Step |
Hyp |
Ref |
Expression |
1 |
|
hgt750leme.o |
|
2 |
|
hgt750leme.n |
|
3 |
|
hgt750leme.0 |
|
4 |
|
hgt750leme.h |
|
5 |
|
hgt750leme.k |
|
6 |
|
hgt750leme.1 |
|
7 |
|
hgt750leme.2 |
|
8 |
2
|
nnnn0d |
|
9 |
|
3nn0 |
|
10 |
9
|
a1i |
|
11 |
|
ssidd |
|
12 |
8 10 11
|
reprfi2 |
|
13 |
|
diffi |
|
14 |
12 13
|
syl |
|
15 |
|
vmaf |
|
16 |
15
|
a1i |
|
17 |
|
ssidd |
|
18 |
2
|
nnzd |
|
19 |
18
|
adantr |
|
20 |
9
|
a1i |
|
21 |
|
simpr |
|
22 |
21
|
eldifad |
|
23 |
17 19 20 22
|
reprf |
|
24 |
|
c0ex |
|
25 |
24
|
tpid1 |
|
26 |
|
fzo0to3tp |
|
27 |
25 26
|
eleqtrri |
|
28 |
27
|
a1i |
|
29 |
23 28
|
ffvelrnd |
|
30 |
16 29
|
ffvelrnd |
|
31 |
|
rge0ssre |
|
32 |
4
|
adantr |
|
33 |
32 29
|
ffvelrnd |
|
34 |
31 33
|
sseldi |
|
35 |
30 34
|
remulcld |
|
36 |
|
1ex |
|
37 |
36
|
tpid2 |
|
38 |
37 26
|
eleqtrri |
|
39 |
38
|
a1i |
|
40 |
23 39
|
ffvelrnd |
|
41 |
16 40
|
ffvelrnd |
|
42 |
5
|
adantr |
|
43 |
42 40
|
ffvelrnd |
|
44 |
31 43
|
sseldi |
|
45 |
41 44
|
remulcld |
|
46 |
|
2ex |
|
47 |
46
|
tpid3 |
|
48 |
47 26
|
eleqtrri |
|
49 |
48
|
a1i |
|
50 |
23 49
|
ffvelrnd |
|
51 |
16 50
|
ffvelrnd |
|
52 |
42 50
|
ffvelrnd |
|
53 |
31 52
|
sseldi |
|
54 |
51 53
|
remulcld |
|
55 |
45 54
|
remulcld |
|
56 |
35 55
|
remulcld |
|
57 |
14 56
|
fsumrecl |
|
58 |
|
3re |
|
59 |
58
|
a1i |
|
60 |
|
1nn0 |
|
61 |
|
0nn0 |
|
62 |
|
7nn0 |
|
63 |
|
9nn0 |
|
64 |
|
5nn0 |
|
65 |
|
5nn |
|
66 |
|
nnrp |
|
67 |
65 66
|
ax-mp |
|
68 |
64 67
|
rpdp2cl |
|
69 |
63 68
|
rpdp2cl |
|
70 |
63 69
|
rpdp2cl |
|
71 |
62 70
|
rpdp2cl |
|
72 |
61 71
|
rpdp2cl |
|
73 |
60 72
|
rpdpcl |
|
74 |
73
|
a1i |
|
75 |
74
|
rpred |
|
76 |
75
|
resqcld |
|
77 |
|
4nn0 |
|
78 |
|
4nn |
|
79 |
|
nnrp |
|
80 |
78 79
|
ax-mp |
|
81 |
60 80
|
rpdp2cl |
|
82 |
77 81
|
rpdp2cl |
|
83 |
60 82
|
rpdpcl |
|
84 |
83
|
a1i |
|
85 |
84
|
rpred |
|
86 |
76 85
|
remulcld |
|
87 |
|
fveq1 |
|
88 |
87
|
eleq1d |
|
89 |
88
|
notbid |
|
90 |
89
|
cbvrabv |
|
91 |
90
|
ssrab3 |
|
92 |
|
ssfi |
|
93 |
12 91 92
|
sylancl |
|
94 |
15
|
a1i |
|
95 |
|
ssidd |
|
96 |
18
|
adantr |
|
97 |
9
|
a1i |
|
98 |
91
|
a1i |
|
99 |
98
|
sselda |
|
100 |
95 96 97 99
|
reprf |
|
101 |
27
|
a1i |
|
102 |
100 101
|
ffvelrnd |
|
103 |
94 102
|
ffvelrnd |
|
104 |
38
|
a1i |
|
105 |
100 104
|
ffvelrnd |
|
106 |
94 105
|
ffvelrnd |
|
