Step |
Hyp |
Ref |
Expression |
1 |
|
pntlem1.r |
|
2 |
|
pntlem1.a |
|
3 |
|
pntlem1.b |
|
4 |
|
pntlem1.l |
|
5 |
|
pntlem1.d |
|
6 |
|
pntlem1.f |
|
7 |
|
pntlem1.u |
|
8 |
|
pntlem1.u2 |
|
9 |
|
pntlem1.e |
|
10 |
|
pntlem1.k |
|
11 |
|
pntlem1.y |
|
12 |
|
pntlem1.x |
|
13 |
|
pntlem1.c |
|
14 |
|
pntlem1.w |
|
15 |
|
pntlem1.z |
|
16 |
|
pntlem1.m |
|
17 |
|
pntlem1.n |
|
18 |
|
pntlem1.U |
|
19 |
|
pntlem1.K |
|
20 |
1 2 3 4 5 6 7 8 9 10
|
pntlemc |
|
21 |
20
|
simp3d |
|
22 |
21
|
simp3d |
|
23 |
1 2 3 4 5 6
|
pntlemd |
|
24 |
23
|
simp1d |
|
25 |
20
|
simp1d |
|
26 |
|
2z |
|
27 |
|
rpexpcl |
|
28 |
25 26 27
|
sylancl |
|
29 |
24 28
|
rpmulcld |
|
30 |
|
3nn0 |
|
31 |
|
2nn |
|
32 |
30 31
|
decnncl |
|
33 |
|
nnrp |
|
34 |
32 33
|
ax-mp |
|
35 |
|
rpmulcl |
|
36 |
34 3 35
|
sylancr |
|
37 |
29 36
|
rpdivcld |
|
38 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
|
pntlemb |
|
39 |
38
|
simp1d |
|
40 |
39
|
rpred |
|
41 |
38
|
simp2d |
|
42 |
41
|
simp1d |
|
43 |
40 42
|
rplogcld |
|
44 |
|
rpexpcl |
|
45 |
43 26 44
|
sylancl |
|
46 |
37 45
|
rpmulcld |
|
47 |
22 46
|
rpmulcld |
|
48 |
47
|
rpred |
|
49 |
24 25
|
rpmulcld |
|
50 |
|
8re |
|
51 |
|
8pos |
|
52 |
50 51
|
elrpii |
|
53 |
|
rpdivcl |
|
54 |
49 52 53
|
sylancl |
|
55 |
54 43
|
rpmulcld |
|
56 |
22 55
|
rpmulcld |
|
57 |
56
|
rpred |
|
58 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
|
pntlemg |
|
59 |
58
|
simp1d |
|
60 |
58
|
simp2d |
|
61 |
|
eluznn |
|
62 |
59 60 61
|
syl2anc |
|
63 |
62
|
nnred |
|
64 |
59
|
nnred |
|
65 |
63 64
|
resubcld |
|
66 |
57 65
|
remulcld |
|
67 |
|
fzfid |
|
68 |
7
|
rpred |
|
69 |
|
elfznn |
|
70 |
|
nndivre |
|
71 |
68 69 70
|
syl2an |
|
72 |
39
|
adantr |
|
73 |
69
|
adantl |
|
74 |
73
|
nnrpd |
|
75 |
72 74
|
rpdivcld |
|
76 |
1
|
pntrf |
|
77 |
76
|
ffvelrni |
|
78 |
75 77
|
syl |
|
79 |
78 72
|
rerpdivcld |
|
80 |
79
|
recnd |
|
81 |
80
|
abscld |
|
82 |
71 81
|
resubcld |
|
83 |
74
|
relogcld |
|
84 |
82 83
|
remulcld |
|
85 |
67 84
|
fsumrecl |
|
86 |
49
|
rpcnd |
|
87 |
20
|
simp2d |
|
88 |
87
|
rpred |
|
89 |
21
|
simp2d |
|
90 |
88 89
|
rplogcld |
|
91 |
43 90
|
rpdivcld |
|
92 |
91
|
rpcnd |
|
93 |
|
rpcnne0 |
|
94 |
52 93
|
mp1i |
|
95 |
|
4re |
|
96 |
|
4pos |
|
97 |
95 96
|
elrpii |
|
98 |
|
rpcnne0 |
|
99 |
97 98
|
mp1i |
|
100 |
|
divmuldiv |
|
101 |
86 92 94 99 100
|
syl22anc |
|
102 |
10
|
