Step |
Hyp |
Ref |
Expression |
1 |
|
lgamcvg.g |
|
2 |
|
lgamcvg.a |
|
3 |
|
nnuz |
|
4 |
|
1zzd |
|
5 |
|
eqid |
|
6 |
|
1nn0 |
|
7 |
6
|
a1i |
|
8 |
2 7
|
dmgmaddnn0 |
|
9 |
5 8
|
lgamcvg |
|
10 |
|
seqex |
|
11 |
10
|
a1i |
|
12 |
2
|
eldifad |
|
13 |
12
|
abscld |
|
14 |
|
arch |
|
15 |
13 14
|
syl |
|
16 |
|
eqid |
|
17 |
|
simprl |
|
18 |
17
|
nnzd |
|
19 |
|
eqid |
|
20 |
19
|
logcn |
|
21 |
20
|
a1i |
|
22 |
|
eqid |
|
23 |
22
|
dvlog2lem |
|
24 |
12
|
ad2antrr |
|
25 |
|
eluznn |
|
26 |
25
|
ex |
|
27 |
26
|
ad2antrl |
|
28 |
27
|
imp |
|
29 |
28
|
nncnd |
|
30 |
|
1cnd |
|
31 |
29 30
|
addcld |
|
32 |
28
|
peano2nnd |
|
33 |
32
|
nnne0d |
|
34 |
24 31 33
|
divcld |
|
35 |
34 30
|
addcld |
|
36 |
|
ax-1cn |
|
37 |
|
eqid |
|
38 |
37
|
cnmetdval |
|
39 |
35 36 38
|
sylancl |
|
40 |
34 30
|
pncand |
|
41 |
40
|
fveq2d |
|
42 |
24 31 33
|
absdivd |
|
43 |
32
|
nnred |
|
44 |
32
|
nnrpd |
|
45 |
44
|
rpge0d |
|
46 |
43 45
|
absidd |
|
47 |
46
|
oveq2d |
|
48 |
42 47
|
eqtrd |
|
49 |
39 41 48
|
3eqtrd |
|
50 |
13
|
ad2antrr |
|
51 |
17
|
adantr |
|
52 |
51
|
nnred |
|
53 |
|
simplrr |
|
54 |
|
eluzle |
|
55 |
54
|
adantl |
|
56 |
|
nnleltp1 |
|
57 |
51 28 56
|
syl2anc |
|
58 |
55 57
|
mpbid |
|
59 |
50 52 43 53 58
|
lttrd |
|
60 |
31
|
mulid1d |
|
61 |
59 60
|
breqtrrd |
|
62 |
|
1red |
|
63 |
50 62 44
|
ltdivmuld |
|
64 |
61 63
|
mpbird |
|
65 |
49 64
|
eqbrtrd |
|
66 |
|
cnxmet |
|
67 |
66
|
a1i |
|
68 |
|
1rp |
|
69 |
|
rpxr |
|
70 |
68 69
|
mp1i |
|
71 |
|
elbl3 |
|
72 |
67 70 30 35 71
|
syl22anc |
|
73 |
65 72
|
mpbird |
|
74 |
23 73
|
sseldi |
|
75 |
74
|
fmpttd |
|
76 |
27
|
ssrdv |
|
77 |
76
|
resmptd |
|
78 |
|
nnex |
|
79 |
78
|
mptex |
|
80 |
79
|
a1i |
|
81 |
|
oveq1 |
|
82 |
81
|
oveq2d |
|
83 |
|
eqid |
|
84 |
|
ovex |
|
85 |
82 83 84
|
fvmpt |
|
86 |
85
|
adantl |
|
87 |
3 4 12 4 80 86
|
divcnvshft |
|
88 |
|
1cnd |
|
89 |
78
|
mptex |
|
90 |
89
|
a1i |
|
91 |
12
|
adantr |
|
92 |
|
simpr |
|
93 |
92
|
nncnd |
|
94 |
|
1cnd |
|
95 |
93 94
|
addcld |
|
96 |
92
|
peano2nnd |
|
97 |
96
|
nnne0d |
|
98 |
91 95 97
|
divcld |
|
99 |
86 98
|
eqeltrd |
|
100 |
82
|
oveq1d |
|
101 |
|
eqid |
|
102 |
|
ovex |
|
103 |
100 101 102
|
fvmpt |
|
104 |
103
|
adantl |
|
105 |
86
|
oveq1d |
|
106 |
104 105
|
eqtr4d |
|
107 |
3 4 87 88 90 99 106
|
climaddc1 |
|
108 |
|
0p1e1 |
|
109 |
107 108
|
breqtrdi |
|
110 |
109
|
adantr |
|
111 |
|
climres |
|
112 |
18 89 111
|
sylancl |
|
113 |
110 112
|
mpbird |
|
114 |
77 113
|
eqbrtrrd |
|
115 |
68
|
a1i |
