Step |
Hyp |
Ref |
Expression |
1 |
|
perfectlem.1 |
|
2 |
|
perfectlem.2 |
|
3 |
|
perfectlem.3 |
|
4 |
|
perfectlem.4 |
|
5 |
|
1red |
|
6 |
1 2 3 4
|
perfectlem1 |
|
7 |
6
|
simp3d |
|
8 |
7
|
nnred |
|
9 |
2
|
nnred |
|
10 |
7
|
nnge1d |
|
11 |
|
2cn |
|
12 |
|
exp1 |
|
13 |
11 12
|
ax-mp |
|
14 |
|
df-2 |
|
15 |
13 14
|
eqtri |
|
16 |
|
2re |
|
17 |
16
|
a1i |
|
18 |
|
1zzd |
|
19 |
1
|
peano2nnd |
|
20 |
19
|
nnzd |
|
21 |
|
1lt2 |
|
22 |
21
|
a1i |
|
23 |
|
1re |
|
24 |
1
|
nnrpd |
|
25 |
|
ltaddrp |
|
26 |
23 24 25
|
sylancr |
|
27 |
|
ax-1cn |
|
28 |
1
|
nncnd |
|
29 |
|
addcom |
|
30 |
27 28 29
|
sylancr |
|
31 |
26 30
|
breqtrd |
|
32 |
|
ltexp2a |
|
33 |
17 18 20 22 31 32
|
syl32anc |
|
34 |
15 33
|
eqbrtrrid |
|
35 |
6
|
simp1d |
|
36 |
35
|
nnred |
|
37 |
5 5 36
|
ltaddsubd |
|
38 |
34 37
|
mpbid |
|
39 |
|
0lt1 |
|
40 |
39
|
a1i |
|
41 |
|
peano2rem |
|
42 |
36 41
|
syl |
|
43 |
|
expgt1 |
|
44 |
16 19 22 43
|
mp3an2i |
|
45 |
|
posdif |
|
46 |
23 36 45
|
sylancr |
|
47 |
44 46
|
mpbid |
|
48 |
2
|
nngt0d |
|
49 |
|
ltdiv2 |
|
50 |
5 40 42 47 9 48 49
|
syl222anc |
|
51 |
38 50
|
mpbid |
|
52 |
2
|
nncnd |
|
53 |
52
|
div1d |
|
54 |
51 53
|
breqtrd |
|
55 |
5 8 9 10 54
|
lelttrd |
|
56 |
|
eluz2b2 |
|
57 |
2 55 56
|
sylanbrc |
|
58 |
|
fzfid |
|
59 |
|
dvdsssfz1 |
|
60 |
2 59
|
syl |
|
61 |
58 60
|
ssfid |
|
62 |
61
|
ad2antrr |
|
63 |
|
ssrab2 |
|
64 |
63
|
a1i |
|
65 |
64
|
sselda |
|
66 |
65
|
nnred |
|
67 |
65
|
nnnn0d |
|
68 |
67
|
nn0ge0d |
|
69 |
|
df-tp |
|
70 |
7 2
|
prssd |
|
71 |
70
|
ad2antrr |
|
72 |
|
simplrl |
|
73 |
72
|
snssd |
|
74 |
71 73
|
unssd |
|
75 |
69 74
|
eqsstrid |
|
76 |
6
|
simp2d |
|
77 |
76
|
nnzd |
|
78 |
7
|
nnzd |
|
79 |
|
dvdsmul2 |
|
80 |
77 78 79
|
syl2anc |
|
81 |
76
|
nncnd |
|
82 |
76
|
nnne0d |
|
83 |
52 81 82
|
divcan2d |
|
84 |
80 83
|
breqtrd |
|
85 |
|
breq1 |
|
86 |
84 85
|
syl5ibrcom |
|
87 |
86
|
ad2antrr |
|
88 |
2
|
nnzd |
|
89 |
|
iddvds |
|
90 |
88 89
|
syl |
|
91 |
|
breq1 |
|
92 |
90 91
|
syl5ibrcom |
|
93 |
92
|
ad2antrr |
|
94 |
|
simplrr |
|
95 |
|
breq1 |
|
96 |
94 95
|
syl5ibrcom |
|
97 |
87 93 96
|
3jaod |
|
98 |
|
eltpi |
|
99 |
97 98
|
impel |
|
100 |
75 99
|
ssrabdv |
|
101 |
62 66 68 100
|
fsumless |
|
102 |
|
simpr |
|
103 |
|
disjsn |
|