fveq2i |
|
103 |
3 25
|
rpdivcld |
|
104 |
103
|
rpred |
|
105 |
104
|
relogefd |
|
106 |
102 105
|
syl5eq |
|
107 |
106
|
oveq2d |
|
108 |
43
|
rpcnd |
|
109 |
3
|
rpcnne0d |
|
110 |
25
|
rpcnne0d |
|
111 |
|
divdiv2 |
|
112 |
108 109 110 111
|
syl3anc |
|
113 |
107 112
|
eqtrd |
|
114 |
113
|
oveq2d |
|
115 |
25
|
rpcnd |
|
116 |
108 115
|
mulcld |
|
117 |
|
divass |
|
118 |
86 116 109 117
|
syl3anc |
|
119 |
24
|
rpcnd |
|
120 |
119 115 108 115
|
mul4d |
|
121 |
115
|
sqvald |
|
122 |
121
|
oveq2d |
|
123 |
115
|
sqcld |
|
124 |
119 108 123
|
mul32d |
|
125 |
120 122 124
|
3eqtr2d |
|
126 |
125
|
oveq1d |
|
127 |
114 118 126
|
3eqtr2d |
|
128 |
|
8t4e32 |
|
129 |
128
|
a1i |
|
130 |
127 129
|
oveq12d |
|
131 |
29
|
rpcnd |
|
132 |
131 108
|
mulcld |
|
133 |
|
rpcnne0 |
|
134 |
34 133
|
mp1i |
|
135 |
|
divdiv1 |
|
136 |
132 109 134 135
|
syl3anc |
|
137 |
32
|
nncni |
|
138 |
3
|
rpcnd |
|
139 |
|
mulcom |
|
140 |
137 138 139
|
sylancr |
|
141 |
140
|
oveq2d |
|
142 |
36
|
rpcnne0d |
|
143 |
|
div23 |
|
144 |
131 108 142 143
|
syl3anc |
|
145 |
136 141 144
|
3eqtr2d |
|
146 |
101 130 145
|
3eqtrd |
|
147 |
146
|
oveq1d |
|
148 |
54
|
rpcnd |
|
149 |
91
|
rpred |
|
150 |
|
4nn |
|
151 |
|
nndivre |
|
152 |
149 150 151
|
sylancl |
|
153 |
152
|
recnd |
|
154 |
148 108 153
|
mul32d |
|
155 |
108
|
sqvald |
|
156 |
155
|
oveq2d |
|
157 |
37
|
rpcnd |
|
158 |
157 108 108
|
mulassd |
|
159 |
156 158
|
eqtr4d |
|
160 |
147 154 159
|
3eqtr4d |
|
161 |
58
|
simp3d |
|
162 |
152 65 55
|
lemul2d |
|
163 |
161 162
|
mpbid |
|
164 |
160 163
|
eqbrtrrd |
|
165 |
46
|
rpred |
|
166 |
55
|
rpred |
|
167 |
166 65
|
remulcld |
|
168 |
165 167 22
|
lemul2d |
|
169 |
164 168
|
mpbid |
|
170 |
22
|
rpcnd |
|
171 |
55
|
rpcnd |
|
172 |
65
|
recnd |
|
173 |
170 171 172
|
mulassd |
|
174 |
169 173
|
breqtrrd |
|
175 |
|
fzfid |
|
176 |
62
|
nnzd |
|
177 |
87 176
|
rpexpcld |
|
178 |
39 177
|
rpdivcld |
|
179 |
178
|
rprege0d |
|
180 |
|
flge0nn0 |
|
181 |
|
nn0p1nn |
|
182 |
179 180 181
|
3syl |
|
183 |
|
nnuz |
|
184 |
182 183
|
eleqtrdi |
|
185 |
|
fzss1 |
|
186 |
184 185
|
syl |
|
187 |
186
|
sselda |
|
188 |
187 84
|
syldan |
|
189 |
175 188
|
fsumrecl |
|
190 |
|
eluzfz2 |
|
191 |
60 190
|
syl |
|
192 |
|
oveq1 |
|
193 |
192
|
oveq2d |
|
194 |
|
oveq2 |
|
195 |
194
|
oveq2d |
|
196 |
195
|
fveq2d |
|
197 |
196
|
oveq1d |
|
198 |
197
|
oveq1d |