|
116 |
19
|
ellogdm |
|
117 |
36 115 116
|
mpbir2an |
|
118 |
117
|
a1i |
|
119 |
16 18 21 75 114 118
|
climcncf |
|
120 |
|
logf1o |
|
121 |
|
f1of |
|
122 |
120 121
|
mp1i |
|
123 |
19
|
logdmss |
|
124 |
123 74
|
sseldi |
|
125 |
122 124
|
cofmpt |
|
126 |
|
frn |
|
127 |
|
cores |
|
128 |
75 126 127
|
3syl |
|
129 |
76
|
resmptd |
|
130 |
125 128 129
|
3eqtr4d |
|
131 |
|
fvres |
|
132 |
117 131
|
mp1i |
|
133 |
|
log1 |
|
134 |
132 133
|
eqtrdi |
|
135 |
119 130 134
|
3brtr3d |
|
136 |
78
|
mptex |
|
137 |
|
climres |
|
138 |
18 136 137
|
sylancl |
|
139 |
135 138
|
mpbid |
|
140 |
15 139
|
rexlimddv |
|
141 |
12 88
|
addcld |
|
142 |
8
|
dmgmn0 |
|
143 |
141 142
|
logcld |
|
144 |
78
|
mptex |
|
145 |
144
|
a1i |
|
146 |
82
|
fvoveq1d |
|
147 |
|
eqid |
|
148 |
|
fvex |
|
149 |
146 147 148
|
fvmpt |
|
150 |
149
|
adantl |
|
151 |
98 94
|
addcld |
|
152 |
2
|
adantr |
|
153 |
152 96
|
dmgmdivn0 |
|
154 |
151 153
|
logcld |
|
155 |
150 154
|
eqeltrd |
|
156 |
146
|
oveq2d |
|
157 |
|
eqid |
|
158 |
|
ovex |
|
159 |
156 157 158
|
fvmpt |
|
160 |
159
|
adantl |
|
161 |
150
|
oveq2d |
|
162 |
160 161
|
eqtr4d |
|
163 |
3 4 140 143 145 155 162
|
climsubc2 |
|
164 |
143
|
subid1d |
|
165 |
163 164
|
breqtrd |
|
166 |
|
elfznn |
|
167 |
166
|
adantl |
|
168 |
|
oveq1 |
|
169 |
|
id |
|
170 |
168 169
|
oveq12d |
|
171 |
170
|
fveq2d |
|
172 |
171
|
oveq2d |
|
173 |
|
oveq2 |
|
174 |
173
|
fvoveq1d |
|
175 |
172 174
|
oveq12d |
|
176 |
|
ovex |
|
177 |
175 5 176
|
fvmpt |
|
178 |
167 177
|
syl |
|
179 |
92 3
|
eleqtrdi |
|
180 |
12
|
ad2antrr |
|
181 |
|
1cnd |
|
182 |
180 181
|
addcld |
|
183 |
167
|
peano2nnd |
|
184 |
183
|
nnrpd |
|
185 |
167
|
nnrpd |
|
186 |
184 185
|
rpdivcld |
|
187 |
186
|
relogcld |
|
188 |
187
|
recnd |
|
189 |
182 188
|
mulcld |
|
190 |
167
|
nncnd |
|
191 |
167
|
nnne0d |
|
192 |
182 190 191
|
divcld |
|
193 |
192 181
|
addcld |
|
194 |
8
|
ad2antrr |
|
195 |
194 167
|
dmgmdivn0 |
|
196 |
193 195
|
logcld |
|
197 |
189 196
|
subcld |
|
198 |
178 179 197
|
fsumser |
|
199 |
|
fzfid |
|
200 |
199 197
|
fsumcl |
|
201 |
198 200
|
eqeltrrd |
|
202 |
143
|
adantr |
|
203 |
202 154
|
subcld |
|
204 |
160 203
|
eqeltrd |
|
205 |
180 188
|
mulcld |
|
206 |
180 190 191
|
divcld |
|
207 |
206 181
|
addcld |
|
208 |
2
|
ad2antrr |
|
209 |
208 167
|
dmgmdivn0 |
|
210 |
207 209
|
logcld |
|
211 |
205 210
|
subcld |
|
212 |
199 211
|
fsumcl |
|
213 |
200 212
|
nncand |
|
214 |
189 196 205 210
|
sub4d |
|
215 |
180 181
|
pncan2d |
|
216 |
