Step |
Hyp |
Ref |
Expression |
1 |
|
pcoass.2 |
|
2 |
|
pcoass.3 |
|
3 |
|
pcoass.4 |
|
4 |
|
pcoass.5 |
|
5 |
|
pcoass.6 |
|
6 |
|
pcoass.7 |
|
7 |
|
iftrue |
|
8 |
7
|
fveq2d |
|
9 |
8
|
adantl |
|
10 |
|
2cn |
|
11 |
|
elicc01 |
|
12 |
11
|
simp1bi |
|
13 |
12
|
adantr |
|
14 |
13
|
recnd |
|
15 |
|
mulcom |
|
16 |
10 14 15
|
sylancr |
|
17 |
11
|
simp2bi |
|
18 |
17
|
adantr |
|
19 |
|
simpr |
|
20 |
|
0re |
|
21 |
|
4nn |
|
22 |
|
nnrecre |
|
23 |
21 22
|
ax-mp |
|
24 |
20 23
|
elicc2i |
|
25 |
13 18 19 24
|
syl3anbrc |
|
26 |
|
2rp |
|
27 |
10
|
mul02i |
|
28 |
23
|
recni |
|
29 |
28
|
2timesi |
|
30 |
|
2ne0 |
|
31 |
|
recdiv2 |
|
32 |
10 30 10 30 31
|
mp4an |
|
33 |
|
2t2e4 |
|
34 |
33
|
oveq2i |
|
35 |
32 34
|
eqtri |
|
36 |
35 35
|
oveq12i |
|
37 |
|
halfcn |
|
38 |
|
2halves |
|
39 |
37 38
|
ax-mp |
|
40 |
36 39
|
eqtr3i |
|
41 |
29 40
|
eqtri |
|
42 |
10 28 41
|
mulcomli |
|
43 |
20 23 26 27 42
|
iccdili |
|
44 |
25 43
|
syl |
|
45 |
16 44
|
eqeltrd |
|
46 |
2 3 5
|
pcocn |
|
47 |
1 46
|
pcoval1 |
|
48 |
1 2
|
pcoval1 |
|
49 |
47 48
|
eqtr4d |
|
50 |
45 49
|
sylan2 |
|
51 |
50
|
anassrs |
|
52 |
9 51
|
eqtrd |
|
53 |
52
|
adantlr |
|
54 |
|
simplll |
|
55 |
12
|
ad2antlr |
|
56 |
55
|
adantr |
|
57 |
|
letric |
|
58 |
55 23 57
|
sylancl |
|
59 |
58
|
orcanai |
|
60 |
|
simplr |
|
61 |
|
halfre |
|
62 |
23 61
|
elicc2i |
|
63 |
56 59 60 62
|
syl3anbrc |
|
64 |
62
|
simp1bi |
|
65 |
|
readdcl |
|
66 |
64 23 65
|
sylancl |
|
67 |
23
|
a1i |
|
68 |
62
|
simp2bi |
|
69 |
67 64 67 68
|
leadd1dd |
|
70 |
40 69
|
eqbrtrrid |
|
71 |
61
|
a1i |
|
72 |
62
|
simp3bi |
|
73 |
|
2lt4 |
|
74 |
|
2re |
|
75 |
|
4re |
|
76 |
|
2pos |
|
77 |
|
4pos |
|
78 |
74 75 76 77
|
ltrecii |
|
79 |
73 78
|
mpbi |
|
80 |
23 61 79
|
ltleii |
|
81 |
80
|
a1i |
|
82 |
64 67 71 71 72 81
|
le2addd |
|
83 |
|
ax-1cn |
|
84 |
|
2halves |
|
85 |
83 84
|
ax-mp |
|
86 |
82 85
|
breqtrdi |
|
87 |
|
1re |
|
88 |
61 87
|
elicc2i |
|
89 |
66 70 86 88
|
syl3anbrc |
|
90 |
63 89
|
syl |
|
91 |
2 3
|
pco0 |
|
92 |
4 91
|
eqtr4d |
|
93 |
1 46 92
|
pcoval2 |
|
94 |
54 90 93
|
syl2anc |
|
95 |
85
|
oveq2i |
|
96 |
|
2cnd |
