Step |
Hyp |
Ref |
Expression |
1 |
|
fzfid |
|
2 |
|
rpcn |
|
3 |
2
|
adantl |
|
4 |
|
rpdivcl |
|
5 |
4
|
adantlr |
|
6 |
5
|
relogcld |
|
7 |
|
elfznn0 |
|
8 |
|
reexpcl |
|
9 |
6 7 8
|
syl2an |
|
10 |
7
|
adantl |
|
11 |
10
|
faccld |
|
12 |
9 11
|
nndivred |
|
13 |
12
|
recnd |
|
14 |
1 3 13
|
fsummulc2 |
|
15 |
|
simplr |
|
16 |
|
nn0uz |
|
17 |
15 16
|
eleqtrdi |
|
18 |
3
|
adantr |
|
19 |
18 13
|
mulcld |
|
20 |
|
oveq2 |
|
21 |
|
fveq2 |
|
22 |
|
fac0 |
|
23 |
21 22
|
eqtrdi |
|
24 |
20 23
|
oveq12d |
|
25 |
24
|
oveq2d |
|
26 |
17 19 25
|
fsum1p |
|
27 |
6
|
recnd |
|
28 |
27
|
exp0d |
|
29 |
28
|
oveq1d |
|
30 |
|
1div1e1 |
|
31 |
29 30
|
eqtrdi |
|
32 |
31
|
oveq2d |
|
33 |
3
|
mulid1d |
|
34 |
32 33
|
eqtrd |
|
35 |
|
1zzd |
|
36 |
|
nn0z |
|
37 |
36
|
ad2antlr |
|
38 |
|
fz1ssfz0 |
|
39 |
38
|
sseli |
|
40 |
39 19
|
sylan2 |
|
41 |
|
oveq2 |
|
42 |
|
fveq2 |
|
43 |
41 42
|
oveq12d |
|
44 |
43
|
oveq2d |
|
45 |
35 35 37 40 44
|
fsumshftm |
|
46 |
|
0p1e1 |
|
47 |
46
|
oveq1i |
|
48 |
47
|
sumeq1i |
|
49 |
48
|
a1i |
|
50 |
|
1m1e0 |
|
51 |
50
|
oveq1i |
|
52 |
|
fzoval |
|
53 |
37 52
|
syl |
|
54 |
51 53
|
syl5eqr |
|
55 |
54
|
sumeq1d |
|
56 |
45 49 55
|
3eqtr4d |
|
57 |
34 56
|
oveq12d |
|
58 |
14 26 57
|
3eqtrd |
|
59 |
58
|
mpteq2dva |
|
60 |
59
|
oveq2d |
|
61 |
|
reelprrecn |
|
62 |
61
|
a1i |
|
63 |
|
1cnd |
|
64 |
|
recn |
|
65 |
64
|
adantl |
|
66 |
|
1cnd |
|
67 |
62
|
dvmptid |
|
68 |
|
rpssre |
|
69 |
68
|
a1i |
|
70 |
|
eqid |
|
71 |
70
|
tgioo2 |
|
72 |
|
ioorp |
|
73 |
|
iooretop |
|
74 |
72 73
|
eqeltrri |
|
75 |
74
|
a1i |
|
76 |
62 65 66 67 69 71 70 75
|
dvmptres |
|
77 |
|
fzofi |
|
78 |
77
|
a1i |
|
79 |
3
|
adantr |
|
80 |
|
elfzonn0 |
|
81 |
|
peano2nn0 |
|
82 |
80 81
|
syl |
|
83 |
|
reexpcl |
|
84 |
6 82 83
|
syl2an |
|
85 |
82
|
adantl |
|
86 |
85
|
faccld |
|
87 |
84 86
|
nndivred |
|
88 |
87
|
recnd |
|
89 |
79 88
|
mulcld |
|
90 |
78 89
|
fsumcl |
|
91 |
6 15
|
reexpcld |
|
92 |
|
faccl |
|
93 |
92
|
ad2antlr |
|
94 |
91 93
|
nndivred |
|
95 |
94
|
recnd |
|
96 |
|
ax-1cn |
|
97 |
|
subcl |
|
98 |
95 96 97
|
sylancl |
|
99 |
77
|
a1i |
|
100 |
89
|
an32s |
|
101 |
100
|
3impa |
|
102 |
|
reexpcl |
|
103 |
6 80 102
|
syl2an |
|
104 |
80
|
adantl |
|
105 |
104
|
faccld |
|
106 |
103 105
|
nndivred |
|
107 |
106
|
recnd |
|
108 |
88 107
|
subcld |
|
109 |
108
|
an32s |
|
110 |
109
|
3impa |
|
111 |
61
|
a1i |
|
112 |
2
|
adantl |
|
113 |
|
1cnd |
|
114 |
76
|
adantr |
|
115 |
88
|
an32s |
|
116 |
|
negex |
|
117 |
116
|
a1i |
|
118 |
|
cnelprrecn |
|
119 |
118
|
a1i |
|
120 |
27
|
adantlr |
|
121 |
|
negex |
|
122 |
121
|
a1i |
|
123 |
|
id |
|
124 |
80
|
adantl |
|
125 |
124 81
|
syl |
|
126 |
|
expcl |
|
127 |
123 125 126
|
syl2anr |
|
128 |
125
|
faccld |
|
129 |
128
|
nncnd |
|
130 |
129
|
adantr |
|
131 |
128
|
nnne0d |
|
132 |
131
|
adantr |
|
133 |
127 130 132
|
divcld |
|
134 |
|
expcl |
|
135 |
123 124 134
|