104 |
102 103
|
sylibr |
|
105 |
69
|
a1i |
|
106 |
|
tpfi |
|
107 |
106
|
a1i |
|
108 |
75
|
sselda |
|
109 |
108
|
nncnd |
|
110 |
104 105 107 109
|
fsumsplit |
|
111 |
7
|
nncnd |
|
112 |
|
id |
|
113 |
112
|
sumsn |
|
114 |
7 111 113
|
syl2anc |
|
115 |
|
id |
|
116 |
115
|
sumsn |
|
117 |
2 52 116
|
syl2anc |
|
118 |
114 117
|
oveq12d |
|
119 |
|
incom |
|
120 |
8 54
|
gtned |
|
121 |
|
disjsn2 |
|
122 |
120 121
|
syl |
|
123 |
119 122
|
syl5eqr |
|
124 |
|
df-pr |
|
125 |
124
|
a1i |
|
126 |
|
prfi |
|
127 |
126
|
a1i |
|
128 |
70
|
sselda |
|
129 |
128
|
nncnd |
|
130 |
123 125 127 129
|
fsumsplit |
|
131 |
81 52
|
mulcld |
|
132 |
52 131 81 82
|
divdird |
|
133 |
35
|
nncnd |
|
134 |
|
1cnd |
|
135 |
133 134 52
|
subdird |
|
136 |
52
|
mulid2d |
|
137 |
136
|
oveq2d |
|
138 |
135 137
|
eqtrd |
|
139 |
138
|
oveq2d |
|
140 |
133 52
|
mulcld |
|
141 |
52 140
|
pncan3d |
|
142 |
139 141
|
eqtrd |
|
143 |
142
|
oveq1d |
|
144 |
133 52 81 82
|
divassd |
|
145 |
143 144
|
eqtrd |
|
146 |
52 81 82
|
divcan3d |
|
147 |
146
|
oveq2d |
|
148 |
132 145 147
|
3eqtr3d |
|
149 |
118 130 148
|
3eqtr4d |
|
150 |
149
|
ad2antrr |
|
151 |
72
|
nncnd |
|
152 |
|
id |
|
153 |
152
|
sumsn |
|
154 |
151 151 153
|
syl2anc |
|
155 |
150 154
|
oveq12d |
|
156 |
110 155
|
eqtrd |
|
157 |
1
|
nnnn0d |
|
158 |
|
expp1 |
|
159 |
11 157 158
|
sylancr |
|
160 |
|
2nn |
|
161 |
|
nnexpcl |
|
162 |
160 157 161
|
sylancr |
|
163 |
162
|
nncnd |
|
164 |
|
mulcom |
|
165 |
163 11 164
|
sylancl |
|
166 |
159 165
|
eqtrd |
|
167 |
166
|
oveq1d |
|
168 |
|
2cnd |
|
169 |
168 163 52
|
mulassd |
|
170 |
|
2prm |
|
171 |
|
coprm |
|
172 |
170 88 171
|
sylancr |
|
173 |
3 172
|
mpbid |
|
174 |
|
2z |
|
175 |
|
rpexp1i |
|
176 |
174 88 157 175
|
mp3an2i |
|
177 |
173 176
|
mpd |
|
178 |
|
sgmmul |
|
179 |
134 162 2 177 178
|
syl13anc |
|
180 |
|
pncan |
|
181 |
28 27 180
|
sylancl |
|
182 |
181
|
oveq2d |
|
183 |
182
|
oveq2d |
|
184 |
|
1sgm2ppw |
|
185 |
19 184
|
syl |
|
186 |
183 185
|
eqtr3d |
|
187 |
186
|
oveq1d |
|
188 |
179 4 187
|
3eqtr3d |
|
189 |
167 169 188
|
3eqtrd |
|
190 |
189
|
oveq1d |
|
191 |
|
1nn0 |
|
192 |
|
sgmnncl |
|
193 |
191 2 192
|
sylancr |
|
194 |
193
|
nncnd |
|
195 |
194 81 82
|
divcan3d |
|
196 |
190 144 195
|
3eqtr3d |
|
197 |