215
|
oveq1d |
|
217 |
182 180 188
|
subdird |
|
218 |
188
|
mulid2d |
|
219 |
216 217 218
|
3eqtr3d |
|
220 |
219
|
oveq1d |
|
221 |
188 196 210
|
subsubd |
|
222 |
188 196
|
subcld |
|
223 |
222 210
|
addcomd |
|
224 |
210 196 188
|
subsub2d |
|
225 |
183
|
nncnd |
|
226 |
180 225
|
addcld |
|
227 |
183
|
nnnn0d |
|
228 |
|
dmgmaddn0 |
|
229 |
208 227 228
|
syl2anc |
|
230 |
226 229
|
logcld |
|
231 |
184
|
relogcld |
|
232 |
231
|
recnd |
|
233 |
185
|
relogcld |
|
234 |
233
|
recnd |
|
235 |
230 232 234
|
nnncan2d |
|
236 |
182 190 190 191
|
divdird |
|
237 |
180 190 181
|
add32d |
|
238 |
180 190 181
|
addassd |
|
239 |
237 238
|
eqtr3d |
|
240 |
239
|
oveq1d |
|
241 |
190 191
|
dividd |
|
242 |
241
|
oveq2d |
|
243 |
236 240 242
|
3eqtr3rd |
|
244 |
243
|
fveq2d |
|
245 |
|
logdiv2 |
|
246 |
226 229 185 245
|
syl3anc |
|
247 |
244 246
|
eqtrd |
|
248 |
184 185
|
relogdivd |
|
249 |
247 248
|
oveq12d |
|
250 |
183
|
nnne0d |
|
251 |
180 225 225 250
|
divdird |
|
252 |
225 250
|
dividd |
|
253 |
252
|
oveq2d |
|
254 |
251 253
|
eqtr2d |
|
255 |
254
|
fveq2d |
|
256 |
|
logdiv2 |
|
257 |
226 229 184 256
|
syl3anc |
|
258 |
255 257
|
eqtrd |
|
259 |
235 249 258
|
3eqtr4d |
|
260 |
259
|
oveq2d |
|
261 |
224 260
|
eqtr3d |
|
262 |
221 223 261
|
3eqtrd |
|
263 |
214 220 262
|
3eqtrd |
|
264 |
263
|
sumeq2dv |
|
265 |
199 197 211
|
fsumsub |
|
266 |
|
oveq2 |
|
267 |
266
|
fvoveq1d |
|
268 |
|
oveq2 |
|
269 |
268
|
fvoveq1d |
|
270 |
|
oveq2 |
|
271 |
270
|
fvoveq1d |
|
272 |
|
oveq2 |
|
273 |
272
|
fvoveq1d |
|
274 |
92
|
nnzd |
|
275 |
96 3
|
eleqtrdi |
|
276 |
12
|
ad2antrr |
|
277 |
|
elfznn |
|
278 |
277
|
adantl |
|
279 |
278
|
nncnd |
|
280 |
278
|
nnne0d |
|
281 |
276 279 280
|
divcld |
|
282 |
|
1cnd |
|
283 |
281 282
|
addcld |
|
284 |
2
|
ad2antrr |
|
285 |
284 278
|
dmgmdivn0 |
|
286 |
283 285
|
logcld |
|
287 |
267 269 271 273 274 275 286
|
telfsum |
|
288 |
91
|
div1d |
|
289 |
288
|
fvoveq1d |
|
290 |
289
|
oveq1d |
|
291 |
287 290
|
eqtrd |
|
292 |
264 265 291
|
3eqtr3d |
|
293 |
292
|
oveq2d |
|
294 |
213 293
|
eqtr3d |
|
295 |
171
|
oveq2d |
|
296 |
|
oveq2 |
|
297 |
296
|
fvoveq1d |
|
298 |
295 297
|
oveq12d |
|
299 |
|
ovex |
|
300 |
298 1 299
|
fvmpt |
|
301 |
167 300
|
syl |
|
302 |
301 179 211
|
fsumser |
|
303 |
160
|
eqcomd |
|
304 |
198 303
|
oveq12d |
|
305 |
294 302 304
|
3eqtr3d |
|
306 |
3 4 9 11 165 201 204 305
|
climsub |
|
307 |
|
lgamcl |
|
308 |
8 307
|
syl |
|
309 |
308 143
|
pncand |
|
310 |
306 309
|
breqtrd |
|