107 |
48
|
a1i |
|
108 |
100 107
|
ffvelrnd |
|
109 |
94 108
|
ffvelrnd |
|
110 |
106 109
|
remulcld |
|
111 |
103 110
|
remulcld |
|
112 |
93 111
|
fsumrecl |
|
113 |
86 112
|
remulcld |
|
114 |
59 113
|
remulcld |
|
115 |
|
4re |
|
116 |
|
8re |
|
117 |
115 116
|
pm3.2i |
|
118 |
|
dp2cl |
|
119 |
117 118
|
ax-mp |
|
120 |
58 119
|
pm3.2i |
|
121 |
|
dp2cl |
|
122 |
120 121
|
ax-mp |
|
123 |
|
dpcl |
|
124 |
62 122 123
|
mp2an |
|
125 |
124
|
a1i |
|
126 |
2
|
nnrpd |
|
127 |
126
|
relogcld |
|
128 |
2
|
nnred |
|
129 |
126
|
rpge0d |
|
130 |
128 129
|
resqrtcld |
|
131 |
126
|
rpsqrtcld |
|
132 |
131
|
rpne0d |
|
133 |
127 130 132
|
redivcld |
|
134 |
125 133
|
remulcld |
|
135 |
128
|
resqcld |
|
136 |
134 135
|
remulcld |
|
137 |
|
0re |
|
138 |
|
7re |
|
139 |
|
9re |
|
140 |
|
5re |
|
141 |
140 140
|
pm3.2i |
|
142 |
|
dp2cl |
|
143 |
141 142
|
ax-mp |
|
144 |
139 143
|
pm3.2i |
|
145 |
|
dp2cl |
|
146 |
144 145
|
ax-mp |
|
147 |
139 146
|
pm3.2i |
|
148 |
|
dp2cl |
|
149 |
147 148
|
ax-mp |
|
150 |
138 149
|
pm3.2i |
|
151 |
|
dp2cl |
|
152 |
150 151
|
ax-mp |
|
153 |
137 152
|
pm3.2i |
|
154 |
|
dp2cl |
|
155 |
153 154
|
ax-mp |
|
156 |
|
dpcl |
|
157 |
60 155 156
|
mp2an |
|
158 |
157
|
a1i |
|
159 |
158
|
resqcld |
|
160 |
|
1re |
|
161 |
160 115
|
pm3.2i |
|
162 |
|
dp2cl |
|
163 |
161 162
|
ax-mp |
|
164 |
115 163
|
pm3.2i |
|
165 |
|
dp2cl |
|
166 |
164 165
|
ax-mp |
|
167 |
|
dpcl |
|
168 |
60 166 167
|
mp2an |
|
169 |
168
|
a1i |
|
170 |
159 169
|
remulcld |
|
171 |
41 51
|
remulcld |
|
172 |
30 171
|
remulcld |
|
173 |
14 172
|
fsumrecl |
|
174 |
170 173
|
remulcld |
|
175 |
59 112
|
remulcld |
|
176 |
170 175
|
remulcld |
|
177 |
14 158 169 4 5 29 40 50 6 7
|
hgt750lemf |
|
178 |
|
2re |
|
179 |
178
|
a1i |
|
180 |
|
10nn0 |
|
181 |
|
2nn0 |
|
182 |
181 62
|
deccl |
|
183 |
180 182
|
nn0expcli |
|
184 |
183
|
nn0rei |
|
185 |
184
|
a1i |
|
186 |
180
|
numexp1 |
|
187 |
180
|
nn0rei |
|
188 |
186 187
|
eqeltri |
|
189 |
188
|
a1i |
|
190 |
|
1nn |
|
191 |
|
2lt9 |
|
192 |
178 139 191
|
ltleii |
|
193 |
190 61 181 192
|
declei |
|
194 |
193 186
|
breqtrri |
|
195 |
194
|
a1i |
|
196 |
|
1z |
|
197 |
182
|
nn0zi |
|
198 |
187 196 197
|
3pm3.2i |
|
199 |
|
1lt10 |
|
200 |
198 199
|
pm3.2i |
|
201 |
|
2nn |
|
202 |
|
1lt9 |
|
203 |
160 139 202
|
ltleii |