|
199 |
198
|
sumeq1d |
|
200 |
193 199
|
breq12d |
|
201 |
200
|
imbi2d |
|
202 |
|
oveq1 |
|
203 |
202
|
oveq2d |
|
204 |
|
oveq2 |
|
205 |
204
|
oveq2d |
|
206 |
205
|
fveq2d |
|
207 |
206
|
oveq1d |
|
208 |
207
|
oveq1d |
|
209 |
208
|
sumeq1d |
|
210 |
203 209
|
breq12d |
|
211 |
210
|
imbi2d |
|
212 |
|
oveq1 |
|
213 |
212
|
oveq2d |
|
214 |
|
oveq2 |
|
215 |
214
|
oveq2d |
|
216 |
215
|
fveq2d |
|
217 |
216
|
oveq1d |
|
218 |
217
|
oveq1d |
|
219 |
218
|
sumeq1d |
|
220 |
213 219
|
breq12d |
|
221 |
220
|
imbi2d |
|
222 |
|
oveq1 |
|
223 |
222
|
oveq2d |
|
224 |
|
oveq2 |
|
225 |
224
|
oveq2d |
|
226 |
225
|
fveq2d |
|
227 |
226
|
oveq1d |
|
228 |
227
|
oveq1d |
|
229 |
228
|
sumeq1d |
|
230 |
223 229
|
breq12d |
|
231 |
230
|
imbi2d |
|
232 |
59
|
nncnd |
|
233 |
232
|
subidd |
|
234 |
233
|
oveq2d |
|
235 |
56
|
rpcnd |
|
236 |
235
|
mul01d |
|
237 |
234 236
|
eqtrd |
|
238 |
|
fzfid |
|
239 |
59
|
nnzd |
|
240 |
87 239
|
rpexpcld |
|
241 |
39 240
|
rpdivcld |
|
242 |
241
|
rprege0d |
|
243 |
|
flge0nn0 |
|
244 |
|
nn0p1nn |
|
245 |
242 243 244
|
3syl |
|
246 |
245 183
|
eleqtrdi |
|
247 |
|
fzss1 |
|
248 |
246 247
|
syl |
|
249 |
248
|
sselda |
|
250 |
249 84
|
syldan |
|
251 |
|
elfzle2 |
|
252 |
251
|
adantl |
|
253 |
11
|
simpld |
|
254 |
39 253
|
rpdivcld |
|
255 |
254
|
rpred |
|
256 |
|
elfzelz |
|
257 |
|
flge |
|
258 |
255 256 257
|
syl2an |
|
259 |
252 258
|
mpbird |
|
260 |
73 259
|
jca |
|
261 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
|
pntlemn |
|
262 |
260 261
|
syldan |
|
263 |
249 262
|
syldan |
|
264 |
238 250 263
|
fsumge0 |
|
265 |
237 264
|
eqbrtrd |
|
266 |
265
|
a1i |
|
267 |
|
eqid |
|
268 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 267
|
pntlemi |
|
269 |
56
|
adantr |
|
270 |
269
|
rpred |
|
271 |
|
elfzoelz |
|
272 |
271
|
adantl |
|
273 |
272
|
zred |
|
274 |
59
|
adantr |
|
275 |
274
|
nnred |
|
276 |
273 275
|
resubcld |
|
277 |
270 276
|
remulcld |
|
278 |
|
fzfid |
|
279 |
|
ssun1 |
|
280 |
40
|
adantr |
|
281 |
87
|
adantr |
|
282 |
272
|
peano2zd |
|
283 |
281 282
|
rpexpcld |
|
284 |
280 283
|
rerpdivcld |
|
285 |
281 272
|
rpexpcld |
|
286 |
280 285
|
rerpdivcld |
|
287 |
88
|
adantr |
|
288 |
|
1re |
|
289 |
|
ltle |
|
290 |
288 88 289
|
sylancr |
|
291 |
89 290
|
mpd |
|
292 |
291
|
adantr |
|
293 |
|
uzid |
|
294 |
|
peano2uz |
|
295 |
272 293 294
|
3syl |