syl2anr |
|
136 |
124
|
faccld |
|
137 |
136
|
nncnd |
|
138 |
137
|
adantr |
|
139 |
124
|
adantr |
|
140 |
139
|
faccld |
|
141 |
140
|
nnne0d |
|
142 |
135 138 141
|
divcld |
|
143 |
|
simplll |
|
144 |
|
simpr |
|
145 |
143 144
|
relogdivd |
|
146 |
145
|
mpteq2dva |
|
147 |
146
|
oveq2d |
|
148 |
|
relogcl |
|
149 |
148
|
ad2antrr |
|
150 |
149
|
recnd |
|
151 |
150
|
adantr |
|
152 |
|
0cnd |
|
153 |
150
|
adantr |
|
154 |
|
0cnd |
|
155 |
111 150
|
dvmptc |
|
156 |
68
|
a1i |
|
157 |
74
|
a1i |
|
158 |
111 153 154 155 156 71 70 157
|
dvmptres |
|
159 |
144
|
relogcld |
|
160 |
159
|
recnd |
|
161 |
144
|
rpreccld |
|
162 |
|
dvrelog |
|
163 |
|
relogf1o |
|
164 |
|
f1of |
|
165 |
163 164
|
mp1i |
|
166 |
165
|
feqmptd |
|
167 |
|
fvres |
|
168 |
167
|
mpteq2ia |
|
169 |
166 168
|
eqtrdi |
|
170 |
169
|
oveq2d |
|
171 |
162 170
|
syl5reqr |
|
172 |
111 151 152 158 160 161 171
|
dvmptsub |
|
173 |
147 172
|
eqtrd |
|
174 |
|
df-neg |
|
175 |
174
|
mpteq2i |
|
176 |
173 175
|
eqtr4di |
|
177 |
|
ovexd |
|
178 |
|
nn0p1nn |
|
179 |
124 178
|
syl |
|
180 |
|
dvexp |
|
181 |
179 180
|
syl |
|
182 |
119 127 177 181 129 131
|
dvmptdivc |
|
183 |
124
|
nn0cnd |
|
184 |
183
|
adantr |
|
185 |
|
pncan |
|
186 |
184 96 185
|
sylancl |
|
187 |
186
|
oveq2d |
|
188 |
187
|
oveq2d |
|
189 |
|
facp1 |
|
190 |
139 189
|
syl |
|
191 |
|
peano2cn |
|
192 |
184 191
|
syl |
|
193 |
138 192
|
mulcomd |
|
194 |
190 193
|
eqtrd |
|
195 |
188 194
|
oveq12d |
|
196 |
179
|
nnne0d |
|
197 |
196
|
adantr |
|
198 |
135 138 192 141 197
|
divcan5d |
|
199 |
195 198
|
eqtrd |
|
200 |
199
|
mpteq2dva |
|
201 |
182 200
|
eqtrd |
|
202 |
|
oveq1 |
|
203 |
202
|
oveq1d |
|
204 |
|
oveq1 |
|
205 |
204
|
oveq1d |
|
206 |
111 119 120 122 133 142 176 201 203 205
|
dvmptco |
|
207 |
107
|
an32s |
|
208 |
161
|
rpcnd |
|
209 |
207 208
|
mulneg2d |
|
210 |
|
rpne0 |
|
211 |
210
|
adantl |
|
212 |
207 112 211
|
divrecd |
|
213 |
212
|
negeqd |
|
214 |
209 213
|
eqtr4d |
|
215 |
214
|
mpteq2dva |
|
216 |
206 215
|
eqtrd |
|
217 |
111 112 113 114 115 117 216
|
dvmptmul |
|
218 |
88
|
mulid2d |
|
219 |
|
simplr |
|
220 |
106 219
|
rerpdivcld |
|
221 |
220
|
recnd |
|
222 |
221 79
|
mulneg1d |
|
223 |
211
|
an32s |
|
224 |
107 79 223
|
divcan1d |
|
225 |
224
|
negeqd |
|
226 |
222 225
|
eqtrd |
|
227 |
218 226
|
oveq12d |
|
228 |
88 107
|
negsubd |
|
229 |
227 228
|
eqtrd |
|
230 |
229
|
an32s |
|
231 |
230
|
mpteq2dva |
|
232 |
217 231
|
eqtrd |
|
233 |
71 70 62 75 99 101 110 232
|
dvmptfsum |
|
234 |
|
oveq2 |
|
235 |
|
fveq2 |
|
236 |
234 235
|
oveq12d |
|
237 |
|
oveq2 |
|
238 |
|
fveq2 |
|
239 |
237 238
|
oveq12d |
|
240 |
236 43 24 239 17 13
|
telfsumo2 |
|
241 |
31
|
oveq2d |
|
242 |
240 241
|
eqtrd |
|
243 |
242
|
mpteq2dva |
|
244 |
233 243
|
eqtrd |
|
245 |
62 3 63 76 90 98 244
|
dvmptadd |
|
246 |
|
pncan3 |
|
247 |
96 95 246
|
sylancr |
|
248 |
247
|
mpteq2dva |
|
249 |
60 245 248
|
3eqtrd |
|