|
204 |
201 62 60 203
|
declei |
|
205 |
|
leexp2 |
|
206 |
205
|
biimpa |
|
207 |
200 204 206
|
mp2an |
|
208 |
207
|
a1i |
|
209 |
179 189 185 195 208
|
letrd |
|
210 |
179 185 128 209 3
|
letrd |
|
211 |
|
eqid |
|
212 |
1 2 210 90 211
|
hgt750lema |
|
213 |
|
2z |
|
214 |
213
|
a1i |
|
215 |
74 214
|
rpexpcld |
|
216 |
215 84
|
rpmulcld |
|
217 |
173 175 216
|
lemul2d |
|
218 |
212 217
|
mpbid |
|
219 |
57 174 176 177 218
|
letrd |
|
220 |
158
|
recnd |
|
221 |
220
|
sqcld |
|
222 |
169
|
recnd |
|
223 |
221 222
|
mulcld |
|
224 |
|
3cn |
|
225 |
224
|
a1i |
|
226 |
112
|
recnd |
|
227 |
223 225 226
|
mul12d |
|
228 |
219 227
|
breqtrd |
|
229 |
|
fzfi |
|
230 |
|
diffi |
|
231 |
229 230
|
ax-mp |
|
232 |
|
snfi |
|
233 |
|
unfi |
|
234 |
231 232 233
|
mp2an |
|
235 |
234
|
a1i |
|
236 |
15
|
a1i |
|
237 |
|
fz1ssnn |
|
238 |
237
|
a1i |
|
239 |
238
|
ssdifssd |
|
240 |
201
|
a1i |
|
241 |
240
|
snssd |
|
242 |
239 241
|
unssd |
|
243 |
242
|
sselda |
|
244 |
236 243
|
ffvelrnd |
|
245 |
235 244
|
fsumrecl |
|
246 |
|
chpvalz |
|
247 |
18 246
|
syl |
|
248 |
|
chpf |
|
249 |
248
|
a1i |
|
250 |
249 128
|
ffvelrnd |
|
251 |
247 250
|
eqeltrrd |
|
252 |
245 251
|
remulcld |
|
253 |
127 252
|
remulcld |
|
254 |
86 253
|
remulcld |
|
255 |
59 254
|
remulcld |
|
256 |
1 2 210 90
|
hgt750lemb |
|
257 |
112 253 216
|
lemul2d |
|
258 |
256 257
|
mpbid |
|
259 |
|
3rp |
|
260 |
259
|
a1i |
|
261 |
113 254 260
|
lemul2d |
|
262 |
258 261
|
mpbid |
|
263 |
|
6re |
|
264 |
263 58
|
pm3.2i |
|
265 |
|
dp2cl |
|
266 |
264 265
|
ax-mp |
|
267 |
178 266
|
pm3.2i |
|
268 |
|
dp2cl |
|
269 |
267 268
|
ax-mp |
|
270 |
115 269
|
pm3.2i |
|
271 |
|
dp2cl |
|
272 |
270 271
|
ax-mp |
|
273 |
|
dpcl |
|
274 |
60 272 273
|
mp2an |
|
275 |
274
|
a1i |
|
276 |
275 130
|
remulcld |
|
277 |
116 58
|
pm3.2i |
|
278 |
|
dp2cl |
|
279 |
277 278
|
ax-mp |
|
280 |
116 279
|
pm3.2i |
|
281 |
|
dp2cl |
|
282 |
280 281
|
ax-mp |
|
283 |
58 282
|
pm3.2i |
|
284 |
|
dp2cl |
|
285 |
283 284
|
ax-mp |
|
286 |
137 285
|
pm3.2i |
|
287 |
|
dp2cl |
|
288 |
286 287
|
ax-mp |
|
289 |
|
dpcl |
|
290 |
60 288 289
|
mp2an |
|
291 |
290
|
a1i |
|
292 |
291 128
|
remulcld |
|
293 |
276 292
|
remulcld |
|
294 |
127 293
|
remulcld |
|
295 |
86 294
|
remulcld |
|
296 |
59 295
|
remulcld |
|
297 |
|
vmage0 |
|
298 |