|
296 |
287 292 295
|
leexp2ad |
|
297 |
39
|
adantr |
|
298 |
285 283 297
|
lediv2d |
|
299 |
296 298
|
mpbid |
|
300 |
|
flword2 |
|
301 |
284 286 299 300
|
syl3anc |
|
302 |
|
eluzp1p1 |
|
303 |
301 302
|
syl |
|
304 |
286
|
flcld |
|
305 |
254
|
adantr |
|
306 |
305
|
rpred |
|
307 |
306
|
flcld |
|
308 |
253
|
adantr |
|
309 |
308
|
rpred |
|
310 |
285
|
rpred |
|
311 |
12
|
simpld |
|
312 |
311
|
rpred |
|
313 |
312
|
adantr |
|
314 |
12
|
simprd |
|
315 |
314
|
adantr |
|
316 |
|
elfzofz |
|
317 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
|
pntlemh |
|
318 |
316 317
|
sylan2 |
|
319 |
318
|
simpld |
|
320 |
309 313 310 315 319
|
lttrd |
|
321 |
309 310 320
|
ltled |
|
322 |
308 285 297
|
lediv2d |
|
323 |
321 322
|
mpbid |
|
324 |
|
flwordi |
|
325 |
286 306 323 324
|
syl3anc |
|
326 |
|
eluz2 |
|
327 |
304 307 325 326
|
syl3anbrc |
|
328 |
|
fzsplit2 |
|
329 |
303 327 328
|
syl2anc |
|
330 |
279 329
|
sseqtrrid |
|
331 |
297 283
|
rpdivcld |
|
332 |
331
|
rprege0d |
|
333 |
|
flge0nn0 |
|
334 |
|
nn0p1nn |
|
335 |
332 333 334
|
3syl |
|
336 |
335 183
|
eleqtrdi |
|
337 |
|
fzss1 |
|
338 |
336 337
|
syl |
|
339 |
330 338
|
sstrd |
|
340 |
339
|
sselda |
|
341 |
84
|
adantlr |
|
342 |
340 341
|
syldan |
|
343 |
278 342
|
fsumrecl |
|
344 |
|
fzfid |
|
345 |
|
ssun2 |
|
346 |
345 329
|
sseqtrrid |
|
347 |
346 338
|
sstrd |
|
348 |
347
|
sselda |
|
349 |
348 341
|
syldan |
|
350 |
344 349
|
fsumrecl |
|
351 |
|
le2add |
|
352 |
270 277 343 350 351
|
syl22anc |
|
353 |
268 352
|
mpand |
|
354 |
235
|
adantr |
|
355 |
|
1cnd |
|
356 |
272
|
zcnd |
|
357 |
232
|
adantr |
|
358 |
356 357
|
subcld |
|
359 |
354 355 358
|
adddid |
|
360 |
355 358
|
addcomd |
|
361 |
356 355 357
|
addsubd |
|
362 |
360 361
|
eqtr4d |
|
363 |
362
|
oveq2d |
|
364 |
354
|
mulid1d |
|
365 |
364
|
oveq1d |
|
366 |
359 363 365
|
3eqtr3d |
|
367 |
|
reflcl |
|
368 |
286 367
|
syl |
|
369 |
368
|
ltp1d |
|
370 |
|
fzdisj |
|
371 |
369 370
|
syl |
|
372 |
|
fzfid |
|
373 |
338
|
sselda |
|
374 |
373 341
|
syldan |
|
375 |
374
|
recnd |
|
376 |
371 329 372 375
|
fsumsplit |
|
377 |
366 376
|
breq12d |
|
378 |
353 377
|
sylibrd |
|
379 |
378
|
expcom |
|
380 |
379
|
a2d |
|
381 |
201 211 221 231 266 380
|
fzind2 |
|
382 |
191 381
|
mpcom |
|
383 |
67 84 262 186
|
fsumless |
|
384 |
66 189 85 382 383
|
letrd |
|
385 |
48 66 85 174 384
|
letrd |
|