|
97 |
56
|
recnd |
|
98 |
28
|
a1i |
|
99 |
96 97 98
|
adddid |
|
100 |
41
|
oveq2i |
|
101 |
99 100
|
eqtrdi |
|
102 |
101
|
oveq1d |
|
103 |
95 102
|
syl5eqr |
|
104 |
|
remulcl |
|
105 |
74 56 104
|
sylancr |
|
106 |
105
|
recnd |
|
107 |
37
|
a1i |
|
108 |
106 107 107
|
pnpcan2d |
|
109 |
103 108
|
eqtrd |
|
110 |
109
|
fveq2d |
|
111 |
10 97 15
|
sylancr |
|
112 |
83 10 30
|
divcan1i |
|
113 |
23 61 26 42 112
|
iccdili |
|
114 |
63 113
|
syl |
|
115 |
111 114
|
eqeltrd |
|
116 |
37
|
subidi |
|
117 |
|
1mhlfehlf |
|
118 |
61 87 61 116 117
|
iccshftli |
|
119 |
115 118
|
syl |
|
120 |
2 3
|
pcoval1 |
|
121 |
54 119 120
|
syl2anc |
|
122 |
96 106 107
|
subdid |
|
123 |
10 30
|
recidi |
|
124 |
123
|
oveq2i |
|
125 |
122 124
|
eqtrdi |
|
126 |
125
|
fveq2d |
|
127 |
121 126
|
eqtrd |
|
128 |
94 110 127
|
3eqtrd |
|
129 |
|
iffalse |
|
130 |
129
|
fveq2d |
|
131 |
130
|
adantl |
|
132 |
1 2 4
|
pcoval2 |
|
133 |
54 115 132
|
syl2anc |
|
134 |
128 131 133
|
3eqtr4d |
|
135 |
53 134
|
pm2.61dan |
|
136 |
|
iftrue |
|
137 |
136
|
fveq2d |
|
138 |
137
|
adantl |
|
139 |
|
iftrue |
|
140 |
139
|
adantl |
|
141 |
135 138 140
|
3eqtr4d |
|
142 |
|
elii2 |
|
143 |
|
halfge0 |
|
144 |
|
halflt1 |
|
145 |
61 87 144
|
ltleii |
|
146 |
|
elicc01 |
|
147 |
61 143 145 146
|
mpbir3an |
|
148 |
|
1elunit |
|
149 |
|
iccss2 |
|
150 |
147 148 149
|
mp2an |
|
151 |
150
|
sseli |
|
152 |
10 30
|
div0i |
|
153 |
|
eqid |
|
154 |
20 87 26 152 153
|
icccntri |
|
155 |
37
|
addid2i |
|
156 |
20 61 61 155 85
|
iccshftri |
|
157 |
151 154 156
|
3syl |
|
158 |
1 46 92
|
pcoval2 |
|
159 |
157 158
|
sylan2 |
|
160 |
61 87
|
elicc2i |
|
161 |
160
|
simp1bi |
|
162 |
161
|
recnd |
|
163 |
|
1cnd |
|
164 |
|
2cnd |
|
165 |
30
|
a1i |
|
166 |
162 163 164 165
|
divdird |
|
167 |
166
|
oveq2d |
|
168 |
|
peano2cn |
|
169 |
162 168
|
syl |
|
170 |
169 164 165
|
divcan2d |
|
171 |
167 170
|
eqtr3d |
|
172 |
162 163 171
|
mvrraddd |
|
173 |
172
|
fveq2d |
|
174 |
173
|
adantl |
|
175 |
2 3 5
|
pcoval2 |
|
176 |
159 174 175
|
3eqtrd |
|
177 |
142 176
|
sylan2 |
|
178 |
177
|
anassrs |
|
179 |
|
iffalse |
|
180 |
179
