Step |
Hyp |
Ref |
Expression |
1 |
|
elnn1uz2 |
|
2 |
|
1t1e1 |
|
3 |
2
|
eqcomi |
|
4 |
|
simpl |
|
5 |
|
oveq2 |
|
6 |
5
|
eqcoms |
|
7 |
|
fveq2 |
|
8 |
|
blen1 |
|
9 |
7 8
|
eqtrdi |
|
10 |
9
|
oveq2d |
|
11 |
|
fzo01 |
|
12 |
10 11
|
eqtrdi |
|
13 |
6 12
|
sylan9eqr |
|
14 |
13
|
sumeq1d |
|
15 |
|
oveq2 |
|
16 |
15
|
oveq1d |
|
17 |
16
|
sumeq2sdv |
|
18 |
|
c0ex |
|
19 |
|
ax-1cn |
|
20 |
19 19
|
mulcli |
|
21 |
|
oveq1 |
|
22 |
|
1ex |
|
23 |
22
|
prid2 |
|
24 |
|
0dig2pr01 |
|
25 |
23 24
|
ax-mp |
|
26 |
21 25
|
eqtrdi |
|
27 |
|
oveq2 |
|
28 |
|
2cn |
|
29 |
|
exp0 |
|
30 |
28 29
|
ax-mp |
|
31 |
27 30
|
eqtrdi |
|
32 |
26 31
|
oveq12d |
|
33 |
32
|
sumsn |
|
34 |
18 20 33
|
mp2an |
|
35 |
17 34
|
eqtrdi |
|
36 |
35
|
adantr |
|
37 |
14 36
|
eqtrd |
|
38 |
3 4 37
|
3eqtr4a |
|
39 |
38
|
ex |
|
40 |
39
|
a1d |
|
41 |
40
|
2a1d |
|
42 |
|
eluzge2nn0 |
|
43 |
|
nn0ob |
|
44 |
43
|
bicomd |
|
45 |
42 44
|
syl |
|
46 |
|
blennngt2o2 |
|
47 |
46
|
ex |
|
48 |
45 47
|
sylbid |
|
49 |
48
|
imp |
|
50 |
|
fveqeq2 |
|
51 |
|
id |
|
52 |
|
oveq2 |
|
53 |
52
|
oveq1d |
|
54 |
53
|
sumeq2sdv |
|
55 |
51 54
|
eqeq12d |
|
56 |
50 55
|
imbi12d |
|
57 |
56
|
rspcva |
|
58 |
|
eqeq1 |
|
59 |
|
nncn |
|
60 |
59
|
ad2antll |
|
61 |
|
blennn0elnn |
|
62 |
61
|
nncnd |
|
63 |
62
|
adantr |
|
64 |
63
|
ad2antrl |
|
65 |
|
1cnd |
|
66 |
60 64 65
|
addcan2d |
|
67 |
|
eqcom |
|
68 |
|
nnz |
|
69 |
68
|
ad2antll |
|
70 |
|
fzval3 |
|
71 |
69 70
|
syl |
|
72 |
71
|
eqcomd |
|
73 |
72
|
sumeq1d |
|
74 |
|
nnnn0 |
|
75 |
|
elnn0uz |
|
76 |
74 75
|
sylib |
|
77 |
76
|
ad2antll |
|
78 |
|
2nn |
|
79 |
78
|
a1i |
|
80 |
|
elfzelz |
|
81 |
80
|
adantl |
|
82 |
|
nn0rp0 |
|
83 |
42 82
|
syl |
|
84 |
83
|
adantl |
|
85 |
84
|
adantr |
|
86 |
|
digvalnn0 |
|
87 |
79 81 85 86
|
syl3anc |
|
88 |
87
|
ex |
|
89 |
88
|
ad2antrl |
|
90 |
89
|
imp |
|
91 |
90
|
nn0cnd |
|
92 |
|
2nn0 |
|
93 |
92
|
a1i |
|
94 |
|
elfznn0 |
|
95 |
93 94
|
nn0expcld |
|
96 |
95
|
nn0cnd |
|
97 |
96
|
adantl |
|
98 |
91 97
|
mulcld |
|
99 |
|
oveq1 |
|
100 |
99 27
|
oveq12d |
|
101 |
30
|
oveq2i |
|
102 |
100 101
|
eqtrdi |
|
103 |
77 98 102
|
fsum1p |
|
104 |
42
|
adantl |
|
105 |
42 43
|
syl |
|
106 |
105
|
biimparc |
|
107 |
|
0dig2nn0o |
|
108 |
104 106 107
|
syl2anc |
|
109 |
108
|
ad2antrl |
|
110 |
109
|
oveq1d |
|
111 |
110 2
|
eqtrdi |
|
112 |
|
1z |
|
113 |
112
|
a1i |
|
114 |
|
0p1e1 |
|
115 |
114 112
|
eqeltri |
|
116 |
115
|
a1i |
|
117 |
78
|
a1i |
|
118 |
|
elfzelz |
|
119 |
118
|
adantl |
|
120 |
42
|
adantr |
|
121 |
120 82
|
syl |
|
122 |
117 119 121 86
|
syl3anc |
|
123 |
122
|
ex |
|
124 |
123
|
adantl |
|
125 |
124
|
ad2antrl |
|
126 |
125
|
imp |
|
127 |
126
|
nn0cnd |
|
128 |
|
2cnd |
|
129 |
|
elfznn |
|
130 |
129
|
nnnn0d |
|
131 |
114
|
oveq1i |
|
132 |
130 131
|
eleq2s |
|
133 |
128 132
|
expcld |
|
134 |
133
|
adantl |
|
135 |
127 134
|
mulcld |
|
136 |
|
oveq1 |
|
137 |
|
oveq2 |
|
138 |
