Step |
Hyp |
Ref |
Expression |
1 |
|
ftalem.1 |
|
2 |
|
ftalem.2 |
|
3 |
|
ftalem.3 |
|
4 |
|
ftalem.4 |
|
5 |
|
ftalem4.5 |
|
6 |
|
ftalem4.6 |
|
7 |
|
ftalem4.7 |
|
8 |
|
ftalem4.8 |
|
9 |
|
ftalem4.9 |
|
10 |
1 2 3 4 5 6 7 8 9
|
ftalem4 |
|
11 |
10
|
simprd |
|
12 |
11
|
simp1d |
|
13 |
11
|
simp3d |
|
14 |
13
|
rpred |
|
15 |
14
|
recnd |
|
16 |
12 15
|
mulcld |
|
17 |
|
plyf |
|
18 |
3 17
|
syl |
|
19 |
18 16
|
ffvelrnd |
|
20 |
19
|
abscld |
|
21 |
|
0cn |
|
22 |
|
ffvelrn |
|
23 |
18 21 22
|
sylancl |
|
24 |
23
|
abscld |
|
25 |
10
|
simpld |
|
26 |
25
|
simpld |
|
27 |
26
|
nnnn0d |
|
28 |
14 27
|
reexpcld |
|
29 |
24 28
|
remulcld |
|
30 |
24 29
|
resubcld |
|
31 |
|
fzfid |
|
32 |
1
|
coef3 |
|
33 |
3 32
|
syl |
|
34 |
|
peano2nn0 |
|
35 |
27 34
|
syl |
|
36 |
|
elfzuz |
|
37 |
|
eluznn0 |
|
38 |
35 36 37
|
syl2an |
|
39 |
|
ffvelrn |
|
40 |
33 38 39
|
syl2an2r |
|
41 |
16
|
adantr |
|
42 |
41 38
|
expcld |
|
43 |
40 42
|
mulcld |
|
44 |
31 43
|
fsumcl |
|
45 |
44
|
abscld |
|
46 |
30 45
|
readdcld |
|
47 |
|
fzfid |
|
48 |
|
elfznn0 |
|
49 |
33 48 39
|
syl2an |
|
50 |
|
expcl |
|
51 |
16 48 50
|
syl2an |
|
52 |
49 51
|
mulcld |
|
53 |
47 52
|
fsumcl |
|
54 |
53 44
|
abstrid |
|
55 |
1 2
|
coeid2 |
|
56 |
3 16 55
|
syl2anc |
|
57 |
26
|
nnred |
|
58 |
57
|
ltp1d |
|
59 |
|
fzdisj |
|
60 |
58 59
|
syl |
|
61 |
|
ssrab2 |
|
62 |
|
nnuz |
|
63 |
61 62
|
sseqtri |
|
64 |
|
fveq2 |
|
65 |
64
|
neeq1d |
|
66 |
4
|
nnne0d |
|
67 |
2 1
|
dgreq0 |
|
68 |
3 67
|
syl |
|
69 |
|
fveq2 |
|
70 |
|
dgr0 |
|
71 |
69 70
|
eqtrdi |
|
72 |
2 71
|
syl5eq |
|
73 |
68 72
|
syl6bir |
|
74 |
73
|
necon3d |
|
75 |
66 74
|
mpd |
|
76 |
65 4 75
|
elrabd |
|
77 |
|
infssuzle |
|
78 |
63 76 77
|
sylancr |
|
79 |
6 78
|
eqbrtrid |
|
80 |
|
nn0uz |
|
81 |
27 80
|
eleqtrdi |
|
82 |
4
|
nnzd |
|
83 |
|
elfz5 |
|
84 |
81 82 83
|
syl2anc |
|
85 |
79 84
|
mpbird |
|
86 |
|
fzsplit |
|
87 |
85 86
|
syl |
|
88 |
|
fzfid |
|
89 |
|
elfznn0 |
|
90 |
33 89 39
|
syl2an |
|
91 |
16 89 50
|
syl2an |
|
92 |
90 91
|
mulcld |
|
93 |
60 87 88 92
|
fsumsplit |
|
94 |
56 93
|
eqtrd |
|
95 |
94
|
fveq2d |
|
96 |
1
|
coefv0 |
|
97 |
3 96
|
syl |
|
98 |
97
|
eqcomd |
|
99 |
16
|
exp0d |
|
100 |
98 99
|
oveq12d |
|
101 |
23
|
mulid1d |
|
102 |
100 101
|
eqtrd |
|
103 |
|
1e0p1 |
|
104 |
103
|
oveq1i |
|
105 |
104
|
sumeq1i |
|
106 |
26 62
|
eleqtrdi |
|
107 |
|
elfznn |
|
108 |
107
|
nnnn0d |
|
109 |
33 108 39
|
syl2an |
|
110 |
16 108 50
|
syl2an |
|
111 |
109 110
|
mulcld |
|
112 |
|
fveq2 |
|
113 |
|
oveq2 |
|
114 |
112 113