|
fveq2d |
|
181 |
180
|
adantl |
|
182 |
|
iffalse |
|
183 |
182
|
adantl |
|
184 |
178 181 183
|
3eqtr4d |
|
185 |
141 184
|
pm2.61dan |
|
186 |
185
|
mpteq2dva |
|
187 |
|
iitopon |
|
188 |
187
|
a1i |
|
189 |
188
|
cnmptid |
|
190 |
|
0elunit |
|
191 |
190
|
a1i |
|
192 |
188 188 191
|
cnmptc |
|
193 |
|
eqid |
|
194 |
|
eqid |
|
195 |
|
eqid |
|
196 |
|
dfii2 |
|
197 |
|
0red |
|
198 |
|
1red |
|
199 |
147
|
a1i |
|
200 |
|
simprl |
|
201 |
200
|
oveq1d |
|
202 |
37 28
|
addcomi |
|
203 |
201 202
|
eqtrdi |
|
204 |
23 61
|
ltnlei |
|
205 |
79 204
|
mpbi |
|
206 |
200
|
breq1d |
|
207 |
205 206
|
mtbiri |
|
208 |
207
|
iffalsed |
|
209 |
200
|
oveq1d |
|
210 |
209 35
|
eqtrdi |
|
211 |
210
|
oveq1d |
|
212 |
203 208 211
|
3eqtr4d |
|
213 |
|
eqid |
|
214 |
|
eqid |
|
215 |
61
|
a1i |
|
216 |
75 77
|
recgt0ii |
|
217 |
20 23 216
|
ltleii |
|
218 |
20 61
|
elicc2i |
|
219 |
23 217 80 218
|
mpbir3an |
|
220 |
219
|
a1i |
|
221 |
|
simprl |
|
222 |
221
|
oveq2d |
|
223 |
221
|
oveq1d |
|
224 |
29 222 223
|
3eqtr4a |
|
225 |
|
retopon |
|
226 |
|
0xr |
|
227 |
61
|
rexri |
|
228 |
|
lbicc2 |
|
229 |
226 227 143 228
|
mp3an |
|
230 |
|
iccss2 |
|
231 |
229 219 230
|
mp2an |
|
232 |
|
iccssre |
|
233 |
20 61 232
|
mp2an |
|
234 |
231 233
|
sstri |
|
235 |
|
resttopon |
|
236 |
225 234 235
|
mp2an |
|
237 |
236
|
a1i |
|
238 |
237 188
|
cnmpt1st |
|
239 |
|
retop |
|
240 |
|
ovex |
|
241 |
|
restabs |
|
242 |
239 231 240 241
|
mp3an |
|
243 |
242
|
eqcomi |
|
244 |
|
resttopon |
|
245 |
225 233 244
|
mp2an |
|
246 |
245
|
a1i |
|
247 |
231
|
a1i |
|
248 |
194
|
iihalf1cn |
|
249 |
248
|
a1i |
|
250 |
243 246 247 249
|
cnmpt1res |
|
251 |
|
oveq2 |
|
252 |
237 188 238 237 250 251
|
cnmpt21 |
|
253 |
|
iccssre |
|
254 |
23 61 253
|
mp2an |
|
255 |
|
resttopon |
|
256 |
225 254 255
|
mp2an |
|
257 |
256
|
a1i |
|
258 |
257 188
|
cnmpt1st |
|
259 |
|
eqid |
|
260 |
254
|
a1i |
|
261 |
|
unitssre |
|
262 |
261
|
a1i |
|
263 |
150 89
|
sseldi |
|
264 |
263
|
adantl |
|
265 |
259
|
cnfldtopon |
|
266 |
265
|
a1i |
|
267 |
266
|
cnmptid |
|
268 |
23
|
a1i |
|
269 |
268
|
recnd |
|
270 |
266 266 269
