337
|
letrd |
|
339 |
267 338
|
eqbrtrd |
|
340 |
93 38 18
|
lemuldiv2d |
|
341 |
339 340
|
mpbid |
|
342 |
60 93 39 265 341
|
letrd |
|
343 |
41 60 39 66 342
|
letrd |
|
344 |
37 12 39 343
|
subled |
|
345 |
35 344
|
eqbrtrd |
|
346 |
12 18 20 345
|
lediv23d |
|
347 |
10 346
|
eqbrtrrid |
|
348 |
16
|
simprd |
|
349 |
|
ltnle |
|
350 |
14 48 349
|
sylancl |
|
351 |
348 350
|
mpbid |
|
352 |
347 351
|
pm2.65i |
|