|
oveq12d |
|
115 |
106 111 114
|
fsumm1 |
|
116 |
105 115
|
syl5eqr |
|
117 |
|
elfznn |
|
118 |
117
|
adantl |
|
119 |
118
|
nnred |
|
120 |
57
|
adantr |
|
121 |
|
peano2rem |
|
122 |
120 121
|
syl |
|
123 |
|
elfzle2 |
|
124 |
123
|
adantl |
|
125 |
120
|
ltm1d |
|
126 |
119 122 120 124 125
|
lelttrd |
|
127 |
119 120
|
ltnled |
|
128 |
126 127
|
mpbid |
|
129 |
|
infssuzle |
|
130 |
6 129
|
eqbrtrid |
|
131 |
63 130
|
mpan |
|
132 |
128 131
|
nsyl |
|
133 |
|
fveq2 |
|
134 |
133
|
neeq1d |
|
135 |
134
|
elrab3 |
|
136 |
118 135
|
syl |
|
137 |
136
|
necon2bbid |
|
138 |
132 137
|
mpbird |
|
139 |
138
|
oveq1d |
|
140 |
117
|
nnnn0d |
|
141 |
16 140 50
|
syl2an |
|
142 |
141
|
mul02d |
|
143 |
139 142
|
eqtrd |
|
144 |
143
|
sumeq2dv |
|
145 |
|
fzfi |
|
146 |
145
|
olci |
|
147 |
|
sumz |
|
148 |
146 147
|
ax-mp |
|
149 |
144 148
|
eqtrdi |
|
150 |
12 15 27
|
mulexpd |
|
151 |
150
|
oveq2d |
|
152 |
33 27
|
ffvelrnd |
|
153 |
12 27
|
expcld |
|
154 |
28
|
recnd |
|
155 |
152 153 154
|
mulassd |
|
156 |
151 155
|
eqtr4d |
|
157 |
7
|
oveq1i |
|
158 |
57
|
recnd |
|
159 |
26
|
nnne0d |
|
160 |
158 159
|
recid2d |
|
161 |
160
|
oveq2d |
|
162 |
25
|
simprd |
|
163 |
23 152 162
|
divcld |
|
164 |
163
|
negcld |
|
165 |
26
|
nnrecred |
|
166 |
165
|
recnd |
|
167 |
164 166 27
|
cxpmul2d |
|
168 |
164
|
cxp1d |
|
169 |
161 167 168
|
3eqtr3d |
|
170 |
157 169
|
syl5eq |
|
171 |
170
|
oveq2d |
|
172 |
152 163
|
mulneg2d |
|
173 |
23 152 162
|
divcan2d |
|
174 |
173
|
negeqd |
|
175 |
171 172 174
|
3eqtrd |
|
176 |
175
|
oveq1d |
|
177 |
23 154
|
mulneg1d |
|
178 |
156 176 177
|
3eqtrd |
|
179 |
149 178
|
oveq12d |
|
180 |
23 154
|
mulcld |
|
181 |
180
|
negcld |
|
182 |
181
|
addid2d |
|
183 |
116 179 182
|
3eqtrd |
|
184 |
102 183
|
oveq12d |
|
185 |
|
fveq2 |
|
186 |
|
oveq2 |
|
187 |
185 186
|
oveq12d |
|
188 |
81 52 187
|
fsum1p |
|
189 |
101
|
oveq1d |
|
190 |
|
1cnd |
|
191 |
23 190 154
|
subdid |
|
192 |
23 180
|
negsubd |
|
193 |
189 191 192
|
3eqtr4d |
|
194 |
184 188 193
|
3eqtr4d |
|
195 |
194
|
fveq2d |
|
196 |
|
1re |
|
197 |
|
resubcl |
|
198 |
196 28 197
|
sylancr |
|
199 |
198
|
recnd |
|
200 |
23 199
|
absmuld |
|
201 |
13
|
rpge0d |
|
202 |
11
|
simp2d |
|
203 |
202
|
rpred |
|
204 |
|
min1 |
|
205 |
196 203 204
|
sylancr |
|
206 |
9 205
|
eqbrtrid |
|
207 |
|
exple1 |
|
208 |
14 201 206 27 207
|
syl31anc |
|
209 |
|
subge0 |
|
210 |
196 28 209
|
sylancr |
|
211 |
208 210
|
mpbird |
|
212 |
198 211
|
absidd |
|
213 |
212
|
oveq2d |
|
214 |
24
|
recnd |
|
215 |
214 190 154