|
cnmptc |
|
271 |
259
|
addcn |
|
272 |
271
|
a1i |
|
273 |
266 267 270 272
|
cnmpt12f |
|
274 |
259 214 196 260 262 264 273
|
cnmptre |
|
275 |
|
oveq1 |
|
276 |
257 188 258 257 274 275
|
cnmpt21 |
|
277 |
193 213 214 194 197 215 220 188 224 252 276
|
cnmpopc |
|
278 |
|
iccssre |
|
279 |
61 87 278
|
mp2an |
|
280 |
|
resttopon |
|
281 |
225 279 280
|
mp2an |
|
282 |
281
|
a1i |
|
283 |
282 188
|
cnmpt1st |
|
284 |
279
|
a1i |
|
285 |
150 157
|
sseldi |
|
286 |
285
|
adantl |
|
287 |
259
|
divccn |
|
288 |
10 30 287
|
mp2an |
|
289 |
288
|
a1i |
|
290 |
37
|
a1i |
|
291 |
266 266 290
|
cnmptc |
|
292 |
266 289 291 272
|
cnmpt12f |
|
293 |
259 195 196 284 262 286 292
|
cnmptre |
|
294 |
|
oveq1 |
|
295 |
294
|
oveq1d |
|
296 |
282 188 283 282 293 295
|
cnmpt21 |
|
297 |
193 194 195 196 197 198 199 188 212 277 296
|
cnmpopc |
|
298 |
|
breq1 |
|
299 |
|
breq1 |
|
300 |
299 251 275
|
ifbieq12d |
|
301 |
298 300 295
|
ifbieq12d |
|
302 |
301
|
equcoms |
|
303 |
302
|
adantr |
|
304 |
303
|
eqcomd |
|
305 |
188 189 192 188 188 297 304
|
cnmpt12 |
|
306 |
6 305
|
eqeltrid |
|
307 |
|
iiuni |
|
308 |
307 307
|
cnf |
|
309 |
306 308
|
syl |
|
310 |
6
|
fmpt |
|
311 |
309 310
|
sylibr |
|
312 |
6
|
a1i |
|
313 |
1 46 92
|
pcocn |
|
314 |
|
eqid |
|
315 |
307 314
|
cnf |
|
316 |
313 315
|
syl |
|
317 |
316
|
feqmptd |
|
318 |
|
fveq2 |
|
319 |
311 312 317 318
|
fmptcof |
|
320 |
1 2 4
|
pcocn |
|
321 |
320 3
|
pcoval |
|
322 |
186 319 321
|
3eqtr4rd |
|
323 |
|
id |
|
324 |
323 143
|
eqbrtrdi |
|
325 |
324
|
iftrued |
|
326 |
323 217
|
eqbrtrdi |
|
327 |
326
|
iftrued |
|
328 |
|
oveq2 |
|
329 |
|
2t0e0 |
|
330 |
328 329
|
eqtrdi |
|
331 |
325 327 330
|
3eqtrd |
|
332 |
|
c0ex |
|
333 |
331 6 332
|
fvmpt |
|
334 |
191 333
|
syl |
|
335 |
148
|
a1i |
|
336 |
61 87
|
ltnlei |
|
337 |
144 336
|
mpbi |
|
338 |
|
breq1 |
|
339 |
337 338
|
mtbiri |
|
340 |
339
|
iffalsed |
|
341 |
|
oveq1 |
|
342 |
341
|
oveq1d |
|
343 |
342 85
|
eqtrdi |
|
344 |
340 343
|
eqtrd |
|
345 |
|
1ex |
|
346 |
344 6 345
|
fvmpt |
|
347 |
335 346
|
syl |
|
348 |
313 306 334 347
|
reparpht |
|
349 |
322 348
|
eqbrtrd |
|