|
sgmval |
|
198 |
27 2 197
|
sylancr |
|
199 |
|
simpr |
|
200 |
63 199
|
sseldi |
|
201 |
200
|
nncnd |
|
202 |
201
|
cxp1d |
|
203 |
202
|
sumeq2dv |
|
204 |
196 198 203
|
3eqtrrd |
|
205 |
204
|
ad2antrr |
|
206 |
101 156 205
|
3brtr3d |
|
207 |
36 8
|
remulcld |
|
208 |
207
|
ad2antrr |
|
209 |
72
|
nnrpd |
|
210 |
208 209
|
ltaddrpd |
|
211 |
72
|
nnred |
|
212 |
208 211
|
readdcld |
|
213 |
208 212
|
ltnled |
|
214 |
210 213
|
mpbid |
|
215 |
206 214
|
condan |
|
216 |
|
elpri |
|
217 |
215 216
|
syl |
|
218 |
217
|
expr |
|
219 |
218
|
ralrimiva |
|
220 |
5 55
|
gtned |
|
221 |
220
|
necomd |
|
222 |
|
1dvds |
|
223 |
88 222
|
syl |
|
224 |
|
breq1 |
|
225 |
|
eqeq1 |
|
226 |
|
eqeq1 |
|
227 |
225 226
|
orbi12d |
|
228 |
224 227
|
imbi12d |
|
229 |
|
1nn |
|
230 |
229
|
a1i |
|
231 |
228 219 230
|
rspcdva |
|
232 |
223 231
|
mpd |
|
233 |
232
|
ord |
|
234 |
233
|
necon1ad |
|
235 |
221 234
|
mpd |
|
236 |
235
|
eqeq2d |
|
237 |
236
|
orbi1d |
|
238 |
237
|
imbi2d |
|
239 |
238
|
ralbidv |
|
240 |
219 239
|
mpbird |
|
241 |
|
isprm2 |
|
242 |
57 240 241
|
sylanbrc |
|
243 |
207
|
ltp1d |
|
244 |
|
peano2re |
|
245 |
207 244
|
syl |
|
246 |
207 245
|
ltnled |
|
247 |
243 246
|
mpbid |
|
248 |
200
|
nnred |
|
249 |
200
|
nnnn0d |
|
250 |
249
|
nn0ge0d |
|
251 |
|
df-tp |
|
252 |
|
snssi |
|
253 |
229 252
|
mp1i |
|
254 |
70 253
|
unssd |
|
255 |
251 254
|
eqsstrid |
|
256 |
|
breq1 |
|
257 |
223 256
|
syl5ibrcom |
|
258 |
86 92 257
|
3jaod |
|
259 |
|
eltpi |
|
260 |
258 259
|
impel |
|
261 |
255 260
|
ssrabdv |
|
262 |
61 248 250 261
|
fsumless |
|
263 |
262
|
adantr |
|
264 |
52 81 82
|
diveq1ad |
|
265 |
264
|
necon3bid |
|
266 |
265
|
biimpar |
|
267 |
266
|
necomd |
|
268 |
221
|
adantr |
|
269 |
267 268
|
nelprd |
|
270 |
|
disjsn |
|
271 |
269 270
|
sylibr |
|
272 |
251
|
a1i |
|
273 |
|
tpfi |
|
274 |
273
|
a1i |
|
275 |
255
|
adantr |
|
276 |
275
|
sselda |
|
277 |
276
|
nncnd |
|
278 |
271 272 274 277
|
fsumsplit |
|
279 |
|
id |
|
280 |
279
|
sumsn |
|
281 |
5 27 280
|
sylancl |
|
282 |
149 281
|
oveq12d |
|
283 |
282
|
adantr |
|
284 |
278 283
|
eqtrd |
|
285 |
204
|
adantr |
|
286 |
263 284 285
|
3brtr3d |
|
287 |
286
|
ex |
|
288 |
287
|
necon1bd |
|
289 |
247 288
|
mpd |
|
290 |
242 289
|
jca |
|