|
subdid |
|
216 |
214
|
mulid1d |
|
217 |
216
|
oveq1d |
|
218 |
213 215 217
|
3eqtrd |
|
219 |
195 200 218
|
3eqtrrd |
|
220 |
219
|
oveq1d |
|
221 |
54 95 220
|
3brtr4d |
|
222 |
43
|
abscld |
|
223 |
31 222
|
fsumrecl |
|
224 |
31 43
|
fsumabs |
|
225 |
|
expcl |
|
226 |
12 38 225
|
syl2an2r |
|
227 |
40 226
|
mulcld |
|
228 |
227
|
abscld |
|
229 |
31 228
|
fsumrecl |
|
230 |
14 35
|
reexpcld |
|
231 |
229 230
|
remulcld |
|
232 |
230
|
adantr |
|
233 |
228 232
|
remulcld |
|
234 |
12
|
adantr |
|
235 |
15
|
adantr |
|
236 |
234 235 38
|
mulexpd |
|
237 |
236
|
oveq2d |
|
238 |
14
|
adantr |
|
239 |
238 38
|
reexpcld |
|
240 |
239
|
recnd |
|
241 |
40 226 240
|
mulassd |
|
242 |
237 241
|
eqtr4d |
|
243 |
242
|
fveq2d |
|
244 |
227 240
|
absmuld |
|
245 |
|
elfzelz |
|
246 |
|
rpexpcl |
|
247 |
13 245 246
|
syl2an |
|
248 |
247
|
rpge0d |
|
249 |
239 248
|
absidd |
|
250 |
249
|
oveq2d |
|
251 |
243 244 250
|
3eqtrd |
|
252 |
227
|
absge0d |
|
253 |
35
|
adantr |
|
254 |
36
|
adantl |
|
255 |
201
|
adantr |
|
256 |
206
|
adantr |
|
257 |
238 253 254 255 256
|
leexp2rd |
|
258 |
239 232 228 252 257
|
lemul2ad |
|
259 |
251 258
|
eqbrtrd |
|
260 |
31 222 233 259
|
fsumle |
|
261 |
230
|
recnd |
|
262 |
228
|
recnd |
|
263 |
31 261 262
|
fsummulc1 |
|
264 |
260 263
|
breqtrrd |
|
265 |
15 27
|
expp1d |
|
266 |
154 15
|
mulcomd |
|
267 |
265 266
|
eqtrd |
|
268 |
267
|
oveq2d |
|
269 |
229
|
recnd |
|
270 |
269 15 154
|
mulassd |
|
271 |
268 270
|
eqtr4d |
|
272 |
229 14
|
remulcld |
|
273 |
|
nnssz |
|
274 |
61 273
|
sstri |
|
275 |
76
|
ne0d |
|
276 |
|
infssuzcl |
|
277 |
63 275 276
|
sylancr |
|
278 |
6 277
|
eqeltrid |
|
279 |
274 278
|
sseldi |
|
280 |
13 279
|
rpexpcld |
|
281 |
|
peano2re |
|
282 |
229 281
|
syl |
|
283 |
282 14
|
remulcld |
|
284 |
229
|
ltp1d |
|
285 |
229 282 13 284
|
ltmul1dd |
|
286 |
|
min2 |
|
287 |
196 203 286
|
sylancr |
|
288 |
9 287
|
eqbrtrid |
|
289 |
288 8
|
breqtrdi |
|
290 |
|
0red |
|
291 |
31 228 252
|
fsumge0 |
|
292 |
290 229 282 291 284
|
lelttrd |
|
293 |
|
lemuldiv2 |
|
294 |
14 24 282 292 293
|
syl112anc |
|
295 |
289 294
|
mpbird |
|
296 |
272 283 24 285 295
|
ltletrd |
|
297 |
272 24 280 296
|
ltmul1dd |
|
298 |
271 297
|
eqbrtrd |
|
299 |
223 231 29 264 298
|
lelttrd |
|
300 |
45 223 29 224 299
|
lelttrd |
|
301 |
45 29 24 300
|
ltsub2dd |
|
302 |
30 45 24
|
ltaddsubd |
|
303 |
301 302
|
mpbird |
|
304 |
20 46 24 221 303
|
lelttrd |
|
305 |
|
2fveq3 |
|
306 |
305
|
breq1d |
|
307 |
306
|
rspcev |
|
308 |
16 304 307
|
syl2anc |
|