243 297
|
syl |
|
299 |
235 244 298
|
fsumge0 |
|
300 |
2 3
|
hgt750lemd |
|
301 |
|
fzfid |
|
302 |
15
|
a1i |
|
303 |
238
|
sselda |
|
304 |
302 303
|
ffvelrnd |
|
305 |
|
vmage0 |
|
306 |
303 305
|
syl |
|
307 |
301 304 306
|
fsumge0 |
|
308 |
2
|
hgt750lemc |
|
309 |
245 276 251 292 299 300 307 308
|
ltmul12ad |
|
310 |
252 293 309
|
ltled |
|
311 |
160
|
a1i |
|
312 |
|
1lt2 |
|
313 |
312
|
a1i |
|
314 |
311 179 128 313 210
|
ltletrd |
|
315 |
128 314
|
rplogcld |
|
316 |
252 293 315
|
lemul2d |
|
317 |
310 316
|
mpbid |
|
318 |
253 294 216
|
lemul2d |
|
319 |
317 318
|
mpbid |
|
320 |
254 295 260
|
lemul2d |
|
321 |
319 320
|
mpbid |
|
322 |
157
|
resqcli |
|
323 |
322 168
|
remulcli |
|
324 |
274 290
|
remulcli |
|
325 |
323 324
|
remulcli |
|
326 |
58 325
|
remulcli |
|
327 |
|
hgt750lem2 |
|
328 |
326 124 327
|
ltleii |
|
329 |
326
|
a1i |
|
330 |
315 131
|
rpdivcld |
|
331 |
126 214
|
rpexpcld |
|
332 |
330 331
|
rpmulcld |
|
333 |
329 125 332
|
lemul1d |
|
334 |
328 333
|
mpbii |
|
335 |
275
|
recnd |
|
336 |
130
|
recnd |
|
337 |
291
|
recnd |
|
338 |
128
|
recnd |
|
339 |
335 336 337 338
|
mul4d |
|
340 |
339
|
oveq2d |
|
341 |
127
|
recnd |
|
342 |
335 337
|
mulcld |
|
343 |
336 338
|
mulcld |
|
344 |
342 343
|
mulcld |
|
345 |
341 344
|
mulcomd |
|
346 |
340 345
|
eqtrd |
|
347 |
342 343 341
|
mulassd |
|
348 |
346 347
|
eqtrd |
|
349 |
348
|
oveq2d |
|
350 |
86
|
recnd |
|
351 |
343 341
|
mulcld |
|
352 |
350 342 351
|
mulassd |
|
353 |
349 352
|
eqtr4d |
|
354 |
353
|
oveq2d |
|
355 |
59
|
recnd |
|
356 |
350 342
|
mulcld |
|
357 |
355 356 351
|
mulassd |
|
358 |
354 357
|
eqtr4d |
|
359 |
135
|
recnd |
|
360 |
341 336 359 132
|
div32d |
|
361 |
359 336 132
|
divcld |
|
362 |
341 361
|
mulcomd |
|
363 |
338
|
sqvald |
|
364 |
363
|
oveq1d |
|
365 |
338 338 336 132
|
divassd |
|
366 |
|
divsqrtid |
|
367 |
126 366
|
syl |
|
368 |
367
|
oveq2d |
|
369 |
364 365 368
|
3eqtrd |
|
370 |
338 336
|
mulcomd |
|
371 |
369 370
|
eqtrd |
|
372 |
371
|
oveq1d |
|
373 |
360 362 372
|
3eqtrrd |
|
374 |
373
|
oveq2d |
|
375 |
358 374
|
eqtrd |
|
376 |
125
|
recnd |
|
377 |
133
|
recnd |
|
378 |
376 377 359
|
mulassd |
|
379 |
334 375 378
|
3brtr4d |
|
380 |
255 296 136 321 379
|
letrd |
|
381 |
114 255 136 262 380
|
letrd |
|
382 |
57 114 136 228 381
|
letrd |
|