136 137
|
oveq12d |
|
139 |
113 116 69 135 138
|
fsumshftm |
|
140 |
111 139
|
oveq12d |
|
141 |
73 103 140
|
3eqtrd |
|
142 |
141
|
adantl |
|
143 |
78
|
a1i |
|
144 |
|
elfzoelz |
|
145 |
144
|
adantl |
|
146 |
|
nn0rp0 |
|
147 |
146
|
adantr |
|
148 |
147
|
adantr |
|
149 |
|
digvalnn0 |
|
150 |
143 145 148 149
|
syl3anc |
|
151 |
150
|
nn0cnd |
|
152 |
151
|
ex |
|
153 |
152
|
ad2antrl |
|
154 |
153
|
imp |
|
155 |
92
|
a1i |
|
156 |
|
elfzonn0 |
|
157 |
155 156
|
nn0expcld |
|
158 |
157
|
nn0cnd |
|
159 |
158
|
adantl |
|
160 |
|
2cnd |
|
161 |
154 159 160
|
mulassd |
|
162 |
161
|
eqcomd |
|
163 |
162
|
sumeq2dv |
|
164 |
163
|
adantl |
|
165 |
|
0cn |
|
166 |
|
pncan1 |
|
167 |
165 166
|
ax-mp |
|
168 |
167
|
a1i |
|
169 |
168
|
oveq1d |
|
170 |
|
fzoval |
|
171 |
68 170
|
syl |
|
172 |
169 171
|
eqtr4d |
|
173 |
172
|
ad2antll |
|
174 |
|
simprlr |
|
175 |
|
elfznn0 |
|
176 |
167
|
oveq1i |
|
177 |
175 176
|
eleq2s |
|
178 |
|
dignn0flhalf |
|
179 |
174 177 178
|
syl2an |
|
180 |
|
eluzelz |
|
181 |
180
|
adantr |
|
182 |
|
nn0z |
|
183 |
|
zob |
|
184 |
180 183
|
syl |
|
185 |
182 184
|
syl5ibr |
|
186 |
185
|
imp |
|
187 |
181 186
|
jca |
|
188 |
187
|
ancoms |
|
189 |
188
|
ad2antrl |
|
190 |
189
|
adantr |
|
191 |
|
zofldiv2 |
|
192 |
190 191
|
syl |
|
193 |
192
|
oveq2d |
|
194 |
179 193
|
eqtrd |
|
195 |
|
2cnd |
|
196 |
195 177
|
expp1d |
|
197 |
196
|
adantl |
|
198 |
194 197
|
oveq12d |
|
199 |
173 198
|
sumeq12dv |
|
200 |
199
|
adantl |
|
201 |
|
oveq1 |
|
202 |
|
oveq2 |
|
203 |
201 202
|
oveq12d |
|
204 |
203
|
cbvsumv |
|
205 |
204
|
eqeq2i |
|
206 |
205
|
biimpi |
|
207 |
206
|
adantr |
|
208 |
207
|
oveq1d |
|
209 |
|
fzofi |
|
210 |
209
|
a1i |
|
211 |
|
2cnd |
|
212 |
158
|
adantl |
|
213 |
151 212
|
mulcld |
|
214 |
213
|
ex |
|
215 |
214
|
adantr |
|
216 |
215
|
ad2antll |
|
217 |
216
|
imp |
|
218 |
210 211 217
|
fsummulc1 |
|
219 |
208 218
|
eqtrd |
|
220 |
164 200 219
|
3eqtr4d |
|
221 |
220
|
oveq2d |
|
222 |
|
eluzelcn |
|
223 |
|
peano2cnm |
|
224 |
222 223
|
syl |
|
225 |
|
2cnd |
|
226 |
|
2ne0 |
|
227 |
226
|
a1i |
|
228 |
224 225 227
|
3jca |
|
229 |
228
|
adantl |
|
230 |
|
divcan1 |
|
231 |
229 230
|
syl |
|
232 |
231
|
oveq2d |
|
233 |
|
1cnd |
|
234 |
233 222
|
jca |
|
235 |
234
|
adantl |
|
236 |
|
pncan3 |
|
237 |
235 236
|
syl |
|
238 |
232 237
|
eqtrd |
|
239 |
238
|
adantr |
|
240 |
239
|
ad2antll |
|
241 |
142 221 240
|
3eqtrrd |
|
242 |
241
|
ex |
|
243 |
242
|
imim2i |
|
244 |
243
|
com13 |
|
245 |
67 244
|
syl5bi |
|
246 |
66 245
|
sylbid |
|
247 |
246
|
ex |
|
248 |
247
|
com23 |
|
249 |
58 248
|
sylbid |
|
250 |
249
|
com23 |
|
251 |
250
|
com14 |
|
252 |
251
|
exp4c |
|
253 |
252
|
com35 |
|
254 |
57 253
|
syl |
|
255 |
254
|
ex |
|
256 |
255
|
pm2.43a |
|
257 |
256
|
com25 |
|
258 |
257
|
impcom |
|
259 |
49 258
|
mpd |
|
260 |
259
|
ex |
|
261 |
41 260
|
jaoi |
|
262 |
1 261
|
sylbi |
|
263 |
262
|